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Permittivity

In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter $ε$ (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivity, thereby storing more energy in the material. In electrostatics, the permittivity plays an important role in determining the capacitance of a capacitor.

In the simplest case, the electric displacement field $D$ resulting from an applied electric field E is
 * $$\mathbf{D} = \varepsilon\ \mathbf{E} ~.$$

More generally, the permittivity is a thermodynamic function of state. It can depend on the frequency, magnitude, and direction of the applied field. The SI unit for permittivity is farad per meter (F/m).

The permittivity is often represented by the relative permittivity $ε$$r$ which is the ratio of the absolute permittivity $ε$ and the vacuum permittivity $ε$$0$
 * $$\kappa = \varepsilon_\mathrm{r} = \frac{\varepsilon}{\varepsilon_0} ~.$$

This dimensionless quantity is also often and ambiguously referred to as the permittivity. Another common term encountered for both absolute and relative permittivity is the dielectric constant which has been deprecated in physics and engineering as well as in chemistry.

By definition, a perfect vacuum has a relative permittivity of exactly 1 whereas at standard temperature and pressure, air has a relative permittivity of $ε$$r air$ ≡ $κ$$air$ ≈ 1.0006.

Relative permittivity is directly related to electric susceptibility ($χ$) by
 * $$\chi = \kappa - 1 $$

otherwise written as
 * $$\varepsilon = \varepsilon_\mathrm{r}\ \varepsilon_0 = ( 1 + \chi )\ \varepsilon_0 ~.$$

The term "permittivity" was introduced in the 1880s by Oliver Heaviside to complement Thomson's (1872) "permeability". Formerly written as $p$, the designation with $ε$ has been in common use since the 1950s.

Units
The SI unit of permittivity is farad per meter (F/m or F·m−1).

 * $$\frac{\text{F}}{\text{m}} = \frac{\text{C}}{\text{V} {\cdot} \text{m}} = \frac{\text{C}^2}{\text{N} {\cdot} \text{m}^2} = \frac{\text{C}^2 {\cdot} \text{s}^2}{\text{kg} {\cdot} \text{m}^3}= \frac{\text{A}^2 {\cdot} \text{s}^4}{\text{kg} {\cdot} \text{m}^3}$$

Explanation
In electromagnetism, the electric displacement field $D$ represents the distribution of electric charges in a given medium resulting from the presence of an electric field $E$. This distribution includes charge migration and electric dipole reorientation. Its relation to permittivity in the very simple case of linear, homogeneous, isotropic materials with "instantaneous" response to changes in electric field is:
 * $$ \mathbf{D} = \varepsilon\ \mathbf{E} $$

where the permittivity $ε$ is a scalar. If the medium is anisotropic, the permittivity is a second rank tensor.

In general, permittivity is not a constant, as it can vary with the position in the medium, the frequency of the field applied, humidity, temperature, and other parameters. In a nonlinear medium, the permittivity can depend on the strength of the electric field. Permittivity as a function of frequency can take on real or complex values.

In SI units, permittivity is measured in farads per meter (F/m or A2·s4·kg−1·m−3). The displacement field $D$ is measured in units of coulombs per square meter (C/m2), while the electric field $E$ is measured in volts per meter (V/m). $D$ and $E$ describe the interaction between charged objects. $D$ is related to the charge densities associated with this interaction, while $E$ is related to the forces and potential differences.

Vacuum permittivity
The vacuum permittivity $ε$$o$ (also called permittivity of free space or the electric constant) is the ratio $D⁄E$ in free space. It also appears in the Coulomb force constant,
 * $$k_\text{e} = \frac{1}{\ 4\pi \varepsilon_0\ }$$

Its value is
 * $$\varepsilon_0 \ \stackrel{\mathrm{def}}{=}\ \frac{1}{c^2\mu_0}  \approx 8.854\,187\,8128(13)\times 10^{-12}\text{ F/m } $$

where
 * $c$ is the speed of light in free space,
 * $µ$$o$ is the vacuum permeability.

The constants $c$ and $µ$$o$ were both defined in SI units to have exact numerical values until the 2019 redefinition of the SI base units. Therefore, until that date, $ε$$o$ could be also stated exactly as a fraction, $$\ \tfrac{1}{c^2\mu_0} = \tfrac{1}{35\,950\,207\,149.472\,7056\pi}\text{ F/m}\ $$ even if the result was irrational (because the fraction contained $π$). In contrast, the ampere was a measured quantity before 2019, but since then the ampere is now exactly defined and it is $μ$$o$ that is an experimentally measured quantity (with consequent uncertainty) and therefore so is the new 2019 definition of $ε$$o$ ($c$ remains exactly defined before and since 2019).

Relative permittivity
The linear permittivity of a homogeneous material is usually given relative to that of free space, as a relative permittivity $ε$$r$ (also called dielectric constant, although this term is deprecated and sometimes only refers to the static, zero-frequency relative permittivity). In an anisotropic material, the relative permittivity may be a tensor, causing birefringence. The actual permittivity is then calculated by multiplying the relative permittivity by $ε$$o$:
 * $$\ \varepsilon = \varepsilon_\mathrm{r}\ \varepsilon_0 = (1 + \chi)\ \varepsilon_0\ ,$$

where $χ$ (frequently written $χ$$e$) is the electric susceptibility of the material.

The susceptibility is defined as the constant of proportionality (which may be a tensor) relating an electric field $E$ to the induced dielectric polarization density $P$ such that
 * $$\ \mathbf{P}\ =\ \varepsilon_0\ \chi\ \mathbf{E}\; ,$$

where $ε$$o$ is the electric permittivity of free space.

The susceptibility of a medium is related to its relative permittivity $ε$$r$ by
 * $$\chi = \varepsilon_\mathrm{r} - 1 ~.$$

So in the case of a vacuum,
 * $$\chi = 0 ~.$$

The susceptibility is also related to the polarizability of individual particles in the medium by the Clausius-Mossotti relation.

The electric displacement $D$ is related to the polarization density $P$ by
 * $$\mathbf{D} = \varepsilon_0\ \mathbf{E} + \mathbf{P} = \varepsilon_0\ (1+\chi)\ \mathbf{E} = \varepsilon_\mathrm{r}\ \varepsilon_0\ \mathbf{E} ~.$$

The permittivity $ε$ and permeability $µ$ of a medium together determine the phase velocity $v = c⁄n$ of electromagnetic radiation through that medium:
 * $$\varepsilon \mu = \frac{ 1 }{\ v^2 } ~.$$

Determining capacitance
The capacitance of a capacitor is based on its design and architecture, meaning it will not change with charging and discharging. The formula for capacitance in a parallel plate capacitor is written as
 * $$C = \varepsilon \ \frac{A}{d}$$

where $$A$$ is the area of one plate, $$d$$ is the distance between the plates, and $$\varepsilon$$ is the permittivity of the medium between the two plates. For a capacitor with relative permittivity $$\kappa$$, it can be said that
 * $$C = \kappa \ \varepsilon_0 \frac{A}{d}$$

Gauss's law
Permittivity is connected to electric flux (and by extension electric field) through Gauss's law. Gauss's law states that for a closed Gaussian surface, $S$,
 * $$\Phi_E = \frac{Q_\text{enc}}{\varepsilon_0} = \oint_S \mathbf{E} \cdot \mathrm{d} \mathbf{A}\ ,$$

where $$\Phi_E$$ is the net electric flux passing through the surface, $$Q_\text{enc}$$ is the charge enclosed in the Gaussian surface, $$\mathbf{E}$$ is the electric field vector at a given point on the surface, and $$\mathrm{d} \mathbf{A}$$ is a differential area vector on the Gaussian surface.

If the Gaussian surface uniformly encloses an insulated, symmetrical charge arrangement, the formula can be simplified to
 * $$E\ A\ \cos \theta = \frac{\; Q_\text{enc} }{\ \varepsilon_0\ }\ ,$$

where $$\ \theta\ $$ represents the angle between the electric field lines and the normal (perpendicular) to $S$.

If all of the electric field lines cross the surface at 90°, the formula can be further simplified to
 * $$\ E = \frac{\; Q_\text{enc} }{\ \varepsilon_0\ A\ } ~.$$

Because the surface area of a sphere is $$\ 4 \pi r^2\ ,$$ the electric field a distance $$r$$ away from a uniform, spherical charge arrangement is
 * $$\ E = \frac{ Q }{\ \varepsilon_0 A\ } = \frac{ Q }{\ \varepsilon_0\ \left(4\ \pi\ r^2\right)\ } = \frac{ Q }{\ 4 \pi\ \varepsilon_0\ r^2\ } ~.$$

This formula applies to the electric field due to a point charge, outside of a conducting sphere or shell, outside of a uniformly charged insulating sphere, or between the plates of a spherical capacitor.

Dispersion and causality
In general, a material cannot polarize instantaneously in response to an applied field, and so the more general formulation as a function of time is
 * $$\mathbf{P}(t) = \varepsilon_0 \int_{-\infty}^t \chi\left(t - t'\right) \mathbf{E}\left(t'\right) \, \operatorname{d}t' ~.$$

That is, the polarization is a convolution of the electric field at previous times with time-dependent susceptibility given by $χ(Δt)$. The upper limit of this integral can be extended to infinity as well if one defines $χ(Δt) = 0$ for $Δt < 0$. An instantaneous response would correspond to a Dirac delta function susceptibility $χ(Δt) = χδ(Δt)$.

It is convenient to take the Fourier transform with respect to time and write this relationship as a function of frequency. Because of the convolution theorem, the integral becomes a simple product,
 * $$\ \mathbf{P}(\omega) = \varepsilon_0\ \chi(\omega)\ \mathbf{E}(\omega) ~.$$

This frequency dependence of the susceptibility leads to frequency dependence of the permittivity. The shape of the susceptibility with respect to frequency characterizes the dispersion properties of the material.

