Appendix C Useful Information: Important constants, Metric Prefixes, SI Units, Useful Formulae, etc.
This appendix is broken into several tables.
Table 3. Important Constants1
| Symbol |
Meaning |
Best Value |
Approximate Value |
| [latex]c[/latex] |
Speed of light in vacuum |
[latex]2.99792458 \times 10^8 \text{m/s}[/latex] |
[latex]3.00 \times 10^8 \text{m/s}[/latex] |
| [latex]G[/latex] |
Gravitational constant |
[latex]6.67408(31) \times 10^{-11} \;\text{N} \cdot \text{m}^2 / \text{kg}^2[/latex] |
[latex]6.67 \times 10^{-11} \;\text{N} \cdot \text{m}^2 / \text{kg}^2[/latex] |
| [latex]N_A[/latex] |
Avogadro’s number |
[latex]6.02214129(27) \times 10^{23}[/latex] |
[latex]6.02 \times 10^{23}[/latex] |
| [latex]k[/latex] |
Boltzmann’s constant |
[latex]1.3806488(13) \times 10^{-23} \;\text{J} / \text{K}[/latex] |
[latex]1.38 \times 10^{-23} \;\text{J} / \text{K}[/latex] |
| [latex]R[/latex] |
Gas constant |
[latex]8.3144621(75) \;\text{J} / \text{mol} \cdot \text{K}[/latex] |
[latex]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}[/latex] |
| [latex]\sigma[/latex] |
Stefan-Boltzmann constant |
[latex]5.670373(21) \times 10^{-8} \;\text{W} / \text{m}^2 \cdot \text{K}[/latex] |
[latex]5.67 \times 10^{-8} \;\text{W} / \text{m}^2 \cdot \text{K}[/latex] |
| [latex]k[/latex] |
Coulomb force constant |
[latex]8.987551788 \dots \times 10^9 \;\text{N} \cdot \text{m}^2 / \text{C}^2[/latex] |
[latex]8.99 \times 10^9 \;\text{N} \cdot \text{m}^2 / \text{C}^2[/latex] |
| [latex]q_e[/latex] |
Charge on electron |
[latex]-1.602176565(35) \times 10^{-19} \;\text{C}[/latex] |
[latex]-1.60 \times 10^{-19} \;\text{C}[/latex] |
| [latex]\varepsilon _0[/latex] |
Permittivity of free space |
[latex]8.854187817 \dots \times 10^{-12} \;\text{C}^2 / \text{N} \cdot \text{m}^2[/latex] |
[latex]8.85 \dots \times 10^{-12} \;\text{C}^2 / \text{N} \text{m}^2[/latex] |
| [latex]\mu _0[/latex] |
Permeability of free space |
[latex]4 \pi \times 10^{-7} \;\text{T} \cdot \;\text{m}/ \text{A}[/latex] |
[latex]1.26 \times 10^{-6} \;\text{T} \cdot \text{m} / \text{A}[/latex] |
| [latex]h[/latex] |
Planck’s constant |
[latex]6.62606957(29) \times 10^{-34} \;\text{J} \cdot \text{s}[/latex] |
[latex]6.63 \times 10^{-34} \;\text{J} \cdot \text{s}[/latex] |
| Symbol |
Meaning |
Best Value |
Approximate Value |
| [latex]m_e[/latex] |
Electron mass |
[latex]9.10938291(40) \times 10^{-31} \text{kg}[/latex] |
[latex]9.11 \times 10^{-31} \text{kg}[/latex] |
| [latex]m_p[/latex] |
Proton mass |
[latex]1.672621777(74) \times 10^{-27} \text{kg}[/latex] |
[latex]1.6726 \times 10^{-27} \text{kg}[/latex] |
| [latex]m_n[/latex] |
Neutron mass |
[latex]1.674927351(74) \times 10^{-27} \text{kg}[/latex] |
[latex]1.6749 \times 10^{-27} \text{kg}[/latex] |
| [latex]\text{u}[/latex] |
Atomic mass unit |
[latex]1.660538921(73) \times 10^{-27} \text{kg}[/latex] |
[latex]1.6605 \times 10^{-27} \text{kg}[/latex] |
| Table 4. Submicroscopic Masses2 |
| Sun |
mass |
[latex]1.99 \times 10^{30} \text{kg}[/latex] |
