Useful Information

This appendix is broken into several tables.

Important Constants^¹
Symbol	Meaning	Best Value	Approximate Value
$c$	Speed of light in vacuum	$2.99792458 \times 10^{8} m / s$	$3.00 \times 10^{8} m / s$
$G$	Gravitational constant	$6.67408 (31) \times 10^{- 11} N \cdot m^{2} / {kg}^{2}$	$6.67 \times 10^{- 11} N \cdot m^{2} / {kg}^{2}$
$N_{A}$	Avogadro’s number	$6.02214129 (27) \times 10^{23}$	$6.02 \times 10^{23}$
$k$	Boltzmann’s constant	$1.3806488 (13) \times 10^{- 23} J / K$	$1.38 \times 10^{- 23} J / K$
$R$	Gas constant	$8.3144621 (75) J / mol \cdot K$	$8.31 J / mol \cdot K = 1.99 cal / mol \cdot K = 0.0821 atm \cdot L / mol \cdot K$
$σ$	Stefan-Boltzmann constant	$5.670373 (21) \times 10^{- 8} W / m^{2} \cdot K$	$5.67 \times 10^{- 8} W / m^{2} \cdot K$
$k$	Coulomb force constant	$8.987551788 . . . \times 10^{9} N \cdot m^{2} / C^{2}$	$8.99 \times 10^{9} N \cdot m^{2} / C^{2}$
$q_{e}$	Charge on electron	$- 1.602176565 (35) \times 10^{- 19} C$	$- 1.60 \times 10^{- 19} C$
$ε_{0}$	Permittivity of free space	$8.854187817 . . . \times 10^{- 12} C^{2} / N \cdot m^{2}$	$8.85 \times 10^{- 12} C^{2} / N \cdot m^{2}$
$μ_{0}$	Permeability of free space	$4 π \times 10^{- 7} T \cdot m / A$	$1.26 \times 10^{- 6} T \cdot m / A$
$h$	Planck’s constant	$6.62606957 (29) \times 10^{- 34} J \cdot s$	$6.63 \times 10^{- 34} J \cdot s$

Submicroscopic Masses^²
Symbol	Meaning	Best Value	Approximate Value
$m_{e}$	Electron mass	$9.10938291 (40) \times 10^{- 31} kg$	$9.11 \times 10^{- 31} kg$
$m_{p}$	Proton mass	$1.672621777 (74) \times 10^{- 27} kg$	$1.6726 \times 10^{- 27} kg$
$m_{n}$	Neutron mass	$1.674927351 (74) \times 10^{- 27} kg$	$1.6749 \times 10^{- 27} kg$
$u$	Atomic mass unit	$1.660538921 (73) \times 10^{- 27} kg$	$1.6605 \times 10^{- 27} kg$

Metric Prefixes for Powers of Ten and Their Symbols
Prefix	Symbol	Value	Prefix	Symbol	Value
tera	T	$10^{12}$	deci	d	$10^{- 1}$
giga	G	$10^{9}$	centi	c	$10^{- 2}$
mega	M	$10^{6}$	milli	m	$10^{- 3}$
kilo	k	$10^{3}$	micro	$μ$	$10^{- 6}$
hecto	h	$10^{2}$	nano	n	$10^{- 9}$
deka	da	$10^{1}$	pico	p	$10^{- 12}$
—	—	$10^{0} (= 1)$	femto	f	$10^{- 15}$

Selected British Units
Length	$1 inch (in .) = 2.54 cm (exactly)$
	$1 foot (ft) = 0.3048 m$
	$1 mile (mi) = 1.609 km$
Force	$1 pound (lb) = 4.448 N$
Energy	$1 British thermal unit (Btu) = 1.055 \times 10^{3} J$
Power	$1 horsepower (hp) = 746 W$
Pressure	$1 lb / {in}^{2} = 6.895 \times 10^{3} Pa$

Other Units
Length	$1 light year (ly) = 9.46 \times 10^{15} m$
	$1 astronomical unit (au) = 1.50 \times 10^{11} m$
	$1 nautical mile = 1.852 km$
	$1 angstrom (Å) = 10^{- 10} m$
Area	$1 acre (ac) = 4.05 \times 10^{3} m^{2}$
	$1 square foot ({ft}^{2}) = 9.29 \times 10^{- 2} m^{2}$
	$1 barn (b) = 10^{- 28} m^{2}$
Volume	$1 liter (L) = 10^{- 3} m^{3}$
	$1 U.S. gallon (gal) = 3.785 \times 10^{- 3} m^{3}$
Mass	$1 solar mass = 1.99 \times 10^{30} kg$
	$1 metric ton = 10^{3} kg$
	$1 atomic mass unit (u) = 1.6605 \times 10^{- 27} kg$
Time	$1 year (y) = 3.16 \times 10^{7} s$
	$1 day (d) = 86, 400 s$
Speed	$1 mile per hour (mph) = 1.609 km / h$
	$1 nautical mile per hour (naut) = 1.852 km / h$
Angle	$1 degree (°) = 1.745 \times 10^{- 2} rad$
	$Math input error$
	$Math input error$
	$1 grad = 1.571 \times 10^{- 2} rad$
Energy	$1 kiloton TNT (kT) = 4.2 \times 10^{12} J$
	$1 kilowatt hour (kW \cdot h) = 3.60 \times 10^{6} J$
	$1 food calorie (kcal) = 4186 J$
	$1 calorie (cal) = 4.186 J$
	$1 electron volt (eV) = 1.60 \times 10^{- 19} J$
Pressure	$1 atmosphere (atm) = 1.013 \times 10^{5} Pa$
	$1 millimeter of mercury (mm Hg) = 133.3 Pa$
	$1 torricelli (torr) = 1 mm Hg = 133.3 Pa$
Nuclear decay rate	$1 curie (Ci) = 3.70 \times 10^{10} Bq$

Useful Formulae
Circumference of a circle with radius $r$ or diameter $d$	$C = 2 π r = π d$
Area of a circle with radius $r$ or diameter $d$	$A = {π r}^{2} = {π d}^{2} / 4$
Area of a sphere with radius $r$	$A = 4 {π r}^{2}$
Volume of a sphere with radius $r$	$V = (4 / 3) ({π r}^{3})$

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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