Moreover, the fact that the polarization can only depend on the electric field at previous times (i.e. effectively $χ(Δt) = 0$ for $Δt < 0$), a consequence of causality, imposes Kramers–Kronig constraints on the susceptibility $χ(0)$.

Complex permittivity

As opposed to the response of a vacuum, the response of normal materials to external fields generally depends on the frequency of the field. This frequency dependence reflects the fact that a material's polarization does not change instantaneously when an electric field is applied. The response must always be causal (arising after the applied field), which can be represented by a phase difference. For this reason, permittivity is often treated as a complex function of the (angular) frequency $ε′$ of the applied field:
 * $$\varepsilon \rightarrow \hat{\varepsilon}(\omega)$$

(since complex numbers allow specification of magnitude and phase). The definition of permittivity therefore becomes
 * $$D_0\ e^{-i \omega t} = \hat{\varepsilon}(\omega)\ E_0\ e^{-i \omega t}\ ,$$

where
 * $ε″$$ω$ and $D$$o$ are the amplitudes of the displacement and electric fields, respectively,
 * $E$ is the imaginary unit, $i^{2} = − 1$.

The response of a medium to static electric fields is described by the low-frequency limit of permittivity, also called the static permittivity $o$$i$ (also $ε$$s$):
 * $$\varepsilon_\mathrm{s} = \lim_{\omega \rightarrow 0} \hat{\varepsilon}(\omega) ~.$$

At the high-frequency limit (meaning optical frequencies), the complex permittivity is commonly referred to as $ε$$DC$ (or sometimes $ε$$∞$ ). At the plasma frequency and below, dielectrics behave as ideal metals, with electron gas behavior. The static permittivity is a good approximation for alternating fields of low frequencies, and as the frequency increases a measurable phase difference $ε$ emerges between $D$ and $E$. The frequency at which the phase shift becomes noticeable depends on temperature and the details of the medium. For moderate field strength ($opt$$δ$), $D$ and $E$ remain proportional, and
 * $$\hat{\varepsilon} = \frac{D_0}{E_0} = |\varepsilon|e^{-i\delta} ~.$$

Since the response of materials to alternating fields is characterized by a complex permittivity, it is natural to separate its real and imaginary parts, which is done by convention in the following way:
 * $$\hat{\varepsilon}(\omega) = \varepsilon'(\omega) - i\varepsilon''(\omega) = \left| \frac{D_0}{E_0} \right| \left( \cos \delta - i\sin \delta  \right) ~.$$

where
 * $E$ is the real part of the permittivity;
 * $o$ is the imaginary part of the permittivity;
 * $ε′$ is the loss angle.

The choice of sign for time-dependence, $e^{−iωt}$, dictates the sign convention for the imaginary part of permittivity. The signs used here correspond to those commonly used in physics, whereas for the engineering convention one should reverse all imaginary quantities.

The complex permittivity is usually a complicated function of frequency $ε″$, since it is a superimposed description of dispersion phenomena occurring at multiple frequencies. The dielectric function $ε(ω)$ must have poles only for frequencies with positive imaginary parts, and therefore satisfies the Kramers–Kronig relations. However, in the narrow frequency ranges that are often studied in practice, the permittivity can be approximated as frequency-independent or by model functions.

At a given frequency, the imaginary part, $δ$, leads to absorption loss if it is positive (in the above sign convention) and gain if it is negative. More generally, the imaginary parts of the eigenvalues of the anisotropic dielectric tensor should be considered.

In the case of solids, the complex dielectric function is intimately connected to band structure. The primary quantity that characterizes the electronic structure of any crystalline material is the probability of photon absorption, which is directly related to the imaginary part of the optical dielectric function $ε(ω)$. The optical dielectric function is given by the fundamental expression:
 * $$\varepsilon(\omega) = 1 + \frac{8\pi^2 e^2}{m^2}\sum_{c,v}\int W_{c,v}(E) \bigl( \varphi (\hbar \omega - E) - \varphi( \hbar\omega + E) \bigr) \, \operatorname{d}x ~.$$

In this expression, $W_{c,v}(E)$ represents the product of the Brillouin zone-averaged transition probability at the energy $ω$ with the joint density of states, $J_{c,v}(E)$; $ε″$ is a broadening function, representing the role of scattering in smearing out the energy levels. In general, the broadening is intermediate between Lorentzian and Gaussian; for an alloy it is somewhat closer to Gaussian because of strong scattering from statistical fluctuations in the local composition on a nanometer scale.

Tensorial permittivity
According to the Drude model of magnetized plasma, a more general expression which takes into account the interaction of the carriers with an alternating electric field at millimeter and microwave frequencies in an axially magnetized semiconductor requires the expression of the permittivity as a non-diagonal tensor:

 * $$\mathbf{D}(\omega) = \begin{vmatrix}

\varepsilon_1 & -i \varepsilon_2 & 0 \\ i \varepsilon_2 &   \varepsilon_1 & 0 \\ 0            &    0             & \varepsilon_z \\ \end{vmatrix} \; \operatorname{\mathbf{E}}(\omega)$$

If $E$$φ$ vanishes, then the tensor is diagonal but not proportional to the identity and the medium is said to be a uniaxial medium, which has similar properties to a uniaxial crystal.

Classification of materials
Materials can be classified according to their complex-valued permittivity $ε$, upon comparison of its real $ε′$ and imaginary $ε″$ components (or, equivalently, conductivity, $2$, when accounted for in the latter). A perfect conductor has infinite conductivity, $σ = ∞$, while a perfect dielectric is a material that has no conductivity at all, $σ = 0$; this latter case, of real-valued permittivity (or complex-valued permittivity with zero imaginary component) is also associated with the name lossless media. Generally, when $σ⁄ωε′ ≪ 1$ we consider the material to be a low-loss dielectric (although not exactly lossless), whereas $σ⁄ωε′ ≫ 1$ is associated with a good conductor; such materials with non-negligible conductivity yield a large amount of loss that inhibit the propagation of electromagnetic waves, thus are also said to be lossy media. Those materials that do not fall under either limit are considered to be general media.

Lossy media
In the case of a lossy medium, i.e. when the conduction current is not negligible, the total current density flowing is:
 * $$J_\text{tot}\ =\ J_\mathrm{c} + J_\mathrm{d} = \sigma\ E\ +\ i\ \omega\ \varepsilon'\ E = i\ \omega\ \hat{\varepsilon}\ E\ $$

where
 * $ε$ is the conductivity of the medium;
 * $$\ \varepsilon'\ =\ \varepsilon_0\ \varepsilon_\mathsf{r}\ $$ is the real part of the permittivity.
 * $$\ \hat{\varepsilon}\ =\ \varepsilon' - i\ \varepsilon''\ $$ is the complex permittivity

Note that this is using the electrical engineering convention of the complex conjugate ambiguity; the physics/chemistry convention involves the complex conjugate of these equations.

The size of the displacement current is dependent on the frequency $σ$ of the applied field $σ$; there is no displacement current in a constant field.

In this formalism, the complex permittivity is defined as:
 * $$\ \hat{\varepsilon}\ =\ \varepsilon' \left(\ 1\ -\ i\ \frac{\sigma}{\ \omega \varepsilon'\ } \ \right)\ =\ \varepsilon'\ -\ i\ \frac{\ \sigma\ }{\ \omega\ } $$

In general, the absorption of electromagnetic energy by dielectrics is covered by a few different mechanisms that influence the shape of the permittivity as a function of frequency:
 * First are the relaxation effects associated with permanent and induced molecular dipoles. At low frequencies the field changes slowly enough to allow dipoles to reach equilibrium before the field has measurably changed. For frequencies at which dipole orientations cannot follow the applied field because of the viscosity of the medium, absorption of the field's energy leads to energy dissipation. The mechanism of dipoles relaxing is called dielectric relaxation and for ideal dipoles is described by classic Debye relaxation.
 * Second are the resonance effects, which arise from the rotations or vibrations of atoms, ions, or electrons. These processes are observed in the neighborhood of their characteristic absorption frequencies.

The above effects often combine to cause non-linear effects within capacitors. For example, dielectric absorption refers to the inability of a capacitor that has been charged for a long time to completely discharge when briefly discharged. Although an ideal capacitor would remain at zero volts after being discharged, real capacitors will develop a small voltage, a phenomenon that is also called soakage or battery action. For some dielectrics, such as many polymer films, the resulting voltage may be less than 1–2% of the original voltage. However, it can be as much as 15–25% in the case of electrolytic capacitors or supercapacitors.

Quantum-mechanical interpretation
In terms of quantum mechanics, permittivity is explained by atomic and molecular interactions.

At low frequencies, molecules in polar dielectrics are polarized by an applied electric field, which induces periodic rotations. For example, at the microwave frequency, the microwave field causes the periodic rotation of water molecules, sufficient to break hydrogen bonds. The field does work against the bonds and the energy is absorbed by the material as heat. This is why microwave ovens work very well for materials containing water. There are two maxima of the imaginary component (the absorptive index) of water, one at the microwave frequency, and the other at far ultraviolet (UV) frequency. Both of these resonances are at higher frequencies than the operating frequency of microwave ovens.

At moderate frequencies, the energy is too high to cause rotation, yet too low to affect electrons directly, and is absorbed in the form of resonant molecular vibrations. In water, this is where the absorptive index starts to drop sharply, and the minimum of the imaginary permittivity is at the frequency of blue light (optical regime).

At high frequencies (such as UV and above), molecules cannot relax, and the energy is purely absorbed by atoms, exciting electron energy levels. Thus, these frequencies are classified as ionizing radiation.

While carrying out a complete ab initio (that is, first-principles) modelling is now computationally possible, it has not been widely applied yet. Thus, a phenomenological model is accepted as being an adequate method of capturing experimental behaviors. The Debye model and the Lorentz model use a first-order and second-order (respectively) lumped system parameter linear representation (such as an RC and an LRC resonant circuit).