|
average radius |
[latex]6.96 \times 10^8 \text{m}[/latex] |
|
Earth-sun distance (average) |
[latex]1.496 \times 10^{11} \text{m}[/latex] |
| Earth |
mass |
[latex]5.9736 \times 10^{24} \text{kg}[/latex] |
|
average radius |
[latex]6.376 \times 10^6 \text{m}[/latex] |
|
orbital period |
[latex]3.16 \times 10^7 \text{s}[/latex] |
| Moon |
mass |
[latex]7.35 \times 10^{22} \text{kg}[/latex] |
|
average radius |
[latex]1.74 \times 10^6 \text{m}[/latex] |
|
orbital period (average) |
[latex]2.36 \times 10^6 \text{s}[/latex] |
|
Earth-moon distance (average) |
[latex]3.84 \times 10^8 \text{m}[/latex] |
| Table 5. Solar System Data |
| Prefix |
Symbol |
Value |
Prefix |
Symbol |
Value |
| tera |
T |
[latex]10^{12}[/latex] |
deci |
d |
[latex]10^{-1}[/latex] |
| giga |
G |
[latex]10^{9}[/latex] |
centi |
c |
[latex]10^{-2}[/latex] |
| mega |
M |
[latex]10^{6}[/latex] |
milli |
m |
[latex]10^{-3}[/latex] |
| kilo |
k |
[latex]10^{3}[/latex] |
micro |
[latex]\mu[/latex] |
[latex]10^{-6}[/latex] |
| hecto |
h |
[latex]10^{2}[/latex] |
nano |
n |
[latex]10^{-9}[/latex] |
| deka |
da |
[latex]10^{1}[/latex] |
pico |
p |
[latex]10^{-12}[/latex] |
| — |
— |
[latex]10^{0} (= 1)[/latex] |
femto |
f |
[latex]10^{-15}[/latex] |
| Table 6. Metric Prefixes for Powers of Ten and Their Symbols |
| Alpha |
A |
[latex]\alpha[/latex] |
Eta |
Η |
[latex]\eta[/latex] |
Nu |
Ν |
[latex]\nu[/latex] |
Tau |
Τ |
[latex]\tau[/latex] |
| Beta |
Β |
[latex]\beta[/latex] |
Theta |
Θ |
[latex]\theta[/latex] |
Xi |
Ξ |
[latex]\xi[/latex] |
Upsilon |
Υ |
[latex]\upsilon[/latex] |
| Gamma |
Γ |
[latex]\gamma[/latex] |
Iota |
Ι |
[latex]\iota[/latex] |
Omicron |
Ο |
[latex]\o[/latex] |
Phi |
Φ |
[latex]\phi[/latex] |
| Delta |
Δ |
[latex]\delta[/latex] |
Kappa |
Κ |
[latex]\kappa[/latex] |
Pi |
Π |
[latex]\pi[/latex] |
Chi |
Χ |
[latex]\chi[/latex] |
| Epsilon |
Ε |
[latex]\epsilon[/latex] |
Lambda |
Λ |
[latex]\lambda[/latex] |
Rho |
Ρ |
[latex]\rho[/latex] |
Psi |
Ψ |
[latex]\psi[/latex] |
| Zeta |
Ζ |
[latex]\zeta[/latex] |
Mu |
Μ |
[latex]\mu[/latex] |
Sigma |
Σ |
[latex]\sigma[/latex] |
Omega |
Ω |
[latex]\omega[/latex] |
| Table 7. The Greek Alphabet |
|
Entity |
Abbreviation |
Name |
| Fundamental units |
Length |
[latex]\text{m}[/latex] |
meter |
|
Mass |
[latex]\text{kg}[/latex] |
kilogram |
|
Time |
[latex]\text{s}[/latex] |
second |
|
Current |
[latex]\text{A}[/latex] |
ampere |
| Supplementary unit |
Angle |
[latex]\text{rad}[/latex] |
radian |
| Derived units |
Force |
[latex]\text{N} = \text{kg} \cdot \text{m} / \text{s}^2[/latex] |
newton |
|
Energy |
[latex]\text{J} = \text{kg} \cdot \text{m}^2 / \text{s}^2[/latex] |
joule |
|
Power |
[latex]\text{W} = \text{J} / \text{s}[/latex] |
watt |
|
Pressure |
[latex]\text{Pa} = \text{N} / \text{m}^2[/latex] |
pascal |
|
Frequency |
[latex]\text{Hz} = 1/ \text{s}[/latex] |
hertz |
|
Electronic potential |
[latex]\text{V} = \text{J} / \text{C}[/latex] |
volt |
|
Capacitance |
[latex]\text{F} = \text{C} / \text{V}[/latex] |
farad |
|
