Physical Constants
Exact and measured values of the speed of light, the Planck, Boltzmann and Avogadro constants, G, R and more.
Since 2019 the SI units are defined by fixing the values of seven constants, so the speed of light, the Planck constant, the elementary charge, the Boltzmann constant and the Avogadro constant are now exact. Others, such as the gravitational constant, are still measured. This table lists the physical constants engineers need most, with their units and whether each is exact or measured.
The table
| Quantity | Symbol | Value | Unit | Status |
|---|---|---|---|---|
| Speed of light in vacuum | c | 299 792 458 | m/s | Exact |
| Planck constant | h | 6.62607015E-34 | J s | Exact |
| Elementary charge | e | 1.602176634E-19 | C | Exact |
| Boltzmann constant | k | 1.380649E-23 | J/K | Exact |
| Avogadro constant | N_A | 6.02214076E23 | 1/mol | Exact |
| Standard gravity | g_n | 9.80665 | m/s2 | Exact (by definition) |
| Standard atmosphere | atm | 101 325 | Pa | Exact (by definition) |
| Molar gas constant | R | 8.314462618 | J/mol K | Exact (N_A x k) |
| Stefan-Boltzmann constant | sigma | 5.670374419E-8 | W/m2 K4 | Computed from exact values |
| Faraday constant | F | 96485.33212000001 | C/mol | Exact (N_A x e) |
| Reduced Planck constant | h-bar | 1.054571817E-34 | J s | Exact (h / 2 pi) |
| Newtonian constant of gravitation | G | 6.6743E-11 | m3/kg s2 | Measured (about 22 ppm uncertainty) |
| Vacuum permittivity | epsilon_0 | 8.8541878128E-12 | F/m | Measured (relative uncertainty 1.5E-10) |
| Vacuum permeability | mu_0 | 1.2566370621E-6 | H/m | Measured (relative uncertainty 1.5E-10) |
| Electron mass | m_e | 9.1093837015E-31 | kg | Measured |
| Proton mass | m_p | 1.6726219237E-27 | kg | Measured |
| Atomic mass unit | u | 1.6605390666E-27 | kg | Measured |
| Fine-structure constant | alpha | 0.00729735257 | (none) | Measured |
Source and notes: CODATA 2018 recommended values (NIST, Tiesinga et al., 2021) and the 2019 redefinition of the SI, which fixed c, h, e, k and N_A exactly. Newer CODATA releases change only the last digits of the measured constants.
How to use this table
- Find the constant (by name or symbol).
- Use the value with the unit shown; the number of digits is the full recommended value.
- For exact constants use all the digits in calculations that need them; for measured constants the last digits are uncertain.
Worked example
- Thermal voltage at 300 K: VT = k T ÷ e = 1.380649E-23 × 300 ÷ 1.602176634E-19 = 25.85 mV (the voltage scale of a semiconductor junction).
- Photon energy at a wavelength of 500 nm: E = h c ÷ λ = 2.48 eV, the energy of green light.
Notes and cautions
- The values are the CODATA 2018 recommendations. The 2022 adjustment changes only the last digits of the measured constants.
- The gravitational constant G is the least precisely known constant: different experiments disagree in the fifth digit.
- Standard gravity (9.80665 m/s²) is a defined value used for the kilogram-force; the real gravity varies from 9.78 m/s² at the equator to 9.83 m/s² at the poles.
Related tools and guides
FAQ
What is the speed of light?
299 792 458 m/s exactly (about 3 × 10⁸ m/s). The meter is defined from it.
What is the universal gas constant?
8.314462618 J/mol·K (exactly Avogadro’s constant times Boltzmann’s constant).
What is the Stefan-Boltzmann constant?
5.670374419 × 10⁻⁸ W/m²·K⁴, used for thermal radiation.
Sources
- Tiesinga, Mohr, Newell and Taylor, “CODATA recommended values of the fundamental physical constants: 2018”, Rev. Mod. Phys. 93, 025010 (2021); BIPM, The International System of Units (SI Brochure), 9th edition.
- CODATA 2018 recommended values (NIST, Tiesinga et al., 2021) and the 2019 redefinition of the SI, which fixed c, h, e, k and N_A exactly. Newer CODATA releases change only the last digits of the measured constants.