Physical Constants Table (CODATA 2022)
Every physical constant in the CODATA 2022 adjustment from NIST, from the speed of light to the tau mass. Search by name or symbol, filter by field, see which values are exact since the 2019 SI redefinition, and copy any value with or without its uncertainty.
How to Use
- Start with the Most used table at the top: c, h, ħ, e, kB, NA, R, G, ε₀, μ₀, the particle masses and more. The full list of 355 constants follows it, A to Z.
- Type in the search box to filter by name, symbol or unit: hbar, epsilon0, proton, mol. Use the category buttons to narrow to universal, electromagnetic, atomic and nuclear, or physico-chemical constants.
- Tick Exact constants only to see the values fixed by the 2019 SI redefinition and everything built from them.
- Click a row to select it. The card at the top shows its value, uncertainty and relative uncertainty, and the readouts and Show Work update.
- Use the copy buttons for the value alone, the value with its ± uncertainty and unit, or a plain number for code such as 6.67430e-11.
| Quantity | Value | Unit |
|---|---|---|
| Most used (33) | ||
| c speed of light in vacuumexact | 299 792 458 | m·s⁻¹ |
| h Planck constantexact | 6.626 070 15 × 10⁻³⁴ | J·Hz⁻¹ |
| ħ reduced Planck constantexact | 1.054 571 817… × 10⁻³⁴ | J·s |
| e elementary chargeexact | 1.602 176 634 × 10⁻¹⁹ | C |
| kB Boltzmann constantexact | 1.380 649 × 10⁻²³ | J·K⁻¹ |
| NA Avogadro constantexact | 6.022 140 76 × 10²³ | mol⁻¹ |
| R molar gas constantexact | 8.314 462 618… | J·mol⁻¹·K⁻¹ |
| F Faraday constantexact | 96 485.332 12… | C·mol⁻¹ |
| G Newtonian constant of gravitation | 6.674 30 × 10⁻¹¹ ± 0.000 15 × 10⁻¹¹ |
m³·kg⁻¹·s⁻² |
| σ Stefan-Boltzmann constantexact | 5.670 374 419… × 10⁻⁸ | W·m⁻²·K⁻⁴ |
| ε0 vacuum electric permittivity | 8.854 187 8188 × 10⁻¹² ± 0.000 000 0014 × 10⁻¹² |
F·m⁻¹ |
| μ0 vacuum mag. permeability | 1.256 637 061 27 × 10⁻⁶ ± 0.000 000 000 20 × 10⁻⁶ |
N·A⁻² |
| Z0 characteristic impedance of vacuum | 376.730 313 412 ± 0.000 000 059 |
ohm |
| me electron mass | 9.109 383 7139 × 10⁻³¹ ± 0.000 000 0028 × 10⁻³¹ |
kg |
| mp proton mass | 1.672 621 925 95 × 10⁻²⁷ ± 0.000 000 000 52 × 10⁻²⁷ |
kg |
| mn neutron mass | 1.674 927 500 56 × 10⁻²⁷ ± 0.000 000 000 85 × 10⁻²⁷ |
kg |
| mu atomic mass constant | 1.660 539 068 92 × 10⁻²⁷ ± 0.000 000 000 52 × 10⁻²⁷ |
kg |
| α fine-structure constant | 7.297 352 5643 × 10⁻³ ± 0.000 000 0011 × 10⁻³ |
|
| R∞ Rydberg constant | 10 973 731.568 157 ± 0.000 012 |
m⁻¹ |
| a0 Bohr radius | 5.291 772 105 44 × 10⁻¹¹ ± 0.000 000 000 82 × 10⁻¹¹ |
m |
| Eh Hartree energy | 4.359 744 722 2060 × 10⁻¹⁸ ± 0.000 000 000 0048 × 10⁻¹⁸ |
J |
| μB Bohr magneton | 9.274 010 0657 × 10⁻²⁴ ± 0.000 000 0029 × 10⁻²⁴ |
J·T⁻¹ |
| Φ0 mag. flux quantumexact | 2.067 833 848… × 10⁻¹⁵ | Wb |
| KJ Josephson constantexact | 483 597.848 4… × 10⁹ | Hz·V⁻¹ |
| RK von Klitzing constantexact | 25 812.807 45… | ohm |
| eV electron voltexact | 1.602 176 634 × 10⁻¹⁹ | J |
| gn standard acceleration of gravityexact | 9.806 65 | m·s⁻² |
| atm standard atmosphereexact | 101 325 | Pa |
| Vm molar volume of ideal gas (273.15 K, 101.325 kPa)exact | 22.413 969 54… × 10⁻³ | m³·mol⁻¹ |
| c2 second radiation constantexact | 1.438 776 877… × 10⁻² | m·K |
| b Wien wavelength displacement law constantexact | 2.897 771 955… × 10⁻³ | m·K |
| ΔνCs hyperfine transition frequency of Cs-133exact | 9 192 631 770 | Hz |
| Kcd luminous efficacyexact | 683 | lm·W⁻¹ |
Worked Example
Reading an uncertainty. The table lists G = 6.674 30 × 10⁻¹¹ m³ kg⁻¹ s⁻² ± 0.000 15 × 10⁻¹¹. The relative standard uncertainty is u/G = 1.5 × 10⁻¹⁵ ÷ 6.6743 × 10⁻¹¹ = 2.2 × 10⁻⁵, or 22 parts per million. In concise form this is written 6.674 30(15) × 10⁻¹¹: the (15) applies to the last two digits.
An exact constant built from others. The molar gas constant is R = NA × k = 6.022 140 76 × 10²³ mol⁻¹ × 1.380 649 × 10⁻²³ J K⁻¹ = 8.314 462 618 15… J mol⁻¹ K⁻¹. Both factors are exact since 2019, so R has no uncertainty; NIST prints it as 8.314 462 618… because the digits go on.
