Physical Constants Reference
Every fundamental physical constant in one searchable reference — CODATA 2022 recommended values, grouped by category, with the 7 exact constants that define the SI base units clearly marked. Search by name or symbol, filter by category, and copy any value with one tap.
The 2019 SI redefinition
Since 20 May 2019, every SI base unit has been defined by fixing the exact numerical value of a physical constant, rather than by a physical artefact or a lab procedure. Seven constants — the caesium hyperfine frequency ΔνCs, the speed of light c, the Planck constant h, the elementary charge e, the Boltzmann constant k_B, the Avogadro constant N_A and the luminous efficacy K_cd — are exact by definition and directly define the second, metre, kilogram, ampere, kelvin, mole and candela. Every other constant on this page is a measured quantity, known only to a finite precision.
SI defining constants
| Symbol | Name | Value | Unit | Copy |
|---|---|---|---|---|
| ΔνCs | Caesium hyperfine frequency Defines the second: the exact frequency of the caesium-133 ground-state hyperfine transition that atomic clocks count. exactDefines the second | 9192631770 | Hz | |
| c | Speed of light in vacuum Defines the metre; the universal speed limit for any signal or massless particle. exactDefines the metre | 299792458 | m s⁻¹ | |
| h | Planck constant Defines the kilogram; the quantum of action linking a photon's energy to its frequency, E = hf. exactDefines the kilogram | 6.62607015 × 10⁻³⁴ | J s | |
| e | Elementary charge Defines the ampere; the electric charge of a single proton (or the negative of an electron's). exactDefines the ampere | 1.602176634 × 10⁻¹⁹ | C | |
| k_B | Boltzmann constant Defines the kelvin; relates the average kinetic energy of particles in a gas to its temperature. exactDefines the kelvin | 1.380649 × 10⁻²³ | J K⁻¹ | |
| N_A | Avogadro constant Defines the mole; the number of elementary entities — atoms, molecules, ions — in one mole of a substance. exactDefines the mole | 6.02214076 × 10²³ | mol⁻¹ | |
| K_cd | Luminous efficacy Defines the candela; the luminous efficacy of monochromatic radiation at 540 terahertz (green light). exactDefines the candela | 683 | lm W⁻¹ |
Universal constants
| Symbol | Name | Value | Unit | Copy |
|---|---|---|---|---|
| G | Newtonian constant of gravitation Sets the strength of gravity in Newton's law F = Gm₁m₂/r²; the least precisely known fundamental constant. | 6.67430 × 10⁻¹¹ | m³ kg⁻¹ s⁻² | |
| ℏ | Reduced Planck constant The Planck constant divided by 2π; the natural unit of angular momentum in quantum mechanics, used in E = ℏω. exact | 1.054571817 × 10⁻³⁴ | J s | |
| σ | Stefan–Boltzmann constant Relates a black body's total radiated power per unit area to the fourth power of its absolute temperature. exact | 5.670374419 × 10⁻⁸ | W m⁻² K⁻⁴ |
Electromagnetic constants
| Symbol | Name | Value | Unit | Copy |
|---|---|---|---|---|
| ε₀ | Vacuum electric permittivity The electric permittivity of free space; sets the strength of the electric force in Coulomb's law. | 8.8541878188 × 10⁻¹² | F m⁻¹ | |
| μ₀ | Vacuum magnetic permeability The magnetic permeability of free space; sets the strength of the magnetic force between electric currents. | 1.25663706127 × 10⁻⁶ | N A⁻² |
Atomic & nuclear constants
| Symbol | Name | Value | Unit | Copy |
|---|---|---|---|---|
| mₑ | Electron mass The rest mass of the electron, the lightest charged elementary particle known. | 9.1093837139 × 10⁻³¹ | kg | |
| m_p | Proton mass The rest mass of the proton, the nucleus of a hydrogen-1 atom. | 1.67262192595 × 10⁻²⁷ | kg | |
| m_n | Neutron mass The rest mass of the neutron, slightly heavier than the proton and unstable when free. | 1.67492750056 × 10⁻²⁷ | kg | |
| α | Fine-structure constant A dimensionless number, about 1/137, measuring the strength of the electromagnetic interaction between charged particles. | 7.2973525643 × 10⁻³ | — | |
| a₀ | Bohr radius The most probable distance between the nucleus and electron in a ground-state hydrogen atom. | 5.29177210544 × 10⁻¹¹ | m | |
| R∞ | Rydberg constant The limiting value of atomic spectral wavenumbers, used to predict the hydrogen emission spectrum. | 10973731.568157 | m⁻¹ | |
| u | Atomic mass constant One twelfth the mass of a carbon-12 atom; the reference unit for atomic and molecular masses (1 u). | 1.66053906892 × 10⁻²⁷ | kg |
Physico-chemical constants
| Symbol | Name | Value | Unit | Copy |
|---|---|---|---|---|
| R | Molar gas constant The constant R in the ideal gas law pV = nRT; equal to the Avogadro constant times the Boltzmann constant. exact | 8.314462618 | J mol⁻¹ K⁻¹ | |
| F | Faraday constant The electric charge carried by one mole of electrons; used to relate current and time to moles in electrolysis. exact | 96485.33212 | C mol⁻¹ | |
| eV | Electronvolt The kinetic energy gained by an electron accelerated through a potential difference of one volt; a convenient energy unit in atomic and particle physics. exact | 1.602176634 × 10⁻¹⁹ | J | |
| g₀ | Standard gravity The conventional value of Earth's gravitational acceleration, used to define the kilogram-force and other gravity-based units. exact | 9.80665 | m s⁻² | |
| atm | Standard atmosphere The standard reference pressure, close to the average atmospheric pressure at sea level. exact | 101325 | Pa |
Values are CODATA 2022 recommended values. A constant marked "exact" is fixed by definition — either one of the 7 SI defining constants or an exact product of them — while every other value is measured, with uncertainty in its last digit(s).
