Appendix C. Useful Information

Table 1. Important Constants[1]
Symbol Meaning Best Value Approximate Value
c Speed of light in vacuum 2.99792458 × 108 m/s 3.00 × 108 m/s
G Gravitational constant 6.67384(80) × 10−11 N · m2/kg2 6.67 × 10−11 N · m2/kg2
NA Avogadro’s number 6.02214129(27) × 1023 6.02 × 1023
k Boltzmann’s constant 1.3806488(13) × 10−23 J/K 1.38 × 10−23 J/K
R Gas constant 8.3144621(75) J/mol · K 8.31 J/mol · K = 1.99 cal/mol · K = 0.0821 atm · L/mol · K
σ Stefan-Boltzmann constant 5.670373(21) × 10−8 W/m2 · K 5.67 × 10−8 W/m2 · K
k Coulomb force constant 8.987551788… × 109 N · m2/C2 8.99 × 109 N · m2/C2
qe Charge on electron −1.602176565(35) × 10−19 C −1.60 × 10−19 C
ε0 Permittivity of free space 8.854187817… × 10−12 C2/N · m2 8.85 × 10−12 C2/N · m2
µ0 Permeability of free space 4π × 10−7 T · m/A 1.26 × 10−6 T · m/A
h Planck’s constant 6.62606957(29) × 10−34 J · s 6.63 × 10−34 J · s

Return to Top

Table 2. Submicroscopic Masses[2]
Symbol Meaning Best Value Approximate Value
me Electron mass 9.10938291(40) × 10−31 kg 9.11 × 10−31 kg
mp Proton mass 1.672621777(74) × 10−27 kg 1.6726 × 10−27 kg
mn Neutron mass 1.674927351(74) × 10−27 kg 1.6749 × 10−27 kg
u Atomic mass unit 1.660538921(73) × 10−27 kg 1.6605 × 10−27 kg

Return to Top

Table 3. Solar System Data
Sun mass 1.99 × 1030 kg
average radius 6.96 × 108 m
Earth-sun distance (average) 1.496 × 1011 m
Earth mass 5.9736 × 1024 kg
average radius 6.376 × 106 m
orbital period 3.16 × 107 s
Moon mass 7.35 × 1022 kg
average radius 1.74 × 106 m
orbital period (average) 2.36 × 106 s
Earth-moon distance (average) 3.84 × 108 m

Return to Top

Table 4. Metric Prefixes for Powers of Ten and Their Symbols
Prefix Symbol Value Prefix Symbol Value
tera T 1012 deci d 10−1
giga G 109 centi c 10−2
mega M 106 milli m 10−3
kilo k 103 micro µ 10−6
hecto h 102 nano n 10−9
deka da 101 pico p 10−12
— — 100 (= 1) femto f 10−15

Return to Top

Table 5. The Greek Alphabet
Alpha Α α Eta Η η Nu Ν ν
Beta Β β Tau Τ τ 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

Return to Top

Table 6. 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 ⋅ m/s2 newton
Energy J = kg ⋅ m2/s2 joule
Power W = J/s watt
Pressure Pa = N/m2 pascal
Frequency Hz = 1/s hertz
Electronic potential V = J/C volt
Capacitance F = C/V farad
Charge C = s ⋅ A coulomb
Resistance Ω = V/A ohm
Magnetic field T = N/(A ⋅ m) tesla
Nuclear decay rate Bq = 1/s becquerel

Return to Top

Table 7. 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 × 103 J
Power 1 horsepower (hp) = 746 W
Pressure 1 lb/in2 = 6.895 × 103 Pa

Return to Top

Table 8. Other Units
Length 1 light year (ly) = 9.46 × 1015 m
1 astronomical unit (au) = 1.50 × 1011 m
1 nautical mile = 1.852 km
1 angstrom (Å) = 10−10 m
Area 1 acre (ac) = 4.05 × 103 m2
1 square foot (ft2) = 9.29 × 10−2 m2
1 barn (b) = 10−28 m2
Volume 1 liter (L) = 10−3 m3
1 U.S. gallon (gal) = 3.785 × 10−3 m3
Mass 1 solar mass = 1.99 × 1030 kg
1metric ton = 103 kg
1 atomic mass unit (u) = 1.6605 × 10−27 kg
Time 1 year (y) = 3.16 × 107 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 × 10−2 rad
1 minute of arc (′) = 1/60 degree
1 second of arc (′′) = 1/60 minute of arc
1 grad = 1.571 × 10−2 rad
Energy 1 kiloton TNT (kT) = 4.2 × 1012 J
1 kilowatt hour (kW ⋅ h) = 3.60 × 106 J
1 food calorie (kcal) = 4186 J
1 calorie (cal) = 4.186 J
1 electron volt (eV) = 1.60 × 10−19 J
Pressure 1 atmosphere (atm) = 1.013 × 105 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 × 1010 Bq

Return to Top

Table 9. Useful Formulae
Circumference of a circle with radius r or diameter d [latex]C=2\pi{r}=\pi{d}\\[/latex]
Area of a circle with radius r or diameter d [latex]A=\pi{r}^{2}=\frac{\pi{d}^{2}}{4}\\[/latex]
Area of a sphere with radius r [latex]A=4\pi{r}^{2}\\[/latex]
Volume of a sphere with radius r [latex]V=\frac{4}{3}\left(\pi{r}^{3}\right)\\[/latex]

Return to Top

  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. ↵