Measurement
The relative permittivity of a material can be found by a variety of static electrical measurements. The complex permittivity is evaluated over a wide range of frequencies by using different variants of dielectric spectroscopy, covering nearly 21 orders of magnitude from 10−6 to 1015 hertz. Also, by using cryostats and ovens, the dielectric properties of a medium can be characterized over an array of temperatures. In order to study systems for such diverse excitation fields, a number of measurement setups are used, each adequate for a special frequency range.

Various microwave measurement techniques are outlined in Chen et al.. Typical errors for the Hakki–Coleman method employing a puck of material between conducting planes are about 0.3%.
 * Low-frequency time domain measurements ( to Hz)
 * Low-frequency frequency domain measurements ( to Hz)
 * Reflective coaxial methods ( to Hz)
 * Transmission coaxial method ( to Hz)
 * Quasi-optical methods ( to Hz)
 * Terahertz time-domain spectroscopy ( to Hz)
 * Fourier-transform methods ( to Hz)

At infrared and optical frequencies, a common technique is ellipsometry. Dual polarisation interferometry is also used to measure the complex refractive index for very thin films at optical frequencies.

For the 3D measurement of dielectric tensors at optical frequency, Dielectric tensor tomography can be used.

title: Permittivity


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User talk:Bobn

Hello there, welcome to the 'pedia! I hope you like the place and decide to stay. If you need any questions answered about the project then check out Help or drop me a line. BTW, great start on Ulysses (novel) -- although the / pages really aren't necessary here and the ones you still see around are an artifact of the old software that used to run the site (they used to be called "subpages" and had special features that are no longer in effect). I would suggest either having the characters linked, like so Hades and then add info into that pre-existing article. You could add more info in the Hades article under a heading like, "Hades as portrayed in the novel Ulysses", for example. Or if you only want to have an article about this particular subject then the form Hades (Ulysses novel) would work. I personally would go for the first choice because who wants to write Hades each and every time you want to link to that article? I look forward to be seeing more of your contributions in special:Recentchanges. Power to the wiki! --maveric149

Opps! I quess I should have been paying better attention there. :) How about just writting about the book on the main page and if that gets too long then think about the best way to break it up? --maveric149

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User talk:Bobn


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Real data type

A real data type is a data type used in a computer program to represent an approximation of a real number. Because the real numbers are not countable, computers cannot represent them exactly using a finite amount of information. Most often, a computer will use a rational approximation to a real number.

Rational numbers
The most general data type for a rational number (a number that can be expressed as a fraction) stores the numerator and the denominator as integers. For example 1/3, which can be calculated to any desired precision. Rational number are used, for example, in Interpress from Xerox Corporation.

Fixed-point numbers
A fixed-point data type uses the same, implied, denominator for all numbers. The denominator is usually a power of two. For example, in a hypothetical fixed-point system that uses the denominator 65,536 (216), the hexadecimal number 0x12345678 (0x1234.5678 with sixteen fractional bits to the right of the assumed radix point) means 0x12345678/65536 or 305419896/65536, 4660 + the fractional value 22136/65536, or about 4660.33777. An integer is a fixed-point number with a fractional part of zero.

Floating-point numbers
A floating-point data type is a compromise between the flexibility of a general rational number data type and the speed of fixed-point arithmetic. It uses some of the bits in the data type to specify an exponent for the denominator, today usually power of two although both ten and sixteen have been used.

Decimal numbers
The decimal type is similar to fixed-point or floating-point data type, but with a denominator that is a power of 10 instead of a power of 2.

title: Real data type


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History of the Czech lands

The history of the Czech lands – an area roughly corresponding to the present-day Czech Republic – starts approximately 800 years BCE. A simple chopper from that age was discovered at the Red Hill archeological site in Brno. Many different primitive cultures left their traces throughout the Stone Age, which lasted approximately until 2000 BCE. The most widely known culture present in the Czech lands during the pre-historical era is the Únětice Culture, leaving traces for about five centuries from the end of the Stone Age to the start of the Bronze Age. Celts – who came during the 5th century BCE – are the first people known by name. One of the Celtic tribes were the Boii (plural), who gave the Czech lands their first name Boiohaemum – Latin for the Land of Boii. Before the beginning of the Common Era the Celts were mostly pushed out by Germanic tribes. The most notable of those tribes were the Marcomanni and traces of their wars with the Roman Empire were left in south Moravia.

After the turbulent times of the Migration Period, the Czech lands were ultimately settled by the Slavic tribes. The year of 623 marks the formation of the first known state in the Czech lands, when Samo united the local Slavic tribes, defended their lands from the Avars to the east and – few years later – won the battle of Wogastisburg against the Franks invading the Czech lands from the west. The next state appearing in the Czech lands after the dissolution of the Samo's state was probably the Great Moravia. The center of its power lay in the area of Moravia and present-day western Slovakia. In 863, Cyril and Methodius, two scholars from Greece, brought Christianity to the Great Moravia and established the first Slavic script – Glagolitsa. The Great Moravia fell during the Magyar invasion at the start of the 10th century.

A new state formed around the tribe of Premyslids, who founded the Duchy of Bohemia. The duchy existed largely within the sphere of influence of the East Franconia and later the Holy Roman Empire. The duchy sided with the Roman Catholic Church during the East-West Schism and in 1212, the duke Ottokar I was granted the hereditary title of king for his service to the Holy Roman Emperor Frederick II. The Přemyslid dynasty died out at the start of the 14th century and was replaced by the Luxembourg dynasty. The most notable of the Luxembourg rulers was the Charles IV, who was elected the Emperor of the Holy Roman Empire. He established the Archbishopric of Prague and Charles University, the first university north of the Alps and east of Paris. The start of the 15th century saw the rise of Proto-Protestantic sentiments in the Czech lands. The execution of Jan Hus sparked the Hussite Wars and the religious split that followed them. The Jagiellon dynasty ascended the Czech throne in 1471. They ruled for half a century before the king Louis Jagiellon died in the Battle of Mohács and the empty throne was given to the House of Habsburg.

After the death of the Emperor Rudolf II of Habsburg, the religious and political tensions grew, resulting in the Second Defenestration of Prague, which sparked the Thirty Years War. Many of the Czech nobles supported the Protestant side and were stripped of their properties as a result. Germanization and recatholicisation of the Czech lands followed. The spread of Romanticism during the late 18th century went hand in hand with the movement of the Czech National Revival. After 1848, the leading representatives of the Czech National Revival increased their political efforts to gain more autonomy for the Czech lands within the Habsburg Monarchy.

The start of World War I opened the possibility of gaining full independence and formation of a sovereign state. In the Cleveland Agreement of 1915, the Czech and Slovak representatives declared their goal of creating a common state, based on the right of a people to self-determination. After the capitulation of Austria-Hungary three years later, the Czechoslovak Republic became a reality. The so-called First Republic lasted for 20 years, cut short by the advent of the World War II. Following the end of World War II, the Communist Party of Czechoslovakia took power in 1948, and Czechoslovakia became a member of the Eastern Bloc. In August 1968, armies of the Warsaw Pact invaded Czechoslovakia to prevent further attempts at the reformation of the Communist system. In November 1989, the Velvet Revolution replaced the Communist regime with a democratic Czech and Slovak Federative Republic. Three years later, Czech and Slovak representatives agreed to the Dissolution of Czechoslovakia and the formation of separate states. In 1999, the Czech Republic joined Nato and in 2004, became a member of the European Union.

Stone Age
A simple chopper – left by the ancestors of the present-day Homo Sapiens – dated to 800,000 BCE was uncovered in Red Hill in Brno. First evidence of human camps was found in Přezletice near Prague and in Stránská skála near Brno which dates to about 200,000 years after that. Stone tools were found in the Kůlna Cave in central Moravia, with the estimated age of 120,000 years. More stone tools and the skeletal remains of a Neanderthal man were found at the same site in a 50,000-year-old layer.

Human remains from 45,000 years ago were found in Koněprusy Caves in Zlatý kůň at Beroun District. Human remains from 30,000 years BCE were found in Mladeč caves mammoth tusks with complex engravings (again around 30,000 BCE) were found both in Pavlov and Předmostí at Přerov, making south Moravia one of the most important archeological areas in Europe.

The archeological site in Předmostí at Přerov represents the largest accumulation of human remains of the Gravettian culture, known for creating so-called Venus figurines. One of such figurines is the famous Venus of Dolní Věstonice (29,000–25,000 BCE) found in Dolní Věstonice in south Moravia along with many other artifacts from that time. Another Venus figurine is the Venus of Petřkovice, found in what is today Ostrava. Remains of mammoth hunters from 22,000 BCE were also found in the aforementioned Kůlna Cave along with the remains of reindeer hunters and horse hunters, dated to about 10,000 years later. Approximately between 5500 and 4500 BCE, people of the Linear Pottery culture resided in Czech lands. Their settlement was discovered in Bylany near Kutná hora. Their culture was succeeded by the Lengyel culture, Funnelbeaker culture and Stroke-ornamented ware culture, which coexisted in the Czech Lands during the end of the Stone Age.

Copper Age and Bronze Age

Corded Ware culture in the north and Baden culture in the south were the predominant cultures in the Czech Lands throughout the Copper Age. The Bell Beaker culture represented the transition from the Copper Age to the Bronze Age. With the start of the Bronze Age, Únětice culture appeared. This culture got its name from a village near Prague, where the first discovery was made in the 1870s. Many of their burial mounds were uncovered, mostly in central Bohemia. It was followed by the Middle Bronze Age Tumulus culture from around 1600 BC. The Urnfield culture is blanket term for various Late Bronze Age cultures dating from c. 1300-800 BC who cremated their dead and buried the urns with their ashes. The Hallstatt culture was the last culture of the Late Bronze Age and Early Iron Age. The key archeological site of the Hallstatt culture in the Czech Lands is the Býčí skála Cave, where a rare bronze statue of a bull was found. Many of these archeological sites were occupied by multiple cultures throughout the ancient times.

