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Useful Information

This appendix is broken into several tables.

Important Constants1
Symbol Meaning Best Value Approximate Value
c Speed of light in vacuum 2\text{.}\text{99792458}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{8}\phantom{\rule{0.15em}{0ex}}\text{m}/\text{s} 3\text{.}\text{00}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{8}\phantom{\rule{0.15em}{0ex}}\text{m}/\text{s}
G Gravitational constant 6\text{.}\text{67408}\left(\text{31}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{11}}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{kg}}^{2} 6\text{.}\text{67}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{11}}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{kg}}^{2}
{N}_{A} Avogadro’s number 6.02214076\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{\text{23}} 6\text{.}\text{02}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{\text{23}}
k Boltzmann’s constant 1.380649\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{23}}\phantom{\rule{0.15em}{0ex}}\text{J}/\text{K} 1\text{.}\text{38}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{23}}\phantom{\rule{0.15em}{0ex}}\text{J}/\text{K}
R Gas constant 8\text{.}\text{3144621}\left(\text{75}\right)\phantom{\rule{0.15em}{0ex}}\text{J}/\text{mol}\cdot \text{K} 8\text{.}\text{31}\phantom{\rule{0.15em}{0ex}}\text{J}/\text{mol}\cdot \text{K}=1\text{.}\text{99}\phantom{\rule{0.20em}{0ex}}\text{cal}/\text{mol}\cdot \text{K}=0\text{.}\text{0821}\text{atm}\cdot \text{L}/\text{mol}\cdot \text{K}
\text{σ} Stefan-Boltzmann constant 5\text{.}\text{670373}\left(\text{21}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-8}\phantom{\rule{0.15em}{0ex}}\text{W}/{\text{m}}^{2}\cdot \text{K} 5\text{.}\text{67}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-8}\phantom{\rule{0.15em}{0ex}}\text{W}/{\text{m}}^{2}\cdot \text{K}
k Coulomb force constant 8\text{.}\text{987551788}\text{.}\text{.}\text{.}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{9}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{C}}^{2} 8.99\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{9}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{C}}^{2}
{q}_{e} Charge on electron -1.602176634\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{19}}\phantom{\rule{0.15em}{0ex}}\text{C} -1\text{.}\text{60}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{19}}\phantom{\rule{0.15em}{0ex}}\text{C}
{\text{ε}}_{0} Permittivity of free space 8\text{.}\text{854187817}\text{.}\text{.}\text{.}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{12}}\phantom{\rule{0.15em}{0ex}}{\text{C}}^{2}/\text{N}\cdot {\text{m}}^{2} 8\text{.}\text{85}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{12}}\phantom{\rule{0.15em}{0ex}}{\text{C}}^{2}/\text{N}\cdot {\text{m}}^{2}
{\text{μ}}_{0} Permeability of free space 4\pi \phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-7}\phantom{\rule{0.15em}{0ex}}\text{T}\cdot \text{m}/\text{A} 1\text{.}\text{26}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-6}\phantom{\rule{0.15em}{0ex}}\text{T}\cdot \text{m}/\text{A}
