This appendix is broken into several tables.
Important Constants
| Symbol |
Meaning |
Current Recommended Value |
Approximate Value |
| [latex]c[/latex] |
Speed of light in vacuum (exact) |
[latex]2.99792458\times10^{8}\ \mathrm{m/s}[/latex] |
[latex]3.00\times10^{8}\ \mathrm{m/s}[/latex] |
| [latex]G[/latex] |
Gravitational constant |
[latex]6.67430(15)\times10^{-11}\ \mathrm{N\,m^2/kg^2}[/latex] |
[latex]6.67\times10^{-11}\ \mathrm{N\,m^2/kg^2}[/latex] |
| [latex]N_A[/latex] |
Avogadro constant (exact) |
[latex]6.02214076\times10^{23}\ \mathrm{mol^{-1}}[/latex] |
[latex]6.02\times10^{23}\ \mathrm{mol^{-1}}[/latex] |
| [latex]k_B[/latex] |
Boltzmann constant (exact) |
[latex]1.380649\times10^{-23}\ \mathrm{J/K}[/latex] |
[latex]1.38\times10^{-23}\ \mathrm{J/K}[/latex] |
| [latex]R[/latex] |
Universal gas constant |
[latex]8.314462618\ \mathrm{J/(mol\cdot K)}[/latex] |
[latex]8.314\ \mathrm{J/(mol\cdot K)}[/latex] |
| [latex]\sigma[/latex] |
Stefan–Boltzmann constant |
[latex]5.670374419\times10^{-8}\ \mathrm{W/(m^2\cdot K^4)}[/latex] |
[latex]5.67\times10^{-8}\ \mathrm{W/(m^2\cdot K^4)}[/latex] |
| [latex]k_e[/latex] |
Coulomb constant |
[latex]8.9875517923\times10^{9}\ \mathrm{N\,m^2/C^2}[/latex] |
[latex]8.99\times10^{9}\ \mathrm{N\,m^2/C^2}[/latex] |
| [latex]e[/latex] |
Elementary charge (exact) |
[latex]1.602176634\times10^{-19}\ \mathrm{C}[/latex] |
[latex]1.60\times10^{-19}\ \mathrm{C}[/latex] |
| [latex]\varepsilon_0[/latex] |
Vacuum permittivity |
[latex]8.8541878188\times10^{-12}\ \mathrm{F/m}[/latex] |
[latex]8.85\times10^{-12}\ \mathrm{F/m}[/latex] |
| [latex]\mu_0[/latex] |
Vacuum permeability |
[latex]1.25663706127\times10^{-6}\ \mathrm{N/A^2}[/latex] |
[latex]1.26\times10^{-6}\ \mathrm{N/A^2}[/latex] |
| [latex]h[/latex] |
Planck constant (exact) |
[latex]6.62607015\times10^{-34}\ \mathrm{J\cdot s}[/latex] |
[latex]6.63\times10^{-34}\ \mathrm{J\cdot s}[/latex] |
Submicroscopic Masses
| Symbol |
Meaning |
Current Recommended Value |
Approximate Value |
| [latex]m_e[/latex] |
Electron mass |
[latex]9.1093837015\times10^{-31}\ \mathrm{kg}[/latex] |
[latex]9.11\times10^{-31}\ \mathrm{kg}[/latex] |
| [latex]m_p[/latex] |
Proton mass |
[latex]1.67262192369\times10^{-27}\ \mathrm{kg}[/latex] |
[latex]1.673\times10^{-27}\ \mathrm{kg}[/latex] |
| [latex]m_n[/latex] |
Neutron mass |
[latex]1.67492749804\times10^{-27}\ \mathrm{kg}[/latex] |
[latex]1.675\times10^{-27}\ \mathrm{kg}[/latex] |
| [latex]u[/latex] |
Unified atomic mass unit (dalton) |
[latex]1.66053906892\times10^{-27}\ \mathrm{kg}[/latex] |
[latex]1.6605\times10^{-27}\ \mathrm{kg}[/latex] |
Solar System Data
| Sun |
Mass |
[latex]1.9885\times10^{30}\ \mathrm{kg}[/latex] |
| Mean radius |