Iron Age
The area was settled by the Celtic tribes at the start of the Iron Age. The most prominent tribe in Bohemia were the Boii (plural), who gave the area the name of Boiohaemia (Latin for the land of Boii), which later turned into Bohemia. Before the start of the 1st century CE, they were pushed out by various Germanic tribes (Marcomanni, Quadi, Lombards). Around 60 to 50 BC, the Dacian king Burebista established an empire that extended its reach into the lands of the Boii. The Dacian occupation primarily affected modern-day Slovakia but also held sway over regions of present-day Czech Republic and Pannonia. Following Burebista's demise in 44 BC, his empire crumbled, liberating the lands of the Boii from Dacian rule. Traces of Roman army camps were found in south Moravia, most notably near Mušov. The winter camp in Mušov was built to house approximately 20,000 soldiers. The Romans were repeatedly at war with the Marcomanni tribe during the first two centuries CE. Germanic towns are described on the Map of Ptolemaios from the 2nd century, e.g. Coridorgis for Jihlava.

Arrival of the Slavs
The following centuries of what is known as the Great Migration once again changed the ethnic composition of the Czech Lands. In the 6th century, Slavic tribes, displaced by Langobard and Thuringian tribes began to move into the Czech Lands from the east. They fought with neighboring Avars – Turko-Tartar nomads – who seized the Pannonia and frequently raided the Slavic lands and even the Frankish Empire.

Samo's realm
In 623 – according to the Chronicle of Fredegar – the Slavic tribes revolted against the oppression of the Avars. During this time, the Frankish merchant Samo allegedly came to the Czech lands with his entourage and joined with the Slavs to defeat the Avars. Thus the Slavs adopted Samo as their ruler. Later Samo and the Slavs came into conflict with the Frankish empire whose ruler Dagobert I wanted to extend his rule to the east. That led to the Battle of Wogastisburg in 631, in which the newly established Realm of Samo successfully defended its autonomy. The realm disintegrated after Samo's death.

Great Moravia

The realm of Great Moravia probably was established in the area of today's Moravia and western Slovakia in the 830s. It saw the rise of the first ever Slavic literary culture in the Old Church Slavonic language and the creation of the Glagolitic alphabet, the first alphabet dedicated to a Slavic language. Glagolitic was later simplified into the Cyrillic alphabet that is today used in Russia and many countries in eastern Europe and central Asia. Glagolitic was created by St. Cyril and St. Methodius, who arrived in Great Moravia in 863 from Thessaloniki in Byzantine Empire. They were invited by the king Rastislav who invited them to introduce literacy and a legal system to Great Moravia. His nephew and successor Svatopluk I's diplomacy was oriented more towards Rome. Great Moravia was taken under the protection of the Holy See in 880 and six years after, he expelled the disciples of Methodius after their teacher's death. During his reign, Great Moravia's sphere of influence reached its peak. After his death, the realm was split among his sons and soon after fell to ruin due to infighting and constant Magyar raids during the start of the 10th century.

Duchy of Bohemia
Bořivoj from Levý Hradec was the first known member of the Přemyslid dynasty. In 880, he moved his residence to Prague Castle, which laid the foundation of the city of Prague that emerged centuries later. He was a vassal to the kings of Great Moravia and was baptised during the christanisation of Great Moravia by St. Cyril and St. Methodius. His son Spytihněv I together with the head of another major Bohemian tribe Witizla used the collapse of Great Moravia and in 895 swore allegiance to the East Frankish king Arnulf of Carinthia. Spytihněv's nephew Wenceslaus (later proclaimed a saint by the Catholic Church) ruled from 921 and had to submit to the Saxon king Henry I in order to maintain his ducal authority. He was murdered by his younger brother Boleslaus I. Boleslaus I expanded the Duchy of Bohemia eastwards conquering the lands of Moravia and Silesia and areas around Kraków. He stopped paying tribute to the Saxon king igniting a war which he lost and was forced to recognize Saxon suzerainty over the Duchy of Bohemia. The Bishopric of Prague was founded in 973 during the reign of his son Boleslaus II. The bishopric was subordinated to the Archbishopric of Mainz. In 1002, during the reign of the duke Vladivoj, the Duchy of Bohemia formally became a part of the Holy Roman Empire. After a period of dynastic infighting, Oldřich took power. His son Břetislav I led many ambitious conquests and later revolted against the Holy Roman Emperor Henry III hoping to gain a full autonomy for the Duchy of Bohemia. Despite the initial success in Battle at Brůdek, he could not withstand the second invasion of the imperial army and ultimately had to renounce all of his conquests save for Moravia and recognize Henry III as his sovereign. After Břetislav's death, the infighting among Přemyslids continued – a consequence of seniority inheritance laws. Among the more notable rulers belong (Vratislaus II and Vladislaus) who were awarded lifetime titles of kings by the Holy Roman Emperors for their services.

Late Přemyslids
In 1212 Ottokar I was granted a hereditary title of the King of Bohemia by the Holy Roman Emperor Frederick II. Thus began the Kingdom of Bohemia, which lasted de iure until the end of World War I. His reign marked the start of the German eastward colonization, which over time significantly altered the language composition of the Czech Lands. His son Wenceslaus I had to deal with the Mongol invasion of Europe at the start of 1240s. He managed to defend Bohemia, but Moravian lands were heavily plundered. When the Duke of Austria Frederick II died in 1246 without male heirs, Wenceslaus I tried to secure the Austrian lands by marrying his eldest son Vladislaus to Frederick's niece Gertrude. This plan failed because of Vladislaus's premature death in the year after. Wenceslaus I then decided for the invasion of Austria and he was successful. His successor, Ottokar II, continued the expansion of the realm. He gained more territory south of Austria and led two crusades against the pagan Old Prussians. He was hoping to gain the Imperial crown, but lost in the 1273 election to Rudolf of Habsburg, the first in a line of Habsburg emperors. Rudolf of Habsburg demanded that Ottokar II returns all of the lands he had acquired south of Bohemia. Ottokar refused and waged two wars against the emperor which ended with his death at the battlefield of Marchfeld in 1278.

The crown was passed to his 6-year-old son Wenceslaus II. Otto V, Margrave of Brandenburg ruled as a regent in his stead, later replaced by Záviš of Falkenstein, who married Ottokar II's widow. In 1290, Wenceslaus II had Záviš beheaded for alleged treason and began ruling independently. Year later, Przemysł II, the king of Poland, was murdered and Wenceslaus II gained the Polish crown for himself. At the end of the 13th century, huge deposits of silver were found in Kutná Hora, which allowed him to start issuing vast amounts of silver coins called Prague groschen. In 1301, another neighbouring monarch died – Andrew III of Hungary, the last male member of the Árpád dynasty. Wenceslaus II married his son Wenceslaus III to Andrew III's only daughter and had him crowned in Székesfehérvár as the King of Hungary. Four years later, Wenceslaus II died – only 33 years old – probably of tuberculosis. Wenceslaus III abandoned his claim to the Hungarian throne, seeing that his rule was only nominal. Władysław the Elbow-high challenged Wenceslaus III's rule in Poland and conquered Krakow in 1306. Before Wenceslaus III could start his retaliation campaign, he was murdered in Olomouc by unknown assassins.

House of Luxembourg
Wenceslaus III was the last male member of the main branch of Přemyslids. The Holy Roman Emperor Henry VII of the House of Luxembourg married his son John to Wenceslaus III's sister Elisabeth and secured for him the Bohemian throne. John of Luxembourg was raised in Paris, did not speak any Czech and was widely unpopular among the Czech nobility. John never stayed long in the Czech lands, he traveled all across Europe and took part in multiple military conflicts. While crusading in Lithuania in 1336, John lost his eyesight due to ophthalmia, which earned him the nickname John the Blind. A year later he took the side of King Philip VI of France in the Hundred Years' War and died in 1346 in the Battle of Crécy. His eldest son, Charles IV succeeded him on the Bohemian throne.

Earlier in 1346, the Pope Clement VI declared the Emperor Louis IV a heretic and demanded a new Imperial election. Charles IV was the pope's preferred candidate and he was crowned as the King of Romans in November 1346 in Bonn. Charles had been in charge of the administration of Czech Lands since 1333, due to his father's absence and health indisposition. Soon after his coronation as the King of Bohemia and the King of Romans, he settled in Prague and laid the foundations of the New Town expanding the capitol. In 1348 he founded the University of Prague, the first university north of Alps and east of Paris. He also legally established the Lands of the Bohemian Crown (Corona regni Bohemiae in Latin), meaning the core territories no longer belonged to a king or a dynasty but to the Bohemian monarchy (crown) itself. In 1355, Charles IV travelled to Rome where he was crowned the Emperor of the Holy Roman Empire. He ruled as the Holy Roman Emperor for over 20 years and managed to secure the title of the King of Romans for his eldest son Wenceslaus IV. Wenceslaus IV did not share the governance abilities of his father. In 1393, the torture and murder John of Nepomuk – vicar-general of the archbishop Jan of Jenštejn – sparked a noble rebellion. He was imprisoned for two years at Králův Dvůr and was only released after an intervention from his younger brother Sigismund, who had become the King of Hungary. In 1400, Wenceslaus IV was deposed as the Holy Roman Emperor, mainly due to his failure to address the Papal Schism. Two years later, Wenceslaus IV was briefly imprisoned again, this time by his brother Sigismund, who looted Moravia. After the death of Rupert – who had replaced Wenceslaus as the King of Romans – Wenceslaus IV competed with his brother Sigismund and his cousin Jobst of Moravia for the title of the King of Romans. He ultimately surrendered the title to Sigismund in exchange for keeping Bohemia. In 1414, Sigismund called the Council of Constance, which finally resolved the Papal Schism. It also condemned the teaching of Jan Hus, rector of the University of Prague and a popular church reformist. After Jan Hus refused to retract his teachings, he was burnt alive at stake, which prompted the Hussite Wars. The religious military conflicts stopped in 1434 with the battle Battle of Lipany, but the religious tensions continued on. Although Sigismund became the titular King of Bohemia after Wenceslaus IV's death in 1419, it was not until 1436 that he was recognized by the Czech Estates and he died a year after.