h Planck’s constant 6.62607015\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{34}}\phantom{\rule{0.15em}{0ex}}\text{J}\cdot \text{s} 6\text{.}\text{63}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{34}}\phantom{\rule{0.15em}{0ex}}\text{J}\cdot \text{s}
Submicroscopic Masses2
Symbol Meaning Best Value Approximate Value
{m}_{e} Electron mass 9\text{.}\text{10938291}\left(\text{40}\right)×{\text{10}}^{-\text{31}}\text{kg} 9\text{.}\text{11}×{\text{10}}^{-\text{31}}\text{kg}
{m}_{p} Proton mass 1\text{.}\text{672621777}\left(\text{74}\right)×{\text{10}}^{-\text{27}}\text{kg} 1\text{.}\text{6726}×{\text{10}}^{-\text{27}}\text{kg}
{m}_{n} Neutron mass 1\text{.}\text{674927351}\left(\text{74}\right)×{\text{10}}^{-\text{27}}\text{kg} 1\text{.}\text{6749}×{\text{10}}^{-\text{27}}\text{kg}
\text{u} Atomic mass unit 1\text{.}\text{660538921}\left(\text{73}\right)×{\text{10}}^{-\text{27}}\text{kg} 1\text{.}\text{6605}×{\text{10}}^{-\text{27}}\text{kg}
Solar System Data
Sun mass 1\text{.}\text{99}×{\text{10}}^{\text{30}}\text{kg}
average radius 6\text{.}\text{96}×{\text{10}}^{8}\text{m}
Earth-sun distance (average) 1\text{.}\text{496}×{\text{10}}^{\text{11}}\text{m}
Earth mass 5\text{.}\text{9736}×{\text{10}}^{\text{24}}\text{kg}
average radius 6\text{.}\text{376}×{\text{10}}^{6}\text{m}
orbital period 3\text{.}\text{16}×{\text{10}}^{7}\text{s}
Moon mass 7\text{.}\text{35}×{\text{10}}^{\text{22}}\text{kg}
average radius 1\text{.}\text{74}×{\text{10}}^{6}\text{m}
orbital period (average) 2\text{.}\text{36}×{\text{10}}^{6}\text{s}
Earth-moon distance (average) 3\text{.}\text{84}×{\text{10}}^{8}\text{m}
Metric Prefixes for Powers of Ten and Their Symbols
Prefix Symbol Value Prefix Symbol Value
tera T {\text{10}}^{\text{12}} deci d {\text{10}}^{-1}
giga G {\text{10}}^{9} centi c {\text{10}}^{-2}
mega M {\text{10}}^{6} milli m {\text{10}}^{-3}
kilo k {\text{10}}^{3} micro \mu {\text{10}}^{-6}
hecto h {\text{10}}^{2} nano n {\text{10}}^{-9}
deka da {\text{10}}^{1} pico p {\text{10}}^{-\text{12}}
{\text{10}}^{0}\left(=1\right) femto f {\text{10}}^{-\text{15}}
The Greek Alphabet
Alpha \text{Α} \alpha Eta \text{Η} \eta Nu \text{Ν} \nu Tau \text{Τ} \tau
Beta \text{Β} \beta Theta \text{Θ} \theta Xi \text{Ξ} \xi Upsilon \text{Υ} \upsilon
Gamma \text{Γ} \gamma Iota \text{Ι} \iota Omicron \text{Ο} ο Phi \text{Φ} \varphi
Delta \text{Δ} \delta Kappa \text{Κ} \kappa Pi \text{Π} \pi Chi \text{Χ} \chi
Epsilon \text{Ε} \epsilon Lambda \text{Λ} \lambda Rho \text{Ρ} \rho Psi \text{Ψ} \psi
Zeta \text{Ζ} \zeta Mu \text{Μ} \mu Sigma \text{Σ} \sigma Omega \Omega \omega
SI Units
Entity Abbreviation Name
Fundamental units Length m meter
Mass kg kilogram
Time s second
Current A ampere
Supplementary unit Angle rad radian
Derived units Force \text{N}=\text{kg}\cdot \text{m}/{\text{s}}^{2} newton
Energy \text{J}=\text{kg}\cdot {\text{m}}^{2}/{\text{s}}^{2} joule
Power \text{W}=\text{J}/\text{s} watt
Pressure \text{Pa}=\text{N}/{\text{m}}^{2} pascal
Frequency \text{Hz}=1/\text{s} hertz
Electronic potential \text{V}=\text{J}/\text{C} volt
Capacitance \text{F}=\text{C}/\text{V} farad
Charge \text{C}=\text{s}\cdot \text{A} coulomb
Resistance \Omega =\text{V}/\text{A} ohm
Magnetic field \text{T}=\text{N}/\left(\text{A}\cdot \text{m}\right) tesla
Nuclear decay rate \text{Bq}=1/\text{s} becquerel
Selected British Units
