# Physical Constants

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$

( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\id}{\mathrm{id}}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\kernel}{\mathrm{null}\,}$$

$$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$

$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$

$$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$

$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$

$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vectorC}[1]{\textbf{#1}}$$

$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$

$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$

$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\avec}{\mathbf a}$$ $$\newcommand{\bvec}{\mathbf b}$$ $$\newcommand{\cvec}{\mathbf c}$$ $$\newcommand{\dvec}{\mathbf d}$$ $$\newcommand{\dtil}{\widetilde{\mathbf d}}$$ $$\newcommand{\evec}{\mathbf e}$$ $$\newcommand{\fvec}{\mathbf f}$$ $$\newcommand{\nvec}{\mathbf n}$$ $$\newcommand{\pvec}{\mathbf p}$$ $$\newcommand{\qvec}{\mathbf q}$$ $$\newcommand{\svec}{\mathbf s}$$ $$\newcommand{\tvec}{\mathbf t}$$ $$\newcommand{\uvec}{\mathbf u}$$ $$\newcommand{\vvec}{\mathbf v}$$ $$\newcommand{\wvec}{\mathbf w}$$ $$\newcommand{\xvec}{\mathbf x}$$ $$\newcommand{\yvec}{\mathbf y}$$ $$\newcommand{\zvec}{\mathbf z}$$ $$\newcommand{\rvec}{\mathbf r}$$ $$\newcommand{\mvec}{\mathbf m}$$ $$\newcommand{\zerovec}{\mathbf 0}$$ $$\newcommand{\onevec}{\mathbf 1}$$ $$\newcommand{\real}{\mathbb R}$$ $$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$$ $$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$$ $$\newcommand{\bcal}{\cal B}$$ $$\newcommand{\ccal}{\cal C}$$ $$\newcommand{\scal}{\cal S}$$ $$\newcommand{\wcal}{\cal W}$$ $$\newcommand{\ecal}{\cal E}$$ $$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$$ $$\newcommand{\gray}[1]{\color{gray}{#1}}$$ $$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$$ $$\newcommand{\rank}{\operatorname{rank}}$$ $$\newcommand{\row}{\text{Row}}$$ $$\newcommand{\col}{\text{Col}}$$ $$\renewcommand{\row}{\text{Row}}$$ $$\newcommand{\nul}{\text{Nul}}$$ $$\newcommand{\var}{\text{Var}}$$ $$\newcommand{\corr}{\text{corr}}$$ $$\newcommand{\len}[1]{\left|#1\right|}$$ $$\newcommand{\bbar}{\overline{\bvec}}$$ $$\newcommand{\bhat}{\widehat{\bvec}}$$ $$\newcommand{\bperp}{\bvec^\perp}$$ $$\newcommand{\xhat}{\widehat{\xvec}}$$ $$\newcommand{\vhat}{\widehat{\vvec}}$$ $$\newcommand{\uhat}{\widehat{\uvec}}$$ $$\newcommand{\what}{\widehat{\wvec}}$$ $$\newcommand{\Sighat}{\widehat{\Sigma}}$$ $$\newcommand{\lt}{<}$$ $$\newcommand{\gt}{>}$$ $$\newcommand{\amp}{&}$$ $$\definecolor{fillinmathshade}{gray}{0.9}$$
Name Symbol Value Unit
Number $$\pi$$ $$\pi$$ 3.14159265358979323846
Number e e 2.71828182845904523536
Euler’s constant   0.577215664901532860606
Elementary charge $$e$$ $$1.60217733\cdot10^{-19}$$

C

Gravitational constant $$G,\kappa$$ $$6.67259\cdot10^{-11}$$ m$$^3$$kg$$^{-1}$$s$$^{-2}$$
Fine-structure constant $$\alpha=e^2/2hc\varepsilon_0$$ $$\approx1/137$$
Speed of light in vacuum $$c$$ $$2.99792458\cdot10^8$$ m/s (def)
Permittivity of the vacuum $$\varepsilon_0$$ $$8.854187\cdot10^{-12}$$ F/m
Permeability of the vacuum $$\mu_0$$ $$4\pi\cdot10^{-7}$$ H/m
$$(4\pi\varepsilon_0)^{-1}$$   $$8.9876\cdot10^9$$ Nm$$^2$$C$$^{-2}$$
Planck’s constant $$h$$ $$6.6260755\cdot10^{-34}$$

Js

Dirac’s constant $$\hbar=h/2\pi$$ $$1.0545727\cdot10^{-34}$$ Js
Bohr magneton $$\mu_{\rm B}=e\hbar/2m_{\rm e}$$ $$9.2741\cdot10^{-24}$$ Am$$^2$$
Bohr radius $$a_0$$ $$0.52918$$ Å
Rydberg’s constant $$Ry$$ 13.595 eV
Electron Compton wavelength $$\lambda_{\rm Ce}=h/m_{\rm e}c$$ $$2.2463\cdot10^{-12}$$ m
Proton Compton wavelength $$\lambda_{\rm Cp}=h/m_{\rm p}c$$ $$1.3214\cdot10^{-15}$$ m
Reduced mass of the H-atom $$\mu_{\rm H}$$ $$9.1045755\cdot10^{-31}$$ kg
Stefan-Boltzmann’s constant $$\sigma$$ $$5.67032\cdot10^{-8}$$

Wm$$^{-2}$$K$$^{-4}$$

Wien’s constant $$k_{\rm W}$$ $$2.8978\cdot10^{-3}$$ mK
Molar gasconstant $$R$$ 8.31441 J$$\cdot$$mol$$^{-1}\cdot$$K$$^{-1}$$
Avogadro’s constant $$N_{\rm A}$$ $$6.0221367\cdot10^{23}$$ mol$$^{-1}$$
Boltzmann’s constant $$k=R/N_{\rm A}$$ $$1.380658\cdot10^{-23}$$ J/K
Electron mass $$m_{\rm e}$$ $$9.1093897\cdot10^{-31}$$

kg

Proton mass $$m_{\rm p}$$ $$1.6726231\cdot10^{-27}$$ kg
Neutron mass $$m_{\rm n}$$ $$1.674954\cdot10^{-27}$$ kg
Elementary mass unit $$m_{\rm u}=\frac{1}{12}m(^{12}_{~6}$$C) $$1.6605656\cdot10^{-27}$$ kg
Nuclear magneton $$\mu_{\rm N}$$ $$5.0508\cdot10^{-27}$$ J/T
Diameter of the Sun $$D_\odot$$ $$1392\cdot10^6$$

m

Mass of the Sun $$M_\odot$$ $$1.989\cdot10^{30}$$ kg
Rotational period of the Sun $$T_\odot$$ 25.38 days
Radius of Earth $$R_{\rm A}$$ $$6.378\cdot10^6$$ m
Mass of Earth $$M_{\rm A}$$ $$5.976\cdot10^{24}$$ kg
Rotational period of Earth $$T_{\rm A}$$ 23.96 hours
Earth orbital period Tropical year 365.24219879 days
Astronomical unit AU $$1.4959787066\cdot10^{11}$$ m
Light year lj $$9.4605\cdot10^{15}$$ m
Parsec pc $$3.0857\cdot10^{16}$$ m
Hubble constant $$H$$ $$\approx(75\pm25)$$ km$$\cdot$$s$$^{-1}\cdot$$Mpc$$^{-1}$$

This page titled Physical Constants is shared under a CC BY license and was authored, remixed, and/or curated by Johan Wevers.