House of Habsburg
After Sigismunds's death the title of the King of Bohemia went to his son-in-law Albert from the House of Habsburg, who died shortly after. The claim to the Lands of the Bohemian Crown was passed to his unborn son Ladislaus, who gained the nickname Posthumous. He was raised at the court of his distant relative Emperor Frederick III. Although he was crowned the King of Bohemia in 1453, his regent George of Poděbrady continued to effectively rule Bohemia in his stead. Ladislaus died in Prague after fleeing a rebellion in Hungary, aged only seventeen. Many of his contemporaries suspected he was poisoned, but modern examinations of his skeleton proved he died of acute leukemia. With his death the Albertinian Line of the House of Habsburg ended.

House of Poděbrady
In 1458, the estates of Bohemia elected George of Poděbrady as the new King of Bohemia. He had a difficult role trying to maintain a fragile peace between the Catholic side and the Hussite side, for which he earned the nickname King of two peoples. Despite his efforts, he ultimately did not succeed and in 1465, the catholic nobles formed the Unity of Green Mountain and challenged his rule. A year after, he was excommunicated by the new Pope Paul II, which gave a justification for the Hungarian king Matthias Corvinus to invade the Czech Lands and start the Bohemian–Hungarian War.

House of Jagiellon
After the king George's death, the war was continued by Vladislaus II from the House of Jagiellon, who was offered the throne of Bohemia by George of Poděbrady himself. After ten years of fighting, the Bohemian-Hungarian War finally ended by signing of the Peace of Olomouc in 1479, in which Moravia, Silesia and Lusatia were ceded to Matthias Corvinus for the rest of his life and both monarchs were allowed to use the title of King of Bohemia. In 1485, Vladislaus II confirmed right of all Bohemian noblemen and commoners to freely adhere either to Hussitism or Catholicism in the Peace of Kutná Hora. After Matthias Corvinus died in 1490, Vladislaus II was elected the King of Hungary and gained all the territories he ceded 30 years earlier. From then on he ruled from Buda. Although Vladislaus II was married three times, he only had two children late in his life: son Louis and daughter Anne. Vladislaus II's two children married two children of the Holy Roman Emperor Maximilian I as a result of negotiations at the First Congress of Vienna, tying the House of Jagiellon and the House of Habsburg together.

A year after that, in 1516, Vladislaus II died and his ten-year-old son Louis II became the king of both Hungary and Bohemia. In 1521 he refused to pay the agreed annual tribute to the new Ottoman sultan, Süleyman I and executed his ambassadors. War ensued, Belgrade fell to Ottoman hands the same year. In 1526, Louis II led his forces against Suleiman I in the Battle of Mohács, which ended with a decisive defeat of the Hungarian army and Louis II drowned during his attempted retreat. He left no heirs and so the Lands of the Bohemian Crown were inherited by Ferdinand I from the House of Habsburg, as was agreed during the First Congress of Vienna.

Protestantism
After the Battle of Mohács, the Ottomans were unsuccessful in their Siege of Vienna in 1529 and Ferdinand I managed to sign the Treaty of Constantinopole, postponing the Ottoman expansion attempts. Ferdinand and his brother Charles V – who was the Holy Roman Emperor at the same time – had to deal with not only the Ottoman threat, but also with the Schmalkaldic League which formed in 1531 to advance the interests of Lutheran states in the Holy Roman Empire. Largely Protestant Czech nobility had a favorable view of the Schmalkaldic League's goals and so when in 1546 Ferdinand I ordered the Czech estates to raise their army and march against the Protestant Electorate of Saxony as part of the Schmalkaldic War, they did so very reluctantly. The next year the Czech estates refused to gather an army again and rebelled, for which they were punished after the Schmalkaldic League decisively lost the Battle of Mühlberg. As a result, Ferdinand I managed to strengthen his position in the Land of the Bohemian Crown, limit city privileges and begin the process of recatholicization by inviting the Jesuit Order to Prague in 1556.

Maximilian II succeeded Ferdinand I in 1562 and – like his father – ruled from Vienna. He approved Czech Confession (Confessio Bohemica in Latin) – a new document confirming religious freedoms – replacing the older Compacts of Basel, that did not take non-Utraquist Protestants into account. He also showed his religious tolerance by reaffirming the Statuta Judaeorum – a document providing legal protection for the Jews in the Lands of the Bohemian Crown. His son Rudolf II succeeded him in 1576 and in 1583 he moved the royal court to Prague. Thanks to Rudolf's patronage of art, Prague became a major cultural hub of Europe during his reign. He was a reclusive ruler who preferred his hobbies to the daily affairs of the state. In 1605 Rudolf II was forced by his other family members to cede the rule of Hungary to his younger brother Archduke Matthias following the Bocskai Uprising after the Long Turkish War. The differences of opinions between the two brothers ultimately resulted in Rudolf's imprisonment at the Prague Castle and all effective power was given into the hands of Matthias. After Rudolf II's death in 1612 the royal court moved back to Vienna. Matthias did not have any children – same as his brother Rudolf – and he died six years later, aged 62. He was succeeded by his cousin Ferdinand II, Archduke of Austria. The Diets of Bohemia confirmed Ferdinand's position as Matthias' successor only after he had promised to respect the Letter of Majesty – a document granting religious freedoms, signed by Rudolf II. eight years earlier. Ferdinand II did not share the religious benevolence of his predecessors. A year after he was crowned, he prohibited the construction of Protestant ecclesial buildings on royal land. That led to protests among the Protestant nobility – who saw it as a violation of the Letter of Majesty – and the Second Defenestration of Prague in 1618, which sparked the conflict that would become the Thirty Years War. The revolting Bohemian estates then chose Frederick V of Palatinate as their new king and gathered an army in preparation of war. They were joined by Lutheran nobility in Austria. Ferdinand II asked his Spanish relative Philip III for help. Spanish army in the Netherlands made sure forces of Protestant Union could not join the revolt happening in the Lands of the Bohemian Crown and in Austria. After dealing with the Austrian rebels, Ferdinand II decisively defeated Frederick V at the Battle of White Mountain, near Prague. Widespread confiscation of property followed, which was then sold to loyal nobles, often of foreign origin. Ferdinand II also had the 27 leaders of the revolt publicly beheaded and strengthened the royal power over the estates. The Lands of the Bohemian Crown and especially Silesia were some of the territories that were hit the hardest by the devastating Thirty Years War. The war continued even after Ferdinand II's death during the reign of Ferdinand III.

Late Habsburgs
In 1648, the Thirty Years War finally ended with the Peace of Westphalia. Ferdinand III continued the recatholicization and centralization policies of his father. After his death in 1657, he was succeeded by his only surviving son Leopold I. During the fourth Austro-Turkish War in 1663 the Turkish army invaded Moravia before being stopped in the Battle of Saint Gotthard. Leopold continued waging wars with Ottomans and France throughout his long rule. He increased corvée to three days a week which caused the Peasant Revolt of 1680. The infamous Losiny Estate Witch Trials took place between 1678 and 1696 resulting in almost 100 dead. More protests against the increased corvée occurred, but all in vain. In 1705, Leopold I's rule ended and his son Joseph I succeeded him. Joseph I planned to enact many administrative reforms, most of which he did not get the chance to finish, due to his premature death of smallpox. One year before his death he issued letters patent ordering that all Romani people in the Lands of the Bohemian Crown had one of their ears cut off. If they returned after being expelled, all Romani men were to be hanged without a trial. Similar letters patents were published in other territories under his rule and led to mass killings of Romani people. After Joseph I's premature death in 1711, the Austrian throne went to his younger brother Charles VI. Charles VI had no male heirs and with the Pragmatic Sanction of 1713 he ensured that all the titles held by him could be inherited by a woman. Charles VI sought the other European powers' approval, which he gained in exchange for various concessions. Regardless, after her father's death, Maria Theresa had to defend her inheritance from the coalition of Prussia, Bavaria, France, Spain, Saxony and Poland in the War of Austrian Succession, that broke out mere weeks after her coronation in 1740. She ultimately managed to defend her title, but paid for it with the loss of Silesia, which became a part of Prussia. That was the ended the unity of the Lands of the Bohemian Crown. In 1757 during the Seven Years' War, the Prussians invaded Bohemia again and laid siege to Prague, but subsequently lost the Battle of Kolín and were repelled. Maria Theresa was not able to regain Silesia and the war ended in a draw. She tried to follow the ideas of Enlightenment, she established compulsory secular primary schools, but also state censorship of books that were deemed to be against the Catholic religion. Because of her marriage to Francis Stephen of Lorraine, all of her children were considered to be members of a new joint House of Habsburg-Lorraine.