SI defining constants
| Symbol | Name | Value | Unit |
|---|---|---|---|
| ΔνCs | Caesium hyperfine frequency exact Defines the second | 9192631770 | Hz |
| c | Speed of light in vacuum exact Defines the metre | 299792458 | m s⁻¹ |
| h | Planck constant exact Defines the kilogram | 6.62607015 × 10⁻³⁴ | J s |
| e | Elementary charge exact Defines the ampere | 1.602176634 × 10⁻¹⁹ | C |
| k_B | Boltzmann constant exact Defines the kelvin | 1.380649 × 10⁻²³ | J K⁻¹ |
| N_A | Avogadro constant exact Defines the mole | 6.02214076 × 10²³ | mol⁻¹ |
| K_cd | Luminous efficacy exact Defines the candela | 683 | lm W⁻¹ |
Universal constants
| Symbol | Name | Value | Unit |
|---|---|---|---|
| G | Newtonian constant of gravitation | 6.67430 × 10⁻¹¹ | m³ kg⁻¹ s⁻² |
| ℏ | Reduced Planck constant exact | 1.054571817 × 10⁻³⁴ | J s |
| σ | Stefan–Boltzmann constant exact | 5.670374419 × 10⁻⁸ | W m⁻² K⁻⁴ |
Electromagnetic constants
| Symbol | Name | Value | Unit |
|---|---|---|---|
| ε₀ | Vacuum electric permittivity | 8.8541878188 × 10⁻¹² | F m⁻¹ |
| μ₀ | Vacuum magnetic permeability | 1.25663706127 × 10⁻⁶ | N A⁻² |
Atomic & nuclear constants
| Symbol | Name | Value | Unit |
|---|---|---|---|
| mₑ | Electron mass | 9.1093837139 × 10⁻³¹ | kg |
| m_p | Proton mass | 1.67262192595 × 10⁻²⁷ | kg |
| m_n | Neutron mass | 1.67492750056 × 10⁻²⁷ | kg |
| α | Fine-structure constant | 7.2973525643 × 10⁻³ | — |
| a₀ | Bohr radius | 5.29177210544 × 10⁻¹¹ | m |
| R∞ | Rydberg constant | 10973731.568157 | m⁻¹ |
| u | Atomic mass constant | 1.66053906892 × 10⁻²⁷ | kg |
Physico-chemical constants
| Symbol | Name | Value | Unit |
|---|---|---|---|
| R | Molar gas constant exact | 8.314462618 | J mol⁻¹ K⁻¹ |
| F | Faraday constant exact | 96485.33212 | C mol⁻¹ |
| eV | Electronvolt exact | 1.602176634 × 10⁻¹⁹ | J |
| g₀ | Standard gravity exact | 9.80665 | m s⁻² |
| atm | Standard atmosphere exact | 101325 | Pa |
About the Physical Constants Reference
Physical constants are quantities that never change — the same everywhere in the universe and at every point in time — and they appear throughout physics, chemistry and engineering as the fixed numbers that make the laws of nature quantitative. This reference collects the fundamental constants recognized by CODATA (the Committee on Data for Science and Technology), grouped into five categories: the 7 SI defining constants that fix the base units, universal constants (the speed of light, the gravitational constant, the Stefan–Boltzmann constant), electromagnetic constants (vacuum permittivity and permeability), atomic & nuclear constants (particle masses, the fine-structure constant, the Bohr radius, the Rydberg constant), and physico-chemical constants (the gas constant, the Faraday constant, the electronvolt, standard gravity and standard atmosphere). What makes this page unusual for a units-focused site is that seven of these numbers are not just useful — they are the definition of a unit. Since the 2019 SI redefinition, the second, metre, kilogram, ampere, kelvin, mole and candela are each defined by fixing the exact numerical value of one constant (the caesium hyperfine frequency, the speed of light, the Planck constant, the elementary charge, the Boltzmann constant, the Avogadro constant and the luminous efficacy respectively), replacing the old artefacts and lab procedures. Every value here is the CODATA 2022 recommended value, the internationally accepted reference used in physics and engineering worldwide. Use it to look up a constant for a calculation, check whether a value is exact or measured, or explore how the SI base units are actually defined today.