[latex]6.957\times10^{8}\ \mathrm{m}[/latex] |
| Mean Earth–Sun distance (1 AU) |
[latex]1.495978707\times10^{11}\ \mathrm{m}[/latex] |
| Earth |
Mass |
[latex]5.9722\times10^{24}\ \mathrm{kg}[/latex] |
| Mean radius |
[latex]6.371\times10^{6}\ \mathrm{m}[/latex] |
| Orbital period |
[latex]365.25\ \mathrm{d}=3.156\times10^{7}\ \mathrm{s}[/latex] |
| Moon |
Mass |
[latex]7.342\times10^{22}\ \mathrm{kg}[/latex] |
| Mean radius |
[latex]1.7374\times10^{6}\ \mathrm{m}[/latex] |
| Orbital period (sidereal) |
[latex]27.32\ \mathrm{d}=2.3606\times10^{6}\ \mathrm{s}[/latex] |
| Mean Earth–Moon distance |
[latex]3.844\times10^{8}\ \mathrm{m}[/latex] |
Metric Prefixes for Powers of Ten and Their Symbols
| Prefix |
Symbol |
Value |
Prefix |
Symbol |
Value |
| quetta |
Q |
[latex]10^{30}[/latex] |
quecto |
q |
[latex]10^{-30}[/latex] |
| ronna |
R |
[latex]10^{27}[/latex] |
ronto |
r |
[latex]10^{-27}[/latex] |
| yotta |
Y |
[latex]10^{24}[/latex] |
yocto |
y |
[latex]10^{-24}[/latex] |
| zetta |
Z |
[latex]10^{21}[/latex] |
zepto |
z |
[latex]10^{-21}[/latex] |
| exa |
E |
[latex]10^{18}[/latex] |
atto |
a |
[latex]10^{-18}[/latex] |
| peta |
P |
[latex]10^{15}[/latex] |
femto |
f |
[latex]10^{-15}[/latex] |
| tera |
T |
[latex]10^{12}[/latex] |
pico |
p |
[latex]10^{-12}[/latex] |
| giga |
G |
[latex]10^{9}[/latex] |
nano |
n |
[latex]10^{-9}[/latex] |
| mega |
M |
[latex]10^{6}[/latex] |
micro |
[latex]\mu[/latex] |
[latex]10^{-6}[/latex] |
| kilo |
k |
[latex]10^{3}[/latex] |
milli |
m |
[latex]10^{-3}[/latex] |
| hecto |
h |
[latex]10^{2}[/latex] |
centi |
c |
[latex]10^{-2}[/latex] |
| deka |
da |
[latex]10^{1}[/latex] |
deci |
d |
[latex]10^{-1}[/latex] |
| — |
— |
[latex]10^{0}=1[/latex] |
— |
— |
— |
SI Units
|
Quantity |
Symbol |
Unit Name |
| Base units |
Length |
m |
meter |
| Mass |
kg |
kilogram |
| Time |
s |
second |
| Electric current |
A |
ampere |
| Thermodynamic temperature |
K |
kelvin |
| Amount of substance |
mol |
mole |
| Luminous intensity |
cd |
candela |
| Common derived units |
Plane angle |
rad |
radian |
| Frequency |
Hz |
hertz |
| Force |
[latex]\mathrm{N=kg\cdot m/s^2}[/latex] |
newton |
| Energy |
[latex]\mathrm{J=N\cdot m}[/latex] |
joule |
| Power |
[latex]\mathrm{W=J/s}[/latex] |
watt |
| Pressure |
[latex]\mathrm{Pa=N/m^2}[/latex] |
pascal |
| Electric charge |
[latex]\mathrm{C=A\cdot s}[/latex] |
coulomb |
| Electric potential |
[latex]\mathrm{V=J/C}[/latex] |
volt |
| Capacitance |
[latex]\mathrm{F=C/V}[/latex] |
farad |
| Resistance |
[latex]\Omega=\mathrm{V/A}[/latex] |
ohm |
| Magnetic flux density |
[latex]\mathrm{T=N/(A\cdot m)}[/latex] |
tesla |
| Radioactivity |
[latex]\mathrm{Bq=s^{-1}}[/latex] |
becquerel |
Selected U.S. Customary and Imperial Units