House of Habsburg–Lorraine
After the death of Maria Theresa's husband in 1765, her son Joseph II started to rule with her as a co-ruler and since 1780 as the sole ruler. He enforced many reforms, among the most notable are the abolition of serfdom, Patent of Toleration expanding religious freedom and the dissolution of all monastic orders not involved in education, healthcare or science. As part of his centralization efforts, he also pressed for the expansion of German language to all territories under his rule. Both of his wives died relatively young of smallpox and because he had no sons, he was succeeded by his younger brother Leopold II. Although Leopold II only ruled for two years, he spent several weeks in Prague in 1791 and he let himself be crowned the King of Bohemia. The first Czech Industrial Exhibition was prepared in honor of his visit in Clementinum and the Czech Estates commissioned an opera from Mozart for the occasion. Leopold II was succeeded by Francis I, the first-born of his 12 sons. In 1805, Napoleon's army attacked Austria and defeated the Austrian and Russian army in the decisive Battle of Austerlitz in south Moravia. In the Peace of Pressburg, Francis I lost many of his territories and soon after, the Holy Roman Empire dissolved, replaced by the Confederation of the Rhine. Following the end of Napoleonic Wars, the Congress of Vienna reinstated the Austrian Empire as one of the Great Powers of Europe in 1815. Francis I was a proponent of conservatism and his policies suppressed all of the emerging liberal and nationalist movements in his Empire. He was the first of Austrian monarchs to widely utilize the secret police and he increased censorship. His son Ferdinand I became the Austrian Emperor after him. Because of his frequent seizures, he was not capable of ruling and the actual executive power was held by the Regent's Council. In 1836, one year after his succession, he was crowned the King of Bohemia under the name of Ferdinand V. Throughout the 19th century, the nationalist tendencies and movements in the Czech lands known as the Czech National Revival slowly grew, led by activists such as linguists Josef Dobrovský and Josef Jungmann, historian and politician František Palacký or writer Božena Němcová and journalist Karel Havlíček Borovský. The efforts of the Czech National Revival first peaked during the revolutions of 1848. Ferdinand I was forced to abdicate and his successor was his young nephew Francis Joseph I. When he – after losing the war with Italy in 1859 – also lost the war with Prussia in 1866, the Hungarian representatives forced Francis Joseph I to end his absolutist rule over Hungary in the Austro-Hungarian Compromise of 1867. The Czech representatives who hoped for a similar increase in autonomy were left out and the Czech lands remained firmly under the control of Austria.

Austria-Hungary
The newly formed Real union of Austria-Hungary lasted for the next half-a-century. The policies suppressing the National Revival in the Czech lands under the Austrian government continued, as well as the suppression of the Slovak National Revival under the Hungarian government. The end of the 19th century also was a time of a demographic boom and a rapid urbanization. Population in centers of industry doubled or tripled within a few decades. At the start of the 20th century, Austria's unilateral annexation of Bosnia in 1908 caused the Bosnian Crisis and prompted the eventual assassination of Archduke Franz Ferdinand of Austria, sparking the World War I in 1914. Many of the Czech nationalists saw the war as an opportunity for gaining full independence from the Austria-Hungary. Desertion among the Czech conscripts was commonplace and Czechoslovak Legions were formed to fight for the side of Entente Powers. In the Cleveland Agreement of 1915, the Czech and Slovak representatives declared their goal of creating a common state, based on the right of a people to self-determination. When the World War I ended in 1918, the Kingdom of Bohemia officially ceased to exist and a new democratic republic of Czechoslovakia took its place.

Czechoslovakia
The republic of Czechoslovakia was declared in October 1918. It was a democratic presidential republic. In 1920, its defined territory was not inhabited only by Czechs and Slovaks, it contained significant populations of other nationalities: Germans (22.95%), Hungarians (5.47%) and Ruthenians (3.39%). The Great Depression starting at the end of 1920's together with the rise of the National Socialist Party in neighbouring Germany during the 1930s caused increasing tensions between the different nationalist groups in Czechoslovakia. In foreign relations the newly established republic relied heavily on its western allies of Great Britain and France. That proved to be a mistake as in 1938, both allied countries agreed to Hitler's demands and co-signed the Munich Treaty, stripping the Czechoslovakia of its borderlands, leaving it indefensible.

German protectorate
After giving up Sudetenland, the Second Czechoslovak Republic lasted only half-a-year before its full dismemberment before the start of World War II. The Slovak Republic declared its independence from Czechoslovakia and became Germany's client state, while two days later the German Protectorate of Bohemia and Moravia was proclaimed. During the World War II – given the high level of industrialization of pre-war Czechoslovakia – the Protectorate of Bohemia and Moravia served as a major hub of military production for Germany. The oppression of ethnic Czechs increased after the assassination of Reinhard Heydrich by members of the Czech resistance in 1942. After Germany's defeat in 1945, the vast majority of ethnic Germans were forcefully deported from Czechoslovakia.

Rule of the Communist Party
In February 1948, the Communist Party of Czechoslovakia seized power in a coup d'état. Klement Gottwald became the first communist president. He nationalized the country's industry and collectivized its farms to form Sovkhozs inspired by the Soviet model. Czechoslovakia thus became a part of the Eastern Bloc. Attempts at a reformation of the political system during the Prague Spring of 1968 were ended by the invasion of armies of the Warsaw Pact. The Czechoslovakia remained under the rule of the Communist Party until the Velvet Revolution of 1989.

Post-Cold War
One of the leaders of the dissent, Václav Havel became the first president of the democratic Czechoslovakia. Slovakia's demands for sovereignty were fulfilled at the end of 1992, when the representatives of Czechs and Slovaks agreed to split the Czechoslovakia into the Czech Republic and the Slovak Republic. The official start of the current Czech Republic was set on 1 January 1993. The Czech Republic became a member of NATO in 12 March 1999, and the European Union in 1 May 2004.

title: History of the Czech lands


text:
Euro coins

There are eight euro coin denominations, ranging from one cent to two euros (the euro is divided into a hundred cents). The coins first came into use in 2002. They have a common reverse, portraying a map of Europe, but each country in the eurozone has its own design on the obverse, which means that each coin has a variety of different designs in circulation at once. Four European microstates that are not members of the European Union (Andorra, Monaco, San Marino, and Vatican City) use the euro as their currency and also have the right to mint coins with their own designs on the obverse side.

The coins, and various commemorative coins, are minted at numerous national mints across the European Union to strict national quotas. Obverse designs are chosen nationally, while the reverse and the currency as a whole is managed by the European Central Bank (ECB).

History
The euro came into existence on 1 January 1999. It had been a goal of the European Union (EU) and its predecessors since the 1960s. The Maastricht Treaty entered into force in 1993 with the goal of creating economic and monetary union by 1999 for all EU states except the United Kingdom and Denmark (even though Denmark has a fixed exchange rate policy with the euro).

In 1999, the currency was born virtually and in 2002 notes and coins began to circulate. It rapidly replaced the former national currencies and the eurozone has since expanded further to some newer EU states. In 2009 the Lisbon Treaty formalised its political authority, the Eurogroup, alongside the European Central Bank.

In 2004, €2 commemorative coins were allowed to be minted in six states. By 2007, all states but France, Ireland and the Netherlands had minted a commemorative issue and the first eurozone-wide commemorative coin was issued to celebrate 50 years of the Treaty of Rome. In 2009, the second eurozone-wide issue of a 2-euro commemorative coin was issued, celebrating ten years of the Economic and Monetary Union (EMU).

In 2012, the third eurozone-wide issue of a 2-euro commemorative coin was issued, celebrating 10 years of euro coins and notes. Cyprus did not independently issue a €2 commemorative coin until 2017.

As the EU's membership has since expanded in 2004, 2007 and 2013, with further expansions envisaged, the common face of all euro coins from the value of 10c and above were redesigned in 2007 to show a new map.

Slovenia joined the eurozone in 2007, Cyprus and Malta joined in 2008, Slovakia in 2009, Estonia in 2011, Latvia in 2014, Lithuania in 2015 and Croatia in 2023, introducing eight more national-side designs.

Andorra started minting coins in 2014, so as of 2023 there are 24 countries with their own national sides.

Specification
There are eight different denominations of euro coins: €0.01, €0.02, €0.05, €0.10, €0.20, €0.50, €1.00 and €2.00 The €0.01, €0.02 and €0.05 coins show Europe in relation to Asia and Africa in the world. The remaining coins show the EU before its enlargement in May 2004 if minted (before 1 January 2007) a map of Europe if minted after. Coins from Austria, Italy, San Marino, Portugal and the Vatican City show the map if minted in 2008 or later.

The common side was designed by Luc Luycx of the Royal Belgian Mint. They symbolise the unity of the EU. The national sides were designed by the NCBs of the eurozone in separate competitions. There are specifications which apply to all coins such as the requirement of including twelve stars. National designs were not allowed to change until the end of 2008, unless a monarch (whose portrait usually appears on the coins) dies or abdicates. National designs have seen some changes due to a new rule stating that national designs should include the name of the issuing country.

The common side of the €0.01, €0.02 and €0.05 coins depict the denomination, the words 'EURO CENT' beside it, twelve stars and Europe highlighted on a globe in relation to Asia and Africa in the world. The common side of the 10€0.10, €0.20 and €0.50 coins currently depict the denomination on the right, the words 'EURO CENT' underneath it, with twelve stars and the European continent on the left.

Coins minted from 1999 to 2006 depicted only the EU15, rather than the entire European continent, which is on coins minted after 2007. The common side of the €1 and €2 coins depict the denomination on the left, the currency, map of Europe and twelve stars on the right. Similarly, coins minted from 1999 to 2006 depicted the EU15, rather than the whole European continent, which is on coins minted from 2007.

The 1c, 2c and 5c coins, however, keep their old design, showing a geographical map of Europe with the 15 member states of 2002 raised somewhat above the rest of the map.

Common side
All coins have a common reverse side showing how much the coin is worth, with a design by Belgian designer Luc Luycx. The design of the 1c, 2c and 5c coins shows Europe's place in the world as a whole. The 10c coins and above show either the 15 countries that were the European Union in 2002, or, if minted after 2007, the whole European continent. Coins from Italy, San Marino, the Vatican, Austria and Portugal show the new design if minted 2008 or later. The coins symbolise the unity of the EU.

Current design
On 2005 June 7, the European Council decided that the common side of the 10 euro cent to €2 coins should be brought up to date to reflect the enlargement of the EU in 2004. The 1c, 2c and 5c coins show Europe in relation to the rest of the world, therefore they remained unchanged. In 2007, the new design was introduced. The design still retains all elements of the original designs, including the twelve stars, but the map of the fifteen states is replaced by one showing the whole of Europe as a continent, without borders, to stress unity. These coins were not mandatory for existing eurozone members when introduced in 2007, but became so for every member in 2008.

Starting in 2017 the 1, 2, and 5 euro cent coins from individual member states have started adjusting their common side design to a new version, identified by smaller and more rounded numeral and longer lines outside of the stars at the coin's circumference.