How to use this reference
- 1 Search by name or symbol, or tap a category chip — SI defining, universal, electromagnetic, atomic & nuclear, or physico-chemical — to narrow the list.
- 2 Read off the symbol, value and unit for the constant you need; a "defines" badge marks the 7 constants that fix an SI base unit, and an "exact" badge marks every value with zero uncertainty.
- 3 Tap the copy icon on any row to copy the constant as "symbol = value unit," ready to paste into a calculation, spreadsheet or code.
How the SI defines its base units from constants
Before 2019, some SI base units were defined by physical artefacts (the kilogram was a platinum-iridium cylinder kept in a vault in France) or by procedures that were hard to realize with perfect precision. The 2019 redefinition replaced every one of these with a fixed numerical value for a fundamental constant, so each unit is now defined purely in terms of unchanging physics. The second is defined by fixing ΔνCs, the frequency of a specific hyperfine transition in a caesium-133 atom, at exactly 9,192,631,770 Hz — atomic clocks realize the second by counting these oscillations. The metre is defined by fixing the speed of light c at exactly 299,792,458 m/s — since the second is already fixed, this pins down the metre as the distance light travels in 1/299,792,458 of a second. The kilogram is defined by fixing the Planck constant h at exactly 6.62607015×10⁻³⁴ J·s, realized in practice with a Kibble balance that weighs a mass against an electromagnetic force. The ampere is defined by fixing the elementary charge e at exactly 1.602176634×10⁻¹⁹ C — one ampere is the current of 1/e elementary charges flowing per second. The kelvin is defined by fixing the Boltzmann constant k_B at exactly 1.380649×10⁻²³ J/K, which ties temperature directly to particle kinetic energy. The mole is defined by fixing the Avogadro constant N_A at exactly 6.02214076×10²³ per mole — a mole is simply that many elementary entities, no longer tied to a specific mass of carbon-12. The candela is defined by fixing the luminous efficacy K_cd of 540 THz green light at exactly 683 lm/W, connecting a unit of light perception to a unit of radiant power. Every other constant on this page — the gravitational constant, particle masses, the fine-structure constant and the rest — is measured against this exact framework, which is why they carry a finite uncertainty in their last digits instead of an "exact" badge.
Frequently asked questions
What are the fundamental physical constants?
Fundamental physical constants are quantities, such as the speed of light or the charge of an electron, that are believed to be the same everywhere in the universe and unchanging over time. They appear as fixed numbers in the equations of physics and chemistry — for example, the speed of light c sets the maximum speed for any signal, and the Boltzmann constant k_B relates a gas's temperature to the average kinetic energy of its particles. This page lists the CODATA 2022 recommended values for the constants used most often in physics, chemistry and engineering.
Which physical constants are exact?
Seven constants are exact by definition since the 2019 SI redefinition: the caesium hyperfine frequency ΔνCs, the speed of light c, the Planck constant h, the elementary charge e, the Boltzmann constant k_B, the Avogadro constant N_A and the luminous efficacy K_cd. A few others are also exact because they are fixed products of these defining constants or adopted conventions — the reduced Planck constant ℏ = h/2π, the Stefan–Boltzmann constant σ, the molar gas constant R = N_A×k_B, the Faraday constant F = N_A×e, the electronvolt, standard gravity g₀ (9.80665 m/s², fixed by convention) and standard atmosphere (101,325 Pa, fixed by convention). Every value marked "exact" on this page carries no measurement uncertainty; every other value is a measured quantity known only to a finite number of digits.
What changed in the 2019 SI redefinition?
Before 20 May 2019, some SI base units depended on physical artefacts or specific lab procedures — most famously the kilogram, which was defined by a single platinum-iridium cylinder ("Le Grand K") stored in a vault near Paris. The redefinition replaced every such definition with a fixed exact numerical value for a fundamental constant, so any lab with the right equipment can now realize a unit directly from unchanging physics rather than by comparison to a physical object. The kilogram, for instance, is now defined by fixing the Planck constant and is realized with a Kibble balance rather than by weighing an artefact.
What is the difference between the Planck constant and the reduced Planck constant?
The Planck constant h (6.62607015×10⁻³⁴ J·s) and the reduced Planck constant ℏ = h/2π (1.054571817×10⁻³⁴ J·s) are simply two conventions for expressing the same quantum of action. h is used in formulas written in terms of frequency, such as photon energy E = hf, while ℏ is used in formulas written in terms of angular frequency, such as E = ℏω and the uncertainty principle Δx·Δp ≥ ℏ/2. Since h is exact and 2π is an exactly known mathematical constant, ℏ is also exact — it is simply rounded to a finite number of digits like any irrational number, even though it carries zero measurement uncertainty.
Related tools
Put these constants to work: use the scientific notation tool to convert any value between decimal and ×10ⁿ form, the significant figures tool to round a result to the right precision, the dimensional analysis calculator to chain unit conversions step by step, or the unit converter to convert a constant's value into different units.