The common mistake: h where ħ belongs, or the reverse. A photon of frequency f = 5 × 10¹⁴ Hz has energy E = hf = 6.626 070 15 × 10⁻³⁴ × 5 × 10¹⁴ = 3.313 × 10⁻¹⁹ J (2.068 eV). Using ħ = h/2π instead gives 5.273 × 10⁻²⁰ J, too small by a factor of 2π = 6.283. Use ħ only with angular frequency, as in E = ħω.
Show Work
Formulas
CODATA and the 2019 SI
The Committee on Data of the International Science Council (CODATA) set up its Task Group on Fundamental Constants in 1969, and the first recommended set, prepared by E. Richard Cohen and Barry Taylor, appeared in 1973. Because many constants are linked (the Rydberg constant depends on α, mₑ, c and h), the task group does not average each one on its own. It fits all the best measurements together in a single least-squares adjustment, so the values agree with one another. Adjustments now come every four years; the 2022 values on this page were published by NIST in 2024.
On 20 May 2019 the SI was redefined so that the kilogram, ampere, kelvin and mole rest on fixed values of the Planck constant, the elementary charge, the Boltzmann constant and the Avogadro constant. These joined the speed of light (fixed since 1983), the caesium hyperfine frequency and the luminous efficacy Kcd. The International Prototype of the Kilogram, a platinum-iridium cylinder kept near Paris since 1889, stopped being the definition of mass.
One side effect is that constants once exact by definition became measured ones. The vacuum permeability μ₀ was 4π × 10⁻⁷ N/A² exactly; now it follows from the measured fine-structure constant and agrees with the old value to about 1 part in 10¹⁰.
About This Tool
This table holds all 355 entries of the NIST complete listing of the CODATA 2022 values: universal, electromagnetic, atomic and nuclear, and physico-chemical constants, plus the adopted values, X-ray units, atomic and natural units and energy-equivalence factors. Values, uncertainties and units are copied digit for digit from NIST (public domain). Exact values that NIST prints with a trailing … are exact but have more digits than shown. For 38 constants that are defined combinations of others, Show Work works the value out again from the rest of the table and reports how well the two agree. Where a constant has a common unit, such as a mass or a speed, it is also shown in other units.
Source: NIST, CODATA Internationally Recommended 2022 Values of the Fundamental Physical Constants, physics.nist.gov/constants. Everything runs in your browser.
Related tools: Unit Converter, Scientific Notation Converter, and Significant Figures Calculator.
Frequently Asked Questions
What is the value of the gravitational constant G?
CODATA 2022 gives G = 6.674 30(15) × 10⁻¹¹ m³ kg⁻¹ s⁻². The (15) is the standard uncertainty in the last two digits, ± 0.000 15 × 10⁻¹¹, a relative uncertainty of 2.2 × 10⁻⁵. That makes G the least precisely known of the commonly used constants.
Which physical constants are exact?
Since 20 May 2019 the SI fixes seven defining constants exactly, including c = 299 792 458 m/s, h = 6.626 070 15 × 10⁻³⁴ J s, e = 1.602 176 634 × 10⁻¹⁹ C, k = 1.380 649 × 10⁻²³ J/K and the Avogadro constant 6.022 140 76 × 10²³ mol⁻¹. Anything built only from them is exact too, such as ħ = h/2π and the gas constant R. In all, 81 of the 355 listed values are exact.
Is the vacuum permeability μ₀ still exactly 4π × 10⁻⁷?
No. Before 2019 it was fixed at 4π × 10⁻⁷ N/A². Now e and h are fixed instead, so μ₀ = 2αh/(e²c) is measured through the fine-structure constant: 1.256 637 061 27(20) × 10⁻⁶ N/A², a relative uncertainty of 1.6 × 10⁻¹⁰. It differs from 4π × 10⁻⁷ by only 1.3 parts in 10¹⁰.
What does the number in brackets after a constant mean?
It is the standard uncertainty in the last digits shown. The electron mass 9.109 383 7139(28) × 10⁻³¹ kg means 9.109 383 7139 × 10⁻³¹ ± 0.000 000 0028 × 10⁻³¹ kg, a relative uncertainty of 3.1 × 10⁻¹⁰.
How are the gas constant R and the Boltzmann constant related?
R is the Avogadro constant times k: the Boltzmann constant per particle times the number of particles in a mole. 6.022 140 76 × 10²³ × 1.380 649 × 10⁻²³ = 8.314 462 618 15… J mol⁻¹ K⁻¹. Both factors are exact, so R is exact too.
How do I use the Physical Constants Table (CODATA 2022)?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Physics homework
A 500 THz photon carries E = hf = 6.626 070 15 × 10⁻³⁴ × 5 × 10¹⁴ = 3.313 × 10⁻¹⁹ J, or 2.068 eV.
Chemistry
Use R = 8.314 462 618 J mol⁻¹ K⁻¹ in PV = nRT; one mole of ideal gas at 0 °C and 1 atm fills 22.414 L.
Electronics
The thermal voltage kT/e at 300 K is 1.380 649 × 10⁻²³ × 300 ÷ 1.602 176 634 × 10⁻¹⁹ = 25.85 mV, the scale of a diode’s exponential curve.
Programming
Copy constants as code-ready numbers such as 6.67430e-11 or 9.1093837139e-31 instead of retyping them from a textbook.
Checking precision
Compare relative uncertainties before deciding how many digits to carry: G is known to 2.2 × 10⁻⁵, the electron mass to 3.1 × 10⁻¹⁰, and the Rydberg constant to 1.1 × 10⁻¹².
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