Cyprus is shown several hundred kilometers northwest of its real position in order to include it on the map. On the €1 and €2 coins, the island is shown to be directly east of mainland Greece; on the €0.10, €0.20 and €0.50 coins, it appears directly below Crete. The original proposal from the European Commission was to include Turkey on the map, but this design was rejected by the Council.

Initial design
The original designs of the 10c, 20c and 50c coins showed the outline of each of the 15 EU member states. Each state was shown as separate from the others, thus giving Europe the appearance of an archipelago. EU member states outside the eurozone (Denmark, Sweden, and the United Kingdom) were also depicted. Non-EU states were not depicted.

On the €1 and €2 coins, the landmass appeared more cohesive although borders were indicated. As in current issues, all coins featured 12 stars in their design.

The year featured on the coins can date back to 1999, when the currency was formally established (only Belgian, Dutch, Finnish, French and Spanish coins were struck with the 1999 date). These countries traditionally strike coins with the year of minting rather than the year it was put into circulation.

Researchers from the University of Zürich warned that an external ring of metal surrounding an inner pill of a different colour, as in the euro coins, can lead to the release of high levels of nickel, causing allergic reactions with people sensitive to the metal. The researchers also warned that the coins could contain between 240 and 320 times the amount of nickel allowed under the EU nickel directive.

National sides
The obverse side varies from state to state, with each member allowed to choose its own design. Each of the eight coins can have the same design (such as Irish coins), or can vary from coin to coin (such as Italian coins). In monarchies, the national side usually features a portrait of the country's monarch, often in a design carried over from the former currency (e.g. Belgian coins). Republics tend to feature national monuments, symbols, or stylised designs (such as French coins). Engravings on the edge of the €2 coin are also subject to national choice.

There are at present no plans to abolish the national designs in favour of a common European one. However, the Commission has proposed that the 1c, 2c and 5c coins have a common design to keep costs down.

Though they are not members of the EU, Monaco, San Marino, and the Vatican City (and Andorra since 2014) also have euro coins featuring a national side, but a considerable number of these coins were not put into general circulation by the authorities who instead sold them to collectors for prices higher than their face value. Due to this, in 2012, a European Regulation established that: "A minor proportion, not exceeding 5 % of the cumulated total net value and volume of circulation coins issued by a Member State, taking into account only years with positive net issuance, may be put on the market above face value if justified by the special quality of the coin, a special packaging or any additional services provided".

No territories associated with eurozone countries issue their own euro coins. France and the Netherlands have overseas regions with their own currencies.

As of 2023, 24 countries issue euro coins with their own national sides, for a total 192 different euro coins, not counting annual differences or commemorative coins.

Regulations
The basis for the euro coins is derived from a European recommendation from 2003, which allowed changing the national obverse sides of euro coins from 1 January 2004 onwards. However, a number of recommendations and restrictions still apply.

Euro coins must still have a common reverse side, so only the national obverse sides may be varied. Also, the standard national obverse sides per se should not be changed before 2008 at the earliest, unless the head of state depicted on some coins changes before then. (This clause already came into effect for Monaco and the Vatican City, whose heads of state—Rainier III and Pope John Paul II respectively—died in 2005 and whose national obverse sides were changed for 2006).

In 2005, another recommendation added two more guidelines regarding the design of the coins. The state issuing a coin should in some way clearly be identified on the obverse side, either by stating the full name or a clearly identifiable abbreviation of it; and neither name nor the denomination of the coin should be repeated on the obverse, as it is already featured on the common reverse side.

These restrictions do not apply retroactively; only new designs—the national obverse sides for regular issues of states newly joining the euro or of eurozone states which change their design, and €2 commemorative coins issued from 2006 onwards—are subject to them. However, the five countries whose designs violated the first update to the rules (Austria, Belgium, Finland, Germany and Greece) initially were assumed to have to change their design in the future, which Finland did for 2007 and Belgium for 2008.

In 2008, another recommendation changed the rules again:
 * The twelve stars of the European Union surrounding the coin designs need to surround the national design, including year marks and the name of the country. The stars have to appear in the same way as they are aligned on the flag of the European Union.
 * The design of euro coins may not be changed except for two specific circumstances:
 * If a coin design is in violation of the recommendations, it may be updated to bring it into line with them.
 * If a coin design depicts a head of state, it may be updated:
 * every fifteen years to bring it into line with the head of state's current appearance;
 * if the head of state abdicates or dies. However, temporary heads of state may not be used as a reason for changing the design; instead a €2 commemorative coin (potentially a second €2 commemorative coin) will be allowed to be issued.

Finland and Belgium had already corrected their design on the coins issued to include the initials of the country in 2007 and 2008, respectively. Belgium was forced to change its design back to show the original portrait of its monarch, because the 2008 update to follow the recommendations also updated the portrait, which was against the rules. The Belgian coins from 2009 onwards show the original royal portrait of 1999, but otherwise keep the new 2008 coin design as far as the country identification and year mark are concerned. These provisions additionally prohibit further sede vacante sets of coins by the Vatican City, allowing only commemorative coins for such occasions. Finland and Spain updated their designs to meet the new rules about the stars in 2008 and 2010, respectively.

In 2012, a European Regulation approved new specifications of euro coins and named (in article 1 g) a deadline for national sides of regular coins to be updated to fully comply with the current regulation: 20 June 2062.
 * The national side of circulation coins shall not repeat any indication of the denomination, or any parts thereof, of the coin. It shall not repeat the name of the single currency or of its subdivision, unless such indication stems from the use of a different alphabet. However, the edge lettering of the 2-euro coin may include an indication of the denomination, provided that only the figure "2" or the term "euro" in the relevant alphabet, or both, are used.
 * The national side of all denominations of circulation coins shall bear an indication of the issuing Member State by means of the Member State's name or an abbreviation of it.
 * The national side of circulation coins shall bear a circle of 12 stars that shall fully surround the national design, including the year mark and the indication of the issuing Member State's name. This shall not prevent some design elements from extending into the circle of stars, provided that the stars are all clearly and fully visible. The 12 stars shall be depicted as on the Union flag.
 * Changes to the designs used for the national sides of regular coins may only be made once every 15 years, without prejudice to changes necessary to prevent counterfeiting of the currency. Without prejudice of the previous, changes to the designs used for the national sides of regular coins may be made where the Head of State referred to on a coin changes. However, a temporary vacancy or the provisional occupation of the function of Head of State shall not give any additional right to such change.
 * Issuing Member States shall update their national sides of regular coins in order to fully comply with this Regulation by 20 June 2062.

In 2014, a new Regulation regarding euro coins was approved. In it, no changes related to what was mentioned above were established.

, Belgium, Monaco, the Netherlands, Spain and Vatican City have all experienced a change in head of state and have revised their designs to reflect this and the new regulation where applicable.

In 2022, France came to comply with the stars' rule after the design change it made on the 1 and 2 euro coins, in which the year had until then been inserted between the stars of the Union.

, Austria, Germany and Greece still have to include an indication of the issuing Member State. Additionally, Greece, Luxembourg and Slovenia have to comply with the rule of the stars. Finally, Austria must eliminate the denominations on the national side of their euro coins.

Bear in mind that the foregoing refers to "regular" coins since, in the case of the 2 euro commemorative coins, the aforementioned is fulfilled in all coins since 2013. This is due to the fact that each one of these coins supposes a variation in the design, while, as mentioned, "regular" coins were not affected unless the design of the national sides was changed, and have until June 20, 2062 in the event that the design had not been changed before.

Finally, the different States must inform each other of their new draft designs (both of "regular" and 2 euro commemorative coins), as well as the European Council and the European Commission, which must give its approval. In one example, the initial design of Andorran 10, 20 and 50 cent coins did not obtain EU approval because the image of the Pantokrator of San Martí de la Cortinada, included in those coins, violated the principle of religious neutrality. The image of the religious figure was eliminated in the final Andorran coin design. Another example, the 2 euro commemorative coins that Belgium planned to issue in 2015 on the 200th anniversary of the Battle of Waterloo, caused complaints by France and withdrawal of the design. However, Belgium did issue a 2.50 euro collector's coin, taking advantage of the fact that these coins are not submitted to the draft design approval.

Security features
Euro coins have high-security machine-readable features. Sophisticated bi-metal and sandwich technologies have been put into the €1 and €2 coins. The 10c, 20c and 50c coins are made of Nordic gold, which is a unique alloy, difficult to melt and used exclusively for coins. The lettering on the edge of the €2 coin also protects it from counterfeiting.

Features for persons with impaired sight
Euro coins were designed in cooperation with organisations representing blind people, and as a result incorporate many features allowing them to be distinguished by touch alone. In addition, their visual appearance is designed to make them easy to tell apart for persons who cannot read the inscriptions on the coins.

The coins increase in size and weight with value. Of the eight denominations of euro coins, the three lowest denominations are small, resemble copper in colour and are quite thin and light. The next three denominations resemble gold in colour and are thicker as well as heavier. The highest two denominations are bimetallic, being generally larger and thicker than the lower denominations.

In general, the greater the value, the heavier and larger the coin. Copper colour identifies low value; gold colour identifies medium value; two different metals identify high value.

There are also differences within each group. The 2 cent coin has a grooved edge to distinguish it from the 1 and 5 cent coins and also from the US penny, which has the same colour and diameter. Similarly, the 20 cent coin edge is smooth with seven indents to distinguish it from the 10 and 50 cent coins.

While currencies predating the euro were specifically designed in similar ways (different sizes, colours, and ridges) to aid the visually impaired, the euro was the first to have authorities consult organizations representing the blind and visually impaired before the release of the currency.

Commemorative issues
Each state may also mint two 2 euro commemorative coins each year from June 2012. From 2004 to May 2012, countries were only allowed to mint one coin per year. Only €2 coins may be used in this way (for them to be legal tender) and there is a limit on the number that can be issued. The coin must adhere to the normal design criteria, such as the twelve stars, the year and the issuing country.

