Constants
Universal / Physical Constants
| Symbol | Quantity | Value | Unit | Dimension |
|---|---|---|---|---|
| $c$ | 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 | $1.38 \times 10^{-23}$ | $\mathrm{J \, K^{-1}}$ | $\mathrm{ML^{2}T^{-2}K^{-1}}$ |
| $\sigma$ | Stefan–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
| Symbol | Quantity | Value | Unit | Dimension |
|---|---|---|---|---|
| $V_{\text{molar}} = \dfrac{RT}{P}$ | 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
| Symbol | Quantity | Value | Unit | Dimension |
|---|---|---|---|---|
| $g_{\text{earth}}$ | 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 aren’t permitted.