Constants

Universal / Physical Constants

SymbolQuantityValueUnitDimension
$c$Speed of light in vacuum$3 \times 10^{8}$
$\text{(exact) } 299,792,458$		$\mathrm{m \, s^{-1}}$$\mathrm{LT^{-1}}$
$h$Planck constant$6.626 \times 10^{-34}$$\mathrm{J \, s}$$\mathrm{ML^{2}T^{-1}}$
$hc$Photon Energy constant$1242$$\mathrm{eV \cdot nm}$
$\mathrm{MeV \cdot fm}$		$\mathrm{ML^{2}T^{-1}}$
$\hbar = \dfrac{h}{2\pi}$Reduced Planck constant$1.055 \times 10^{-34}$$\mathrm{J \, s}$$\mathrm{ML^{2}T^{-1}}$
$\mu_0$Vacuum Magnetic permeability$4\pi \times 10^{-7}$$\mathrm{N \, A^{-2}}$$\mathrm{MLT^{-2}I^{-2}}$
$\varepsilon_0 = \dfrac{1}{\mu_0\,c^2}$Vacuum Electric permittivity$8.854 \times 10^{-12}$$\mathrm{F \, m^{-1}}$$\mathrm{M^{-1}L^{-3}T^{4}I^{2}}$
$Z_0 = \dfrac{1}{\varepsilon_0}$Characteristic impedance of vacuum$3.77 \times 10^{2}$$\mathrm{\Omega}$$\mathrm{ML^{2}T^{-3}I^{-2}}$
$G$Newtonian constant of gravitation$6.67 \times 10^{-11}$$\mathrm{m^{3} \, kg^{-1} \, s^{-2}}$$\mathrm{L^{3}M^{-1}T^{-2}}$
$R = \dfrac{PV}{nT}$Molar / Universal Gas constant$8.314 \approx 25/3$
$0.082 \approx 1/12$
$62.36$		$\mathrm{J \, mol^{-1} \, K^{-1}}$
$\mathrm{L \,atm \, mol^{-1} \, K^{-1}}$
$\mathrm{L \,torr \, mol^{-1} \, K^{-1}}$		$\mathrm{ML^{2}T^{-2}K^{-1}}$
$N_A$Avagadro constant$6.022 \times 10^{-23}$$\mathrm{mol^{-1}}$$\mathrm{ML^{2}T^{-2}K^{-1}}$
$N_A\,h$Molar Planck constant$4 \times 10^{-10}$$\mathrm{J \, s \, mol^{-1}}$$\mathrm{ML^{2}T^{-2}K^{-1}}$
$k_B = \dfrac{R}{N_A}$Boltzmann constant$1.38 \times 10^{-23}$$\mathrm{J \, K^{-1}}$$\mathrm{ML^{2}T^{-2}K^{-1}}$
$\sigma$Stefanā€“Boltzmann constant$5.67 \times 10^{-8}$$\mathrm{W \, m^{-2} \, K^{-4}}$$\mathrm{MT^{-3}K^{-4}}$
$\mathrm{F} = N_A\,e$Faraday constant$9.65 \times 10^{4}$$\mathrm{C \, mol^{-1}}$$\mathrm{MT^{-3}K^{-4}}$
$e^-$Elementary Charge$1.602 \times 10^{-19}$$\mathrm{C}$$\mathrm{TI}$
$m_e$Electron mass$9.11 \times 10^{-31}$$\mathrm{kg}$$\mathrm{M}$
$m_p$Proton mass$1.6726 \times 10^{-27}$$\mathrm{kg}$$\mathrm{M}$
$m_n$Neutron mass$1.6749 \times 10^{-27}$$\mathrm{kg}$$\mathrm{M}$
$m_p / m_e$Proton-to-electron mass ratio$1.84 \times 10^{3}$$-$Dimensionless
$m_{\mu}$Muon mass$1.88 \times 10^{-28}$$\mathrm{kg}$$\mathrm{M}$
$m_{\tau}$Tau mass$3.16 \times 10^{-27}$$\mathrm{kg}$$\mathrm{M}$
$\alpha = \dfrac{e^2}{2\epsilon_0hc}$Fine Structure constant$7.297 \times 10^{-3} \approx \dfrac{1}{137}$$-$Dimensionless
$\alpha^{-1}$Inverse fine structure constant$137.036$$-$Dimensionless
$m_u = \dfrac{m({}^{12}\mathrm{C})}{N_A}$Atomic mass unit$1.66 \times 10^{-27}$$\mathrm{kg}$$\mathrm{M}$
$\mu_B = \dfrac{he}{4\pi m_e}$Bohr Magneton$9.274 \times 10^{-24}$$\mathrm{J \, T^{-1}}$$\mathrm{L^{2}IT^{-2}}$
$R_{\infty} = \dfrac{m_e e^4}{8\epsilon_0 h^3c}$Rydberg constant$1.10 \times 10^{7}$$\mathrm{m^{-1}}$$\mathrm{L^{-1}}$
$R_{\infty}\,hc$Rydberg Unit of Energy$2.18 \times 10^{-18}$
$13.6$		$\mathrm{J}$
$\mathrm{eV}$		$\mathrm{L^{-1}}$
$a_0 = \dfrac{h\epsilon_0}{\pi e^2 m_e}$Bohr radius$5.29 \times 10^{-11}$$\mathrm{m}$$\mathrm{L}$
$b$Wien wavelength displacement constant$2.90 \times 10^{-3}$$\mathrm{m \, K}$$\mathrm{LK}$
$b^\prime$Wien frequency displacement law constant$5.88 \times 10^{10}$$\mathrm{Hz \, K^{-1}}$$\mathrm{T^{-1}K^{-1}}$
$b_{\text{entropy}}$Wien entropy displacement law constant$3.00 \times 10^{-3}$$\mathrm{m \, K}$$\mathrm{LK}$
$r_e$Classical electron radius$2.82 \times 10^{-15}$$\mathrm{m}$$\mathrm{L}$
$E_{\text{ion}}$Ionization Energy of hydrogen$2.18 \times 10^{-18}$$\mathrm{J}$$\mathrm{ML^{2}T^{-2}}$

