# Astrophysics Formulas – Fundamental Constants and Data

### Abbreviated List of Constants and Astrophysical Data

(Note: the latest concordance model cosmology parameters are given on a separate page.)

The fundamental constants listed here are some of the most commonly used physical constants and are a subset of those recommended by the Committee on Data for Science and Technology (CODATA), and adopted by the National Institute of Science and Technology (NIST). For the full set, and excruciating details on methods, measurements, and uncertainties, consult the original paper CODATA Recommended Values of the Fundamental Physical Constants:
2010
by Mohr, Taylor, and Newell, which was accepted for publication by Reviews of Modern Physics, in June 2012. If you just want to access the full (searchable) list of constants and data, go to NIST. Note that uncertainties are given by a number in parentheses, and represent the uncertainties in the last digits of the quantity in question. Where no uncertainties are given for the fundamental constants (as opposed to astrophysical constants), the quantity is defined to have the exact value given. For example, the speed of light in contemporary physics is now defined to have the given value. The units in the table below are SI units except for “eV” and the atomic mass unit, both of which are accepted for use with SI units.

Astrophysical data such as the solar luminosity, mass, and radius are from solarsystem.nasa.gov.

 Symbol Description Value Unit $e$ elementary charge $1.602 176 565(35) \times 10^{-19}$ C $eV$ electron volt $1.602 176 565(35) \times 10^{-19}$ J $h$ Planck constant $6.626 069 57(29) \times 10^{-34}$ J s $\hbar$ Planck constant/$2\pi$ $1.054 571 726(47) \times 10^{-34}$ J s $c$ speed of light in vacuum $2.99 792 458 \times 10^{8}$ ${\rm m} \ {\rm s}^{-1}$ $G$ Newton’s gravitation constant $6.673 84(80) \times 10^{-11}$ ${\rm m}^{3} \ {\rm kg}^{-1} \ {\rm s}^{-2}$ $\epsilon_{0}$ permittivity of free space $8.854 187 817 \times 10^{-12}$ ${\rm F \ m}^{-1}$ $\mu_{0}$ permeability of free space $12.566 370 614 \times 10^{-7}$ ${\rm N \ A}^{-2}$ $\alpha$ fine structure constant $7.297 352 5698(24) \times 10^{-3}$ dimensionless $\alpha^{-1}$ inverse fine structure constant $137.035 999 074(44)$ dimensionless $R_{\infty}$ Rydberg constant $10 973 731.568 539(55)$ ${\rm m}^{-1}$ $m_{p}$ proton mass $1.672 621 777(74) \times 10^{-27}$ kg $m_{e}$ electron mass $9.109 382 91(40) \times 10^{-31}$ kg $m_{p}/m_{e}$ proton to electron mass ratio $1836.152 672 45(75)$ dimensionless u$={\rm m[^{12}C]/12}$ unified atomic mass unit $1.660 538 921(73) \times 10^{-27}$ kg $k$ Boltzmann constant $1.380 6488(13) \times 10^{-23}$ J $K^{-1}$ $N_{A}$ Avagardo constant $6.022 141 29(27) \times 10^{23}$ ${\rm mol}^{-1}$ $R=N_{A}k$ molar gas constant $8.314 4621(75)$ J ${\rm mol}^{-1} \ {\rm K}^{-1}$ $\sigma$ Stefan-Boltzmann constant $5.670 373(21) \times 10^{-8}$ W ${\rm m}^{-2}$ ${\rm K}^{-4}$

Unit abbreviations reminders.
A: Amperes
C: Coulombs
J: Joules
K: Kelvin
kg: kilograms
m: meters
N: Newtons
s: seconds
W: Watts (Joules per second)