Useful Information

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Useful Information

This appendix is broken into several tables.

(Figure), Important Constants
(Figure), Submicroscopic Masses
(Figure), Solar System Data
(Figure), Metric Prefixes for Powers of Ten and Their Symbols
(Figure), The Greek Alphabet
(Figure), SI units
(Figure), Selected British Units
(Figure), Other Units
(Figure), Useful Formulae

Important Constants^¹
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	$6\text{.}\text{02214129}\left(\text{27}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{\text{23}}$	$6\text{.}\text{02}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{\text{23}}$
$k$	Boltzmann’s constant	$1\text{.}\text{3806488}\left(\text{13}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{23}}\phantom{\rule{0.15em}{0ex}}\text{J}/\text{K}$	$1\text{.}\text{38}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{23}}\phantom{\rule{0.15em}{0ex}}\text{J}/\text{K}$
$R$	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	$-1\text{.}\text{602176565}\left(\text{35}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{19}}\phantom{\rule{0.15em}{0ex}}\text{C}$	$-1\text{.}\text{60}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{19}}\phantom{\rule{0.15em}{0ex}}\text{C}$
${\text{ε}}_{0}$	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	$6\text{.}\text{62606957}\left(\text{29}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{34}}\phantom{\rule{0.15em}{0ex}}\text{J}\cdot \text{s}$	$6\text{.}\text{63}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{34}}\phantom{\rule{0.15em}{0ex}}\text{J}\cdot \text{s}$

Submicroscopic Masses^²
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	$6\text{.}\text{376}×{\text{10}}^{6}\text{m}$ [latex][/latex]
	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.

Footnotes

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