Greece was the first country to issue a commemorative coin, and was followed by other countries. In 2007, every eurozone state participated in the Treaty of Rome programme, in which all member states issued a coin of similar design to commemorate the signing of the Treaty, only differing in the name of the issuing country and language of the text. This was also the case in 2009, in commemoration of the tenth anniversary of the Economic and Monetary Union. The design was selected by electronic voting by EU citizens. In 2012, a common commemorative coin was issued to commemorate the tenth anniversary of euro coins and banknotes. In 2015, a common commemorative coin was issued to commemorate 30 years of the European Union flag. Finally, in 2022 a common commemorative coin was issued to commemorate 35 years of the Erasmus Programme.

In 2006, Germany began issuing a series of coins, the German Bundesländer series, showing each of the states of Germany on its coins; It was originally intended to run until 2021, but one extra issue was added in 2019, which pushed back the last three planned issues (2019, 2020, 2021) by one year. The series ended in 2022. In 2023 a new series (Bundesländer series II) began until 2038.

Spain started a commemorative coin series Patrimonio de la Humanidad de la UNESCO (UNESCO World Heritage) in 2010, commemorating all of Spain's UNESCO World Heritage Sites, which is currently planned until 2058. The order in which the coin for a specific site is issued coincides with the order in which they were declared a UNESCO World Heritage site.

In 2021, France started a commemorative coin series about 2024 Summer Olympics. It will be finished in 2024.

Latvia, Lithuania, Luxembourg, and Malta have also issued a series of 2 euro commemorative coins.

Gold and silver commemorative issues
A legacy of old national practice is the minting of silver and gold commemorative coins. Unlike normal issues, these coins are not legal tender throughout the eurozone, but only in the country where they are issued (e.g. a €10 Finnish commemorative coin cannot be used in Portugal).

However, these gold coins are intended for collectors as their bullion value vastly exceeds their face value. Some silver coins, such as the German €10 commemoratives, are often available at banks and some retailers at face value. These coins, however, generally do not circulate but are kept by collectors.

It is uncertain whether the EU Council of Ministers will grant such coins legal tender status outside national boundaries, as Monaco, San Marino, and the Vatican City also issue this kind of coin.

Belgian 2.50 euro coin
In 2015, Belgium issued a 2.50 euro commemorative coin which is legal tender inside the country. 70,000 coins were minted, commemorating the 200th anniversary of Napoleon's defeat in the Battle of Waterloo.

Belgium originally planned to mint 2 euro commemorative coins for the occasion. This plan was blocked by France, however (after 180,000 of the coins had already been minted; they had to be discarded). Minting the 2.50 euro denomination obviated France's complaints as the coins are not legal tender in the European Union, only in Belgium.

EU law states that any country can issue any new coins it wants as long as they are in an irregular denomination, so it invented a €2.50 coin.

Circulation
The European Central Bank closely monitors the circulation and stock of the euro coins and banknotes. It is a task of the Eurosystem to ensure an efficient and smooth supply of euro coins and to maintain their integrity throughout the eurozone.

Statistics
As of December 2021, there are approximately 141 billion coins in circulation around the eurozone. In contrast, the United States has minted over 300 billion pennies since 1983 when the current copper-plated zinc metallic composition began. Using a population of 341.9 million for the euro area, that is roughly 199 coins of denomination 1c or 2c per capita, and 215 other coins per capita.

Counterfeiting
Approximately 100,000 counterfeit euro coins are taken from circulation annually, and roughly the same number are seized before they can be released. Given a total circulation of 56 billion coins, counterfeit coins are relatively rare. About half the counterfeits feature the German national design, but counterfeits have been detected for every issuing country. The majority of counterfeit coins are €2 (60% in 2011), with most of the rest being €1, and a few 50c coins. The number of counterfeit €2 coins being found annually is decreasing, while numbers of counterfeit €1 and 50-cent coins are increasing.

Total amount of counterfeit coins seized from circulation in:
 * 2017: Pre-circulation: 31,059:   circulation: 160,914
 * 2016: Pre-circulation: 77,084;   circulation: 150,258
 * 2015: Pre-circulation: 20; circulation: 146,889
 * 2014: Pre-circulation: 301,970;       circulation: 192,195
 * 2013: Pre-circulation: 31,051;   circulation: 177,600
 * 2012: 184,000
 * 2011: 157,000
 * 2010: 186,000
 * 2009: 172,100
 * 2008: 195,900
 * 2007: 211,100
 * 2006: 163,800
 * 2005: 100,500
 * 2004: 74,564
 * 2003: 26,191
 * 2002: 2,336

The European Technical and Scientific Centre (ETSC) estimates that up to 2 million counterfeit coins were put into circulation in 2002.

Recent investigations by the European Commission have shown that counterfeit sophistication is increasing, making prompt detection more difficult. In 2008, Irish MEP Eoin Ryan called for tighter regulation over tokens and medals that are being increasingly used for small purchases mainly in vending machines across Europe.

Small-denomination coins
The 1c, 2c, and 5c coins account for approximately 80% of all new coins minted in the eurozone. Due to the expense of producing such low-value coinage, the Commission and some member states have proposed that costs could be cut by having a common design on both sides of these coins, rather than minting numerous different designs.

The €1 and €2 coins are two-toned. The "gold" is an alloy, 75% copper, 20% zinc and 5% nickel. The "silver" is cupronickel, 75% copper and 25% nickel. The 10c, 20c and 50c coins are a proprietary alloy known as "Nordic Gold", consisting of 89% copper, 5% aluminium, 5% zinc and 1% tin. The 1c, 2c, and 5c coins are copper-coated steel fourrées. The copper alloys make the coinage antimicrobial.

Price rounding
The 1c and 2c coins were initially introduced to ensure that the introduction of the euro was not used as an excuse by retailers to heavily round up prices. However, due to the cost of maintaining a circulation of low-value coins, both by business and the mints, Belgium, Finland, Ireland, Italy, the Netherlands and Slovakia round prices to the nearest five cents (Swedish rounding) if paying with cash, while producing only a handful of those coins for collectors, rather than general circulation. The coins are still legal tender and produced outside these states.

Countries with Swedish rounding
The Swedish rounding law in Finland was issued in January 2002, shortly after the coins were put into circulation.

The Netherlands followed suit in September 2004, under pressure from retail businesses, which claimed that dealing with 1- and 2-cent coins was too expensive. After a successful experiment in the town of Woerden in May 2004, retailers in across the Netherlands were permitted in September 2004 to round cash transactions to the nearest five cents since.

In Belgium, rounding has been common practice since 2014; by law, rounding has been obligatory for cash purchases since 1 December 2019. For payments with debit or credit cards, the merchant can choose whether to apply rounding but has to inform the client beforehand. With the obligatory rounding in effect, Belgium's National Bank has stopped production of 1- and 2-cent coins.

Ireland introduced rounding in 2015 after a 2013 trial in Wexford.

In May 2017, the Italian parliament passed a resolution to stop minting 1c and 2c coins starting 1 January 2018 and to introduce Swedish rounding.

The withdrawal of low-circulation coins is due in part to rising metal prices: De Nederlandsche Bank calculated it would save $36 million a year by not using the smaller coins. Other countries such as Germany favoured retaining the coins due to their desire for €1.99 prices, which appear more attractive to the consumer than a €2 price. According to James Debono writing for Malta Today, "scrapping the coins is considered unthinkable for Germany where both consumers and retailers are obsessed with precise pricing." Luxembourg and Malta also declared that they do not wish to remove the coins. This is echoed by the European Central Bank which supports the coins, stating it allows businesses to calculate prices more exactly to attract consumers, such as €0.99.

According to a 2005 Eurobarometer survey of EU citizens, Germans were most sceptical about the removal of the 1c and 2c coins from complete circulation in the eurozone, but on average a majority of Germans still supported their removal (58% for the one cent coin and 52% for the two cent coin in 2005). The Belgians were most supportive of their removal. A similar survey in 2017 found 64% across the eurozone favoring their removal with prices rounded, with over 70% in Belgium, Ireland, Italy, the Netherlands and Slovakia. Only Portugal and Latvia had a plurality in favour of retaining the coins (49% against removal, 45–46% in favour). The same survey in 2021 found that 67% of respondents across the eurozone were in favor of the removal, and all countries in the eurozone showed a plurality of people also in favor.

The Commission in 2010 released its guidelines on daily life euro cash questions, to give citizens guidelines on issues with direct implications for daily life. The guidelines were based on ten guiding principles, including two that still remain: "No surcharges should be imposed on payments in cash" and "Member States should not adopt new rounding rules to the nearest five cent". Following a consultation, a Commission initiative considering the adoption of price rounding was due to be adopted by the end of 2021. Regardless of the Commission's decision, Slovakia proposed introducing rounding from 2022.

Controversy
In spring 2016, controversy arose in the Netherlands after an episode of the television program Keuringsdienst van Waarde showed that euro coins for the Netherlands and other countries were being made by South Korean company Poongsan, a known producer of cluster munitions. Cluster munitions are banned internationally by the 2008 Convention on Cluster Munitions (CCM), because of their indiscriminate and long-term effects on civilians. The CCM prohibits the use, production, stockpiling or transfer of cluster munitions as well as assistance with these acts. After parliamentary questions were posed, the Dutch government stated that the Royal Dutch Mint had ordered around 40 million 'coin blanks' between 2011 and 2016, and that Poongsan was on a list of vetted suppliers of the European Commission's Mint Directors Working Group. Since then, both the Royal Dutch Mint and the Norwegian Mint have excluded Poongsan as a coin blank supplier due to its involvement with cluster munitions. Questions were also raised that year in the European Parliament about Poongsan's presence on the vetted list of coin blank suppliers of the European Commission's Mint Directors Working Group. The Commission responded with claims that responsibility on the issue lies with EU member states.

title: Euro coins