Length 1\phantom{\rule{0.20em}{0ex}}\text{inch}\phantom{\rule{0.20em}{0ex}}\left(\text{in}\text{.}\right)=2\text{.}\text{54}\phantom{\rule{0.20em}{0ex}}\text{cm}\phantom{\rule{0.20em}{0ex}}\left(\text{exactly}\right)
1\phantom{\rule{0.20em}{0ex}}\text{foot}\phantom{\rule{0.20em}{0ex}}\left(\text{ft}\right)=0\text{.}\text{3048}\phantom{\rule{0.20em}{0ex}}\text{m}
1\phantom{\rule{0.20em}{0ex}}\text{mile}\phantom{\rule{0.20em}{0ex}}\left(\text{mi}\right)=1\text{.}\text{609}\phantom{\rule{0.20em}{0ex}}\text{km}
Force 1\phantom{\rule{0.20em}{0ex}}\text{pound}\phantom{\rule{0.20em}{0ex}}\left(\text{lb}\right)=4\text{.}\text{448}\phantom{\rule{0.20em}{0ex}}\text{N}
Energy 1\phantom{\rule{0.20em}{0ex}}\text{British thermal unit}\phantom{\rule{0.20em}{0ex}}\left(\text{Btu}\right)=1\text{.}\text{055}×{\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}\text{J}
Power 1\phantom{\rule{0.20em}{0ex}}\text{horsepower}\phantom{\rule{0.20em}{0ex}}\left(\text{hp}\right)=\text{746}\phantom{\rule{0.20em}{0ex}}\text{W}
Pressure 1\phantom{\rule{0.20em}{0ex}}\text{lb}/{\text{in}}^{2}=6\text{.}\text{895}×{\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}\text{Pa}
Other Units
Length 1\phantom{\rule{0.20em}{0ex}}\text{light year}\phantom{\rule{0.20em}{0ex}}\left(\text{ly}\right)=9\text{.}\text{46}×{\text{10}}^{\text{15}}\phantom{\rule{0.20em}{0ex}}\text{m}
1\phantom{\rule{0.20em}{0ex}}\text{astronomical unit}\phantom{\rule{0.20em}{0ex}}\left(\text{au}\right)=1\text{.}\text{50}×{\text{10}}^{\text{11}}\phantom{\rule{0.20em}{0ex}}\text{m}
1\phantom{\rule{0.20em}{0ex}}\text{nautical mile}=1\text{.}\text{852}\phantom{\rule{0.20em}{0ex}}\text{km}
1\phantom{\rule{0.20em}{0ex}}\text{angstrom}\left(\text{Å}\right)\phantom{\rule{0.20em}{0ex}}={\text{10}}^{-\text{10}}\phantom{\rule{0.20em}{0ex}}\text{m}
Area 1\phantom{\rule{0.20em}{0ex}}\text{acre}\phantom{\rule{0.20em}{0ex}}\left(\text{ac}\right)=4\text{.}\text{05}×{\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{2}
1\phantom{\rule{0.20em}{0ex}}\text{square foot}\phantom{\rule{0.20em}{0ex}}\left({\text{ft}}^{2}\right)=9\text{.}\text{29}×{\text{10}}^{-2}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{2}
1\phantom{\rule{0.20em}{0ex}}\text{barn}\phantom{\rule{0.20em}{0ex}}\left(b\right)={\text{10}}^{-\text{28}}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{2}
Volume 1\phantom{\rule{0.20em}{0ex}}\text{liter}\phantom{\rule{0.20em}{0ex}}\left(L\right)={\text{10}}^{-3}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{3}
1\phantom{\rule{0.20em}{0ex}}\text{U.S. gallon}\phantom{\rule{0.20em}{0ex}}\left(\text{gal}\right)=3\text{.}\text{785}×{\text{10}}^{-3}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{3}
Mass 1\phantom{\rule{0.20em}{0ex}}\text{solar mass}\phantom{\rule{0.20em}{0ex}}=1\text{.}\text{99}×{\text{10}}^{\text{30}}\phantom{\rule{0.20em}{0ex}}\text{kg}
1\phantom{\rule{0.20em}{0ex}}\text{metric ton}={\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}\text{kg}
1\phantom{\rule{0.20em}{0ex}}\text{atomic mass unit}\phantom{\rule{0.20em}{0ex}}\left(u\right)=1\text{.}\text{6605}×{\text{10}}^{-\text{27}}\phantom{\rule{0.20em}{0ex}}\text{kg}
Time 1\phantom{\rule{0.20em}{0ex}}\text{year}\phantom{\rule{0.20em}{0ex}}\left(y\right)=3\text{.}\text{16}×{\text{10}}^{7}\phantom{\rule{0.20em}{0ex}}\text{s}
