# Appendix A Useful Information – Constants, Units, Formulae

This appendix is broken into several tables.

Table 3. Important Constants1

Symbol Meaning Best Value Approximate Value
$c$ Speed of light in vacuum $2.99792458 \times 10^8 \text{m/s}$ $3.00 \times 10^8 \text{m/s}$
$G$ Gravitational constant $6.67408(31) \times 10^{-11} \;\text{N} \cdot \text{m}^2 / \text{kg}^2$ $6.67 \times 10^{-11} \;\text{N} \cdot \text{m}^2 / \text{kg}^2$
$N_A$ Avogadro’s number $6.02214129(27) \times 10^{23}$ $6.02 \times 10^{23}$
$k$ Boltzmann’s constant $1.3806488(13) \times 10^{-23} \;\text{J} / \text{K}$ $1.38 \times 10^{-23} \;\text{J} / \text{K}$
$R$ Gas constant $8.3144621(75) \;\text{J} / \text{mol} \cdot \text{K}$ $8.31 \;\text{J} / \text{mol} \cdot \text{K} = 1.99 \text{cal} / \text{mol} \cdot \text{K} = 0.0821 \text{atm} \cdot \text{L} / \text{mol} \cdot \text{K}$
$\sigma$ Stefan-Boltzmann constant $5.670373(21) \times 10^{-8} \;\text{W} / \text{m}^2 \cdot \text{K}$ $5.67 \times 10^{-8} \;\text{W} / \text{m}^2 \cdot \text{K}$
$k$ Coulomb force constant $8.987551788 \dots \times 10^9 \;\text{N} \cdot \text{m}^2 / \text{C}^2$ $8.99 \times 10^9 \;\text{N} \cdot \text{m}^2 / \text{C}^2$
$q_e$ Charge on electron $-1.602176565(35) \times 10^{-19} \;\text{C}$ $-1.60 \times 10^{-19} \;\text{C}$
$\varepsilon _0$ Permittivity of free space $8.854187817 \dots \times 10^{-12} \;\text{C}^2 / \text{N} \cdot \text{m}^2$ $8.85 \dots \times 10^{-12} \;\text{C}^2 / \text{N} \text{m}^2$
$\mu _0$ Permeability of free space $4 \pi \times 10^{-7} \;\text{T} \cdot \;\text{m}/ \text{A}$ $1.26 \times 10^{-6} \;\text{T} \cdot \text{m} / \text{A}$
$h$ Planck’s constant $6.62606957(29) \times 10^{-34} \;\text{J} \cdot \text{s}$ $6.63 \times 10^{-34} \;\text{J} \cdot \text{s}$
Symbol Meaning Best Value Approximate Value
$m_e$ Electron mass $9.10938291(40) \times 10^{-31} \text{kg}$ $9.11 \times 10^{-31} \text{kg}$
$m_p$ Proton mass $1.672621777(74) \times 10^{-27} \text{kg}$ $1.6726 \times 10^{-27} \text{kg}$
$m_n$ Neutron mass $1.674927351(74) \times 10^{-27} \text{kg}$ $1.6749 \times 10^{-27} \text{kg}$
$\text{u}$ Atomic mass unit $1.660538921(73) \times 10^{-27} \text{kg}$ $1.6605 \times 10^{-27} \text{kg}$
Table 4. Submicroscopic Masses2
 Sun mass $1.99 \times 10^{30} \text{kg}$ average radius $6.96 \times 10^8 \text{m}$ Earth-sun distance (average) $1.496 \times 10^{11} \text{m}$ Earth mass $5.9736 \times 10^{24} \text{kg}$ average radius $6.376 \times 10^6 \text{m}$ orbital period $3.16 \times 10^7 \text{s}$ Moon mass $7.35 \times 10^{22} \text{kg}$ average radius $1.74 \times 10^6 \text{m}$ orbital period (average) $2.36 \times 10^6 \text{s}$ Earth-moon distance (average) $3.84 \times 10^8 \text{m}$ Table 5. Solar System Data
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 $\mu$ $10^{-6}$
hecto h $10^{2}$ nano n $10^{-9}$
deka da $10^{1}$ pico p $10^{-12}$
$10^{0} (= 1)$ femto f $10^{-15}$
Table 6. Metric Prefixes for Powers of Ten and Their Symbols
 Alpha A $\alpha$ Eta Η $\eta$ Nu Ν $\nu$ Tau Τ $\tau$ Beta Β $\beta$ Theta Θ $\theta$ Xi Ξ $\xi$ Upsilon Υ $\upsilon$ Gamma Γ $\gamma$ Iota Ι $\iota$ Omicron Ο ο Phi Φ $\phi$ Delta Δ $\delta$ Kappa Κ $\kappa$ Pi Π $\pi$ Chi Χ $\chi$ Epsilon Ε $\epsilon$ Lambda Λ $\lambda$ Rho Ρ $\rho$ Psi Ψ $\psi$ Zeta Ζ $\zeta$ Mu Μ $\mu$ Sigma Σ $\sigma$ Omega Ω $\omega$ Table 7. The Greek Alphabet