| Length |
[latex]1\ \mathrm{inch}\ (\mathrm{in})=2.54\ \mathrm{cm}\ \text{(exact)}[/latex] |
| [latex]1\ \mathrm{foot}\ (\mathrm{ft})=0.3048\ \mathrm{m}\ \text{(exact)}[/latex] |
| [latex]1\ \mathrm{mile}\ (\mathrm{mi})=1.609344\ \mathrm{km}\ \text{(exact)}[/latex] |
| Force |
[latex]1\ \mathrm{pound\ force}\ (\mathrm{lbf})=4.44822\ \mathrm{N}[/latex] |
| Energy |
[latex]1\ \mathrm{British\ thermal\ unit}\ (\mathrm{Btu})=1055\ \mathrm{J}[/latex] |
| Power |
[latex]1\ \mathrm{horsepower}\ (\mathrm{hp})=746\ \mathrm{W}[/latex] |
| Pressure |
[latex]1\ \mathrm{psi}=6894.76\ \mathrm{Pa}[/latex] |
Other Units
| Length |
[latex]1\ \mathrm{light\text{-}year}\ (\mathrm{ly})=9.461\times10^{15}\ \mathrm{m}[/latex] |
| [latex]1\ \mathrm{astronomical\ unit}\ (\mathrm{AU})=1.495978707\times10^{11}\ \mathrm{m}[/latex] |
| [latex]1\ \mathrm{nautical\ mile}=1.852\ \mathrm{km}\ \text{(exact)}[/latex] |
| [latex]1\ \text{\AA}=10^{-10}\ \mathrm{m}[/latex] |
| Area |
[latex]1\ \mathrm{acre}=4046.86\ \mathrm{m^2}[/latex] |
| [latex]1\ \mathrm{ft^2}=9.2903\times10^{-2}\ \mathrm{m^2}[/latex] |
| [latex]1\ \mathrm{barn}=10^{-28}\ \mathrm{m^2}[/latex] |
| Volume |
[latex]1\ \mathrm{L}=10^{-3}\ \mathrm{m^3}[/latex] |
| [latex]1\ \mathrm{U.S.\ gallon}=3.78541\times10^{-3}\ \mathrm{m^3}[/latex] |
| Mass |
[latex]1\ \mathrm{solar\ mass}=1.9885\times10^{30}\ \mathrm{kg}[/latex] |
| [latex]1\ \mathrm{metric\ ton}=10^3\ \mathrm{kg}[/latex] |
| [latex]1\ \mathrm{u}=1\ \mathrm{Da}=1.66054\times10^{-27}\ \mathrm{kg}[/latex] |
| Time |
[latex]1\ \mathrm{year}=3.156\times10^7\ \mathrm{s}[/latex] |
| [latex]1\ \mathrm{day}=86400\ \mathrm{s}[/latex] |
| Speed |
[latex]1\ \mathrm{mph}=1.60934\ \mathrm{km/h}[/latex] |
| [latex]1\ \mathrm{knot}=1.852\ \mathrm{km/h}[/latex] |
| Angle |
[latex]1^\circ=\pi/180=1.7453\times10^{-2}\ \mathrm{rad}[/latex] |
| [latex]1\ \mathrm{arcminute}=\frac{1}{60}^\circ[/latex] |
| [latex]1\ \mathrm{arcsecond}=\frac{1}{60}\ \mathrm{arcminute}[/latex] |
| [latex]1\ \mathrm{grad}=\pi/200=1.5708\times10^{-2}\ \mathrm{rad}[/latex] |
| Energy |
[latex]1\ \mathrm{kiloton\ TNT}=4.184\times10^{12}\ \mathrm{J}[/latex] |
| [latex]1\ \mathrm{kWh}=3.60\times10^6\ \mathrm{J}[/latex] |
| [latex]1\ \mathrm{kcal}=4184\ \mathrm{J}[/latex] |
| [latex]1\ \mathrm{cal}=4.184\ \mathrm{J}[/latex] |
| [latex]1\ \mathrm{eV}=1.60218\times10^{-19}\ \mathrm{J}[/latex] |
| Pressure |
[latex]1\ \mathrm{atm}=101325\ \mathrm{Pa}[/latex] |
| [latex]1\ \mathrm{mmHg}=133.322\ \mathrm{Pa}[/latex] |
| [latex]1\ \mathrm{torr}=133.322\ \mathrm{Pa}[/latex] |
| Radioactivity and Radiation |
[latex]1\ \mathrm{Ci}=3.70\times10^{10}\ \mathrm{Bq}[/latex] |
| [latex]1\ \mathrm{Gy}=1\ \mathrm{J/kg}[/latex] |
| [latex]1\ \mathrm{Sv}=1\ \mathrm{J/kg}[/latex] |
Useful Formulae
| Circumference of a circle with radius [latex]r[/latex] or diameter [latex]d[/latex] |
[latex]C=2\pi r=\pi d[/latex] |
| Area of a circle with radius [latex]r[/latex] or diameter [latex]d[/latex] |
[latex]A=\pi r^2=\frac{\pi d^2}{4}[/latex] |
| Surface area of a sphere with radius [latex]r[/latex] |
[latex]A=4\pi r^2[/latex] |
| Volume of a sphere with radius [latex]r[/latex] |
[latex]V=\frac{4}{3}\pi r^3[/latex] |
The Greek Alphabet
| Name |
Uppercase |
Lowercase |
| Alpha |
[latex]\mathrm{A}[/latex] |
[latex]\alpha[/latex] |
| Beta |
[latex]\mathrm{B}[/latex] |
[latex]\beta[/latex] |
| Gamma |
[latex]\Gamma[/latex] |
[latex]\gamma[/latex] |
| Delta |
[latex]\Delta[/latex] |
[latex]\delta[/latex] |
| Epsilon |
[latex]\mathrm{E}[/latex] |
[latex]\epsilon[/latex] |
| Zeta |
[latex]\mathrm{Z}[/latex] |
[latex]\zeta[/latex] |
| Eta |
[latex]\mathrm{H}[/latex] |
[latex]\eta[/latex] |
| Theta |
[latex]\Theta[/latex] |
[latex]\theta[/latex] |
| Iota |
[latex]\mathrm{I}[/latex] |
[latex]\iota[/latex] |
| Kappa |
[latex]\mathrm{K}[/latex] |
[latex]\kappa[/latex] |
| Lambda |
[latex]\Lambda[/latex] |
[latex]\lambda[/latex] |
| Mu |
[latex]\mathrm{M}[/latex] |
[latex]\mu[/latex] |
| Nu |
[latex]\mathrm{N}[/latex] |
[latex]\nu[/latex] |
| Xi |
[latex]\Xi[/latex] |
[latex]\xi[/latex] |
| Omicron |
[latex]\mathrm{O}[/latex] |
[latex]\mathrm{o}[/latex] |
| Pi |
[latex]\Pi[/latex] |
[latex]\pi[/latex] |
| Rho |
[latex]\mathrm{P}[/latex] |
[latex]\rho[/latex] |
| Sigma |
[latex]\Sigma[/latex] |
[latex]\sigma[/latex] |
| Tau |
[latex]\mathrm{T}[/latex] |
[latex]\tau[/latex] |
| Upsilon |
[latex]\Upsilon[/latex] |
[latex]\upsilon[/latex] |
| Phi |
[latex]\Phi[/latex] |
[latex]\varphi[/latex] |
| Chi |
[latex]\mathrm{X}[/latex] |
[latex]\chi[/latex] |
| Psi |
[latex]\Psi[/latex] |
[latex]\psi[/latex] |
| Omega |
[latex]\Omega[/latex] |
[latex]\omega[/latex] |
Notes
The numerical values in this appendix are based on the current International System of Units (SI), the 2022 CODATA recommended values of the fundamental physical constants, and data published by the National Institute of Standards and Technology (NIST). Values have been rounded where appropriate for introductory physics calculations.
Some physical constants, including the speed of light in vacuum, the Planck constant, the elementary charge, the Avogadro constant, and the Boltzmann constant, are exact by definition in the modern SI system. Other quantities are determined experimentally and may be refined as measurement techniques improve.
For the most up-to-date reference values, consult the
NIST Fundamental Physical Constants
and the
NIST Constants Database.