1\phantom{\rule{0.20em}{0ex}}\text{day}\phantom{\rule{0.20em}{0ex}}\left(d\right)=\text{86},\text{400}\phantom{\rule{0.20em}{0ex}}\text{s}
Speed 1\phantom{\rule{0.20em}{0ex}}\text{mile per hour}\phantom{\rule{0.20em}{0ex}}\left(\text{mph}\right)=1\text{.}\text{609}\phantom{\rule{0.20em}{0ex}}\text{km}/\text{h}
1\phantom{\rule{0.20em}{0ex}}\text{nautical mile per hour}\phantom{\rule{0.20em}{0ex}}\left(\text{naut}\right)=1\text{.}\text{852}\phantom{\rule{0.20em}{0ex}}\text{km}/\text{h}
Angle 1\phantom{\rule{0.20em}{0ex}}\text{degree}\phantom{\rule{0.20em}{0ex}}\left(°\right)=1\text{.}\text{745}×{\text{10}}^{-2}\phantom{\rule{0.20em}{0ex}}\text{rad}
1\phantom{\rule{0.20em}{0ex}}\text{minute of arc}\phantom{\rule{0.20em}{0ex}}{\left(}^{\text{'}}\right)=1/\text{60}\phantom{\rule{0.20em}{0ex}}\text{degree}
1\phantom{\rule{0.20em}{0ex}}\text{second of arc}\text{}\phantom{\rule{0.20em}{0ex}}{\left(}^{\text{''}}\right)=1/\text{60}\phantom{\rule{0.20em}{0ex}}\text{minute of arc}
1\phantom{\rule{0.20em}{0ex}}\text{grad}=1\text{.}\text{571}×{\text{10}}^{-2}\phantom{\rule{0.20em}{0ex}}\text{rad}
Energy 1\phantom{\rule{0.20em}{0ex}}\text{kiloton TNT}\phantom{\rule{0.20em}{0ex}}\left(\text{kT}\right)=4\text{.}2×{\text{10}}^{\text{12}}\phantom{\rule{0.20em}{0ex}}\text{J}
1\phantom{\rule{0.20em}{0ex}}\text{kilowatt hour}\phantom{\rule{0.20em}{0ex}}\left(\text{kW}\cdot h\right)=3\text{.}\text{60}×{\text{10}}^{6}\phantom{\rule{0.20em}{0ex}}\text{J}
1\phantom{\rule{0.20em}{0ex}}\text{food calorie}\phantom{\rule{0.20em}{0ex}}\left(\text{kcal}\right)=\text{4186}\phantom{\rule{0.20em}{0ex}}\text{J}
1\phantom{\rule{0.20em}{0ex}}\text{calorie}\phantom{\rule{0.20em}{0ex}}\left(\text{cal}\right)=4\text{.}\text{186}\phantom{\rule{0.20em}{0ex}}\text{J}
1\phantom{\rule{0.20em}{0ex}}\text{electron volt}\phantom{\rule{0.20em}{0ex}}\left(\text{eV}\right)=1\text{.}\text{60}×{\text{10}}^{-\text{19}}\phantom{\rule{0.20em}{0ex}}\text{J}
Pressure 1\phantom{\rule{0.20em}{0ex}}\text{atmosphere}\phantom{\rule{0.20em}{0ex}}\left(\text{atm}\right)=1\text{.}\text{013}×{\text{10}}^{5}\phantom{\rule{0.20em}{0ex}}\text{Pa}
1\phantom{\rule{0.20em}{0ex}}\text{millimeter of mercury}\phantom{\rule{0.20em}{0ex}}\left(\text{mm}\phantom{\rule{0.20em}{0ex}}\text{Hg}\right)=\text{133}\text{.}3\phantom{\rule{0.20em}{0ex}}\text{Pa}
1\phantom{\rule{0.20em}{0ex}}\text{torricelli}\phantom{\rule{0.20em}{0ex}}\left(\text{torr}\right)=1\phantom{\rule{0.20em}{0ex}}\text{mm}\phantom{\rule{0.20em}{0ex}}\text{Hg}=\text{133}\text{.}3\phantom{\rule{0.20em}{0ex}}\text{Pa}
Nuclear decay rate 1\phantom{\rule{0.20em}{0ex}}\text{curie}\phantom{\rule{0.20em}{0ex}}\left(\text{Ci}\right)=3\text{.}\text{70}×{\text{10}}^{\text{10}}\phantom{\rule{0.20em}{0ex}}\text{Bq}
Useful Formulae
Circumference of a circle with radius r or diameter d C=2\pi r=\mathrm{\pi d}
Area of a circle with radius r or diameter d A={\mathrm{\pi r}}^{2}={\mathrm{\pi d}}^{2}/4
Area of a sphere with radius r A=4{\pi r}^{2}
Volume of a sphere with radius r V=\left(4/3\right)\left({\mathrm{\pi r}}^{3}\right)

Footnotes

  • 1 Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.
  • 2 Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.

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