Entity Abbreviation Name
Fundamental units Length m meter
Mass kg kilogram
Time s second
Current A ampere
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 $\text{T} = \text{N} / (\text{A} \cdot \text{m})$ tesla
Nuclear decay rate $\text{Bq} = 1 / \text{s}$ becquerel
Table 8. SI Units
 Length $1 \;\text{inch} \; (\text{in.}) = 2.54 \;\text{cm} \; (\text{exactly})$ $1 \;\text{foot} \; (\text{ft}) = 0.3048 \;\text{m}$ $1 \;\text{mile} \; (\text{mi}) = 1.609 \;\text{km}$ Force $1 \;\text{pound} \; (\text{lb}) = 4.448 \;\text{N}$ Energy $1 \;\text{British thermal unit} \; (\text{Btu}) = 1.055 \times 10^3 \text{J}$ Power horsepower (hp) = 746 W Pressure lb/in2 = 6.895 x 103 Pa Table 9. Selected British Units
 Length 1 light year (ly)  = 9.46 x 1015 m $1 \; \text{astronomical unit} \;(\text{au}) = 1.50 \times 10^{11} \; \text{m}$ 1 nautical mile = 1.852 km 1 angstrom (Å) = 10-10 m Area $1 \;\text{acre} \;(\text{ac}) = 4.05 \times 10^3 \text{m}^2$ $1 \;\text{square foot} \; (\text{ft}^2) = 9.29 \times 10^{-2} \;\text{m}^2$ $1 \;\text{barn} \;(b) = 10^{-28} \;\text{m}^2$ Volume $1 \;\text{liter} \;(L) = 10^{-3} \; \text{m}^3$ 1 U.S. gallon (gal) = 3.785 x 10-3 m Mass $1 \;\text{solar mass} = 1.99 \times 10^{30} \; \text{kg}$ $1 \;\text{metric ton} = 10^3 \;\text{kg}$ $1 \;\text{atomic mass unit} \;(u)= 1.6605 \times 10^{-27} \;\text{kg}$ Time $1 \;\text{year} \;(\text{y}) = 3.16 \times 10^7 \;\text{s}$ $1 \;\text{day} \;(\text{d}) = 86,400 \;\text{s}$ Speed $1 \;\text{mile per hour} \;(\text{mph}) = 1.609 \;\text{km} / \text{h}$ $1 \;\text{nautical mile per hour} \;(\text{naut}) = 1.852 \;\text{km} / \text{h}$ Angle $1 \;\text{degree} \;(^{\circ}) = 1.745 \times 10^{-2} \;\text{rad}$ $1 \;\text{minute of arc} \; ($‘ $) = 1/60 \;\text{degree}$ $1 \;\text{second of arc} \; (") = 1/60 \;\text{minute of arc}$ $1 \;\text{grad} = 1.571 \times 10^{-2} \;\text{rad}$ Energy $1 \;\text{kiloton TNT} \;(\text{kT}) = 4.2 \times 10^{12} \;\text{J}$ $1 \; \text{kilowatt hour} \;(\text{kW} \cdot h) = 3.60 \times 10^6 \;\text{J}$ $1 \;\text{food calorie} \;(\text{kcal}) = 4186 \;\text{J}$ $1 \;\text{calorie} \;(\text{cal}) = 4.186 \;\text{J}$ $1 \;\text{electron volt} \;(\text{eV}) = 1.60 \times 10^{-19} \;\text{J}$ Pressure $1 \;\text{atmosphere} \;(\text{atm}) = 1.013 \times 10^5 \;\text{Pa}$ $1 \;\text{millimeter of mercury} \;(\text{mm Hg}) = 133.3 \;\text{Pa}$ $1 \;\text{torricelli} \;(\text{torr}) = 1 \;\text{mm Hg} = 133.3 \;\text{Pa}$ Nuclear decay rate $1 \;\text{curie} \;(\text{Ci}) = 3.70 \times 10^{10} \; \text{Bq}$ Table 10. Other Units
 $\text{Circumference of a circle with radius} \; \text{r} \; \text{or diameter} \;\text{d}$ $C = 2 \pi r = \pi d$ $\text{Area of a circle with radius} \; r \;\text{or diameter} d$ $A = \pi r^2 = \pi d^{2}/4$ $\text{Area of a sphere with radius} \; r$ $A = 4 \pi r^2$ $\text{Volume of a sphere with radius} \; r$ $V = (4/3)( \pi r^3)$ Table 11. Useful Formulae
Units of Length
meter (m) = 39.37 inches (in.)

