Useful Information

This appendix is broken into several tables.

[link], Important Constants

[link], Submicroscopic Masses

[link], Solar System Data

[link], Metric Prefixes for Powers of Ten and Their Symbols

[link], The Greek Alphabet

[link], SI units

[link], Selected British Units

[link], Other Units

[link], Useful Formulae

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	$4π \times 10^{- 7} T \cdot m / A$	$1 . 26 \times 10^{- 6} T \cdot m / A$
$h$	Planck’s constant	$6.62606957 (29) \times 10^{- 34} J \cdot s$	$6 . 63 \times 10^{- 34} J \cdot s$

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

4π \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	$1.660538921 (73) \times 10^{- 27} kg$	$1 . 6605 \times 10^{- 27} kg$

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

Solar System Data
Sun	mass	$1 . 99 \times 10^{30} kg$
	average radius	$6 . 96 \times 10^{8} m$
	Earth-sun distance (average)	$1 . 496 \times 10^{11} m$
Earth	mass	$5 . 9736 \times 10^{24} kg$
	average radius	$6 . 376 \times 10^{6} m$
	orbital period	$3 . 16 \times 10^{7} s$
Moon	mass	$7 . 35 \times 10^{22} kg$
	average radius	$1 . 74 \times 10^{6} m$
	orbital period (average)	$2 . 36 \times 10^{6} s$
	Earth-moon distance (average)	$3 . 84 \times 10^{8} m$

Solar System Data

Sun

mass

1 . 99 \times 10^{30} kg

average radius

6 . 96 \times 10^{8} m

Earth-sun distance (average)

1 . 496 \times 10^{11} m

Earth

mass

5 . 9736 \times 10^{24} kg

average radius

6 . 376 \times 10^{6} m

orbital period

3 . 16 \times 10^{7} s

Moon

mass

7 . 35 \times 10^{22} kg

average radius

1 . 74 \times 10^{6} m

orbital period (average)

2 . 36 \times 10^{6} s

Earth-moon distance (average)

3 . 84 \times 10^{8} m

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	$10^{- 15}$

Metric Prefixes for Powers of Ten and Their Symbols

Prefix

Symbol

Value

Prefix

Symbol

Value

tera

10^{12}

deci

10^{- 1}

giga

10^{9}

centi

10^{- 2}

mega

10^{6}

milli

10^{- 3}

kilo

10^{3}

micro

μ

10^{- 6}

hecto

10^{2}

nano

10^{- 9}

deka

10^{1}

pico

10^{- 12}

—

10^{0} (= 1)

femto

10^{- 15}

The Greek Alphabet
Alpha	$Α$	$α$	Eta	$Η$	$η$	Nu	$Ν$	$ν$	Tau	$Τ$	$τ$
Beta	$Β$	$β$	Theta	$Θ$	$θ$	Xi	$Ξ$	$ξ$	Upsilon	$Υ$	$υ$
Gamma	$Γ$	$γ$	Iota	$Ι$	$ι$	Omicron	$Ο$	$ο$	Phi	$Φ$	$ϕ$
Delta	$Δ$	$δ$	Kappa	$Κ$	$κ$	Pi	$Π$	$π$	Chi	$Χ$	$χ$
Epsilon	$Ε$	$ε$	Lambda	$Λ$	$λ$	Rho	$Ρ$	$ρ$	Psi	$Ψ$	$ψ$
Zeta	$Ζ$	$ζ$	Mu	$Μ$	$μ$	Sigma	$Σ$	$σ$	Omega	$Ω$	$ω$

The Greek Alphabet

Alpha

Α

α

Eta

Η

η

Ν

ν

Tau

Τ

τ

Beta

Β

β

Theta

Θ

θ

Ξ

ξ

Upsilon

Υ

υ

Gamma

Γ

γ

Iota

Ι

ι

Omicron

Ο

ο

Phi

Φ

ϕ

Delta

Δ

δ

Kappa

Κ

κ

Π

π

Chi

Χ

χ

Epsilon

Ε

ε

Lambda

Λ

λ

Rho

Ρ

ρ

Psi

Ψ

ψ

Zeta

Ζ

ζ

Μ

μ

Sigma

Σ

σ

Omega

Ω

ω

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	$N = kg \cdot m / s^{2}$	newton
	Energy	$J = kg \cdot m^{2} / s^{2}$	joule
	Power	$W = J / s$	watt
	Pressure	$Pa = N / m^{2}$	pascal
	Frequency	$Hz = 1 / s$	hertz
	Electronic potential	$V = J / C$	volt
	Capacitance	$F = C / V$	farad
	Charge	$C = s \cdot A$	coulomb
	Resistance	$Ω = V / A$	ohm
	Magnetic field	$T = N / (A \cdot m)$	tesla
	Nuclear decay rate	$Bq = 1 / s$	becquerel

SI Units

Entity

Abbreviation

Name

Fundamental units

Length

meter

Mass

kilogram

Time

second

Current

ampere

Supplementary unit

Angle

rad

radian

Derived units

Force

N = kg \cdot m / s^{2}

newton

Energy

J = kg \cdot m^{2} / s^{2}

joule

Power

W = J / s

watt

Pressure

Pa = N / m^{2}

pascal

Frequency

Hz = 1 / s

hertz

Electronic potential

V = J / C

volt

Capacitance

F = C / V

farad

Charge

C = s \cdot A

coulomb

Resistance

Ω = V / A

ohm

Magnetic field

T = N / (A \cdot m)

tesla

Nuclear decay rate

Bq = 1 / s

becquerel

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	$1 lb / {in}^{2} = 6 . 895 \times 10^{3} Pa$

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	$1 degree (°) = 1 . 745 \times 10^{- 2} rad$
	$1 minute of arc (^{'}) = 1 / 60 degree$
	$1 second of arc (^{''}) = 1 / 60 minute of arc$
	$1 grad = 1 . 571 \times 10^{- 2} rad$
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	$1 curie (Ci) = 3 . 70 \times 10^{10} Bq$

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

1 minute of arc (^{'}) = 1 / 60 degree

1 second of arc (^{''}) = 1 / 60 minute of arc

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

Useful Formulae

Circumference of a circle with radius

r

or diameter

d

C = 2 πr = πd

Area of a circle with radius

r

or diameter

d

A = {πr}^{2} = {πd}^{2} / 4

Area of a sphere with radius

r

A = 4 {πr}^{2}

Volume of a sphere with radius

r

V = (4 / 3) ({πr}^{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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