Derived / Composite Constants

SymbolQuantityValueUnitDimension
$V_{\text{molar}} = \dfrac{RT}{P}$Molar Volume of Ideal Gas at:$\text{See Below}$$-$$-$
(normal) $V_{\text{STP}}$$T = 0^{\circ}\mathrm{\,C} = 273.15\mathrm{\,K}\:,\quad P = 101.325\mathrm{\,kPa} = 1\mathrm{\,atm}$$22.4$$\mathrm{L}$$L^{3}$
(new) $V_{\text{STP}}$$T = 0^{\circ}\mathrm{\,C} = 273.15\mathrm{\,K}\:,\quad P = 100\mathrm{\,kPa} = 0.987\mathrm{\,atm}$$22.7$$\mathrm{L}$$L^{3}$
$V_{\text{NTP}}$$T = 20^{\circ}\mathrm{\,C} = 293.15\mathrm{\,K}\:,\quad P = 101.325\mathrm{\,kPa} = 1\mathrm{\,atm}$$24.0$$\mathrm{L}$$L^{3}$
$V_{\text{SATP}}$$T = 25^{\circ}\mathrm{\,C} = 298.15\mathrm{\,K}\:,\quad P = 101.325\mathrm{\,kPa} = 1\mathrm{\,atm}$$24.5$$\mathrm{L}$$L^{3}$

Empirical / Local Constants

SymbolQuantityValueUnitDimension
$g_{\text{earth}}$Earth’s acceleration due to gravity$9.81$$\mathrm{m \, s^{-2}}$$\mathrm{L^{3}M^{-1}T^{-2}}$

Sources

Note: This page includes several unconventional approximations, often tailored for exams where calculators arenā€™t permitted.