= 1.094 yards (yd)

angstrom (Å) = 10–8 cm (exact, definition)

= 10–10 m (exact, definition)

centimeter (cm) = 0.01 m (exact, definition) yard (yd) = 0.9144 m
millimeter (mm) = 0.001 m (exact, definition) inch (in.) = 2.54 cm (exact, definition)
kilometer (km) = 1000 m (exact, definition) mile (US) = 1.60934 km
Units of Volume
liter (L) = 0.001 m3 (exact, definition)

= 1000 cm3 (exact, definition)

= 1.057 (US) quarts

liquid quart (US) = 32 (US) liquid ounces (exact, definition)

= 0.25 (US) gallon (exact, definition)

= 0.9463 L

milliliter (mL) = 0.001 L (exact, definition)

= 1 cm3 (exact, definition)

dry quart = 1.1012 L
microliter (μL)(μL) = 10–6 L (exact, definition)

= 10–3 cm3 (exact, definition)

cubic foot (US) = 28.316 L
Units of Mass
gram (g) = 0.001 kg (exact, definition) ounce (oz) (avoirdupois) = 28.35 g
milligram (mg) = 0.001 g (exact, definition) pound (lb) (avoirdupois) = 0.4535924 kg
kilogram (kg) = 1000 g (exact, definition)

= 2.205 lb

ton (short) =2000 lb (exact, definition)

= 907.185 kg

ton (metric) =1000 kg (exact, definition)

= 2204.62 lb

ton (long) = 2240 lb (exact, definition)

= 1.016 metric ton

Units of Energy
4.184 joule (J) = 1 thermochemical calorie (cal)
1 thermochemical calorie (cal) = 4.184 × 107  erg
erg = 10–7 J (exact, definition)
electron-volt (eV) = 1.60218 × 10−19 J = 23.061 kcal mol−1
liter∙atmosphere = 24.217 cal = 101.325 J (exact, definition)
nutritional calorie (Cal) = 1000 cal (exact, definition) = 4184 J
British thermal unit (BTU) = 1054.804 J  BTU is the amount of energy needed to heat one pound of water by one degree Fahrenheit. Therefore, the exact relationship of BTU to joules and other energy units depends on the temperature at which BTU is measured. 59 °F (15 °C) is the most widely used reference temperature for BTU definition in the United States. At this temperature, the conversion factor is the one provided in this table.

## Footnotes

1. 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. 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.