Reference · fundamental constants
Physical Constants
The constants used across physics2u, with their SI values. The seven SI defining constants are exact by definition since 20 May 2019; the others are measured and carry the stated relative standard uncertainty.
| Symbol | Quantity | Value | Unit | Status |
|---|---|---|---|---|
| \(c\) | Speed of light in vacuum | \(2.99792458\times10^{8}\) | \(\mathrm{m\,s^{-1}}\) | exact · SI defining constant |
| \(h\) | Planck constant | \(6.62607015\times10^{-34}\) | \(\mathrm{J\,s}\) | exact · SI defining constant |
| \(\hbar\) | Reduced Planck constant | \(1.054571817\times10^{-34}\) | \(\mathrm{J\,s}\) | exact (rounded here) · \(h/2\pi\) |
| \(e\) | Elementary charge | \(1.602176634\times10^{-19}\) | \(\mathrm{C}\) | exact · SI defining constant |
| \(k_B\) | Boltzmann constant | \(1.380649\times10^{-23}\) | \(\mathrm{J\,K^{-1}}\) | exact · SI defining constant |
| \(N_A\) | Avogadro constant | \(6.02214076\times10^{23}\) | \(\mathrm{mol^{-1}}\) | exact · SI defining constant |
| \(R\) | Molar gas constant | \(8.314462618\) | \(\mathrm{J\,mol^{-1}\,K^{-1}}\) | exact (rounded here) · \(N_A k_B\) |
| \(\sigma\) | Stefan–Boltzmann constant | \(5.670374419\times10^{-8}\) | \(\mathrm{W\,m^{-2}\,K^{-4}}\) | exact (rounded here) · \(2\pi^5k_B^4/15h^3c^2\) |
| \(G\) | Newtonian constant of gravitation | \(6.6743\times10^{-11}\) | \(\mathrm{m^3\,kg^{-1}\,s^{-2}}\) | rel. unc. 2.2e-05 |
| \(\varepsilon_0\) | Vacuum electric permittivity | \(8.854187813\times10^{-12}\) | \(\mathrm{F\,m^{-1}}\) | rel. unc. 1.5e-10 |
| \(\mu_0\) | Vacuum magnetic permeability | \(1.256637062\times10^{-6}\) | \(\mathrm{N\,A^{-2}}\) | rel. unc. 1.5e-10 · \(\approx 4\pi\times10^{-7}\), no longer exact since 2019 |
| \(m_e\) | Electron mass | \(9.109383702\times10^{-31}\) | \(\mathrm{kg}\) | rel. unc. 3.1e-10 |
| \(m_p\) | Proton mass | \(1.672621924\times10^{-27}\) | \(\mathrm{kg}\) | rel. unc. 3.0e-10 |
| \(m_n\) | Neutron mass | \(1.674927498\times10^{-27}\) | \(\mathrm{kg}\) | rel. unc. 5.7e-10 |
| \(m_u\) | Atomic mass constant | \(1.660539067\times10^{-27}\) | \(\mathrm{kg}\) | rel. unc. 3.0e-10 · \(1\,\mathrm{u}\) |
| \(\alpha\) | Fine-structure constant | \(7.297352569\times10^{-3}\) | \(\text{-}\) | rel. unc. 1.5e-10 · \(e^2/4\pi\varepsilon_0\hbar c\) |
| \(a_0\) | Bohr radius | \(5.291772109\times10^{-11}\) | \(\mathrm{m}\) | rel. unc. 1.5e-10 |
| \(R_\infty\) | Rydberg constant | \(1.097373157\times10^{7}\) | \(\mathrm{m^{-1}}\) | rel. unc. 1.9e-12 |
| \(\mu_B\) | Bohr magneton | \(9.274010078\times10^{-24}\) | \(\mathrm{J\,T^{-1}}\) | rel. unc. 3.0e-10 |
| \(F\) | Faraday constant | \(96485.33212\) | \(\mathrm{C\,mol^{-1}}\) | exact (rounded here) · \(N_A e\) |
| \(\mathrm{eV}\) | Electron volt | \(1.602176634\times10^{-19}\) | \(\mathrm{J}\) | exact |
| \(g_n\) | Standard acceleration of gravity | \(9.80665\) | \(\mathrm{m\,s^{-2}}\) | exact · conventional value |
| \(\mathrm{atm}\) | Standard atmosphere | \(101325\) | \(\mathrm{Pa}\) | exact · conventional value |
Handy combinations
Computed from the values above; rounded for quick estimates.
| Quantity | Value | Unit |
|---|---|---|
| \(k_BT\ \text{at}\ 300\ \mathrm{K}\) | \(0.02585\) | \(\mathrm{eV}\) |
| \(V_T = k_BT/e\ \text{at}\ 300\ \mathrm{K}\) | \(25.85\) | \(\mathrm{mV}\) |
| \(hc\) | \(1239.84\) | \(\mathrm{eV\,nm}\) |
| \(\hbar c\) | \(197.327\) | \(\mathrm{eV\,nm}\) |
| \(1/(4\pi\varepsilon_0)\) | \(8.98755\times10^{9}\) | \(\mathrm{N\,m^2\,C^{-2}}\) |
| \(m_ec^2\) | \(0.5109989\) | \(\mathrm{MeV}\) |
| \(m_pc^2\) | \(938.2721\) | \(\mathrm{MeV}\) |
| \(m_uc^2\) | \(931.4941\) | \(\mathrm{MeV}\) |
| \(m_p/m_e\) | \(1836.1527\) | \(\text{-}\) |
| \(\text{Rydberg energy } hcR_\infty\) | \(13.6057\) | \(\mathrm{eV}\) |
| \(1/\alpha\) | \(137.035999\) | \(\text{-}\) |
Source: CODATA 2018 recommended values, as published by NIST and shipped in SciPy 1.11.4 (scipy.constants). Derived entries were recomputed and cross-checked (for example \(\hbar = h/2\pi\), \(R = N_Ak_B\), \(c^2 = 1/\mu_0\varepsilon_0\), \(a_0\), \(\mu_B\), \(R_\infty\) from \(\alpha\)) to a relative difference below \(10^{-9}\). See also the unit formula sheets and Symbols & Glossary.