Charge |
[latex]\text{C} = \text{s} \cdot \text{A}[/latex] |
coulomb |
|
Resistance |
[latex]\Omega = \text{V} / \text{A}[/latex] |
ohm |
|
Magnetic field |
[latex]\text{T} = \text{N} / (\text{A} \cdot \text{m})[/latex] |
tesla |
|
Nuclear decay rate |
[latex]\text{Bq} = 1 / \text{s}[/latex] |
becquerel |
| Table 8. SI Units |
| Length |
[latex]1 \;\text{inch} \; (\text{in.}) = 2.54 \;\text{cm} \; (\text{exactly})[/latex] |
|
[latex]1 \;\text{foot} \; (\text{ft}) = 0.3048 \;\text{m}[/latex] |
|
[latex]1 \;\text{mile} \; (\text{mi}) = 1.609 \;\text{km}[/latex] |
| Force |
[latex]1 \;\text{pound} \; (\text{lb}) = 4.448 \;\text{N}[/latex] |
| Energy |
[latex]1 \;\text{British thermal unit} \; (\text{Btu}) = 1.055 \times 10^3 \text{J}[/latex] |
| Power |
[latex]1 \;\text{horsepower} \; (\text{hp}) = 746 \;\text{W}[/latex] |
| Pressure |
[latex]1 \;\text{lb} / \text{in}^2 = 6.895 \times 10^3 \;\text{Pa}[/latex] |
| Table 9. Selected British Units |
| Length |
[latex]1 \;\text{light year} \; (\text{ly}) = 9.46 \times 10^{15} \; \text{m}[/latex] |
|
[latex]1 \; \text{astronomical unit} \;(\text{au}) = 1.50 \times 10^{11} \; \text{m}[/latex] |
|
[latex]1 \;\text{nautical mile} = 1.852 \;\text{km}[/latex] |
|
[latex]1 \;\text{angstrom} ( \AA ) = 10^{-10} \text{m}[/latex] |
| Area |
[latex]1 \;\text{acre} \;(\text{ac}) = 4.05 \times 10^3 \text{m}^2[/latex] |
|
[latex]1 \;\text{square foot} \; (\text{ft}^2) = 9.29 \times 10^{-2} \;\text{m}^2[/latex] |
|
[latex]1 \;\text{barn} \;(b) = 10^{-28} \;\text{m}^2[/latex] |
| Volume |
[latex]1 \;\text{liter} \;(L) = 10^{-3} \; \text{m}^3[/latex] |
|
[latex]1 \;\text{U.S. gallon} \;(\text{gal}) = 3.785 \times 10^{-3} \;\text{m}^3[/latex] |
| Mass |
[latex]1 \;\text{solar mass} = 1.99 \times 10^{30} \; \text{kg}[/latex] |
|
[latex]1 \;\text{metric ton} = 10^3 \;\text{kg}[/latex] |
|
[latex]1 \;\text{atomic mass unit} \;(u)= 1.6605 \times 10^{-27} \;\text{kg}[/latex] |
| Time |
[latex]1 \;\text{year} \;(\text{y}) = 3.16 \times 10^7 \;\text{s}[/latex] |
|
[latex]1 \;\text{day} \;(\text{d}) = 86,400 \;\text{s}[/latex] |
| Speed |
[latex]1 \;\text{mile per hour} \;(\text{mph}) = 1.609 \;\text{km} / \text{h}[/latex] |
|
[latex]1 \;\text{nautical mile per hour} \;(\text{naut}) = 1.852 \;\text{km} / \text{h}[/latex] |
| Angle |
[latex]1 \;\text{degree} \;(^{\circ}) = 1.745 \times 10^{-2} \;\text{rad}[/latex] |
|
[latex]1 \;\text{minute of arc} \; ([/latex]‘ [latex]) = 1/60 \;\text{degree}[/latex] |
|
[latex]1 \;\text{second of arc} \; (") = 1/60 \;\text{minute of arc}[/latex] |
|
[latex]1 \;\text{grad} = 1.571 \times 10^{-2} \;\text{rad}[/latex] |
| Energy |
[latex]1 \;\text{kiloton TNT} \;(\text{kT}) = 4.2 \times 10^{12} \;\text{J}[/latex] |
|
[latex]1 \; \text{kilowatt hour} \;(\text{kW} \cdot h) = 3.60 \times 10^6 \;\text{J}[/latex] |
|
[latex]1 \;\text{food calorie} \;(\text{kcal}) = 4186 \;\text{J}[/latex] |
|
[latex]1 \;\text{calorie} \;(\text{cal}) = 4.186 \;\text{J}[/latex] |
|
[latex]1 \;\text{electron volt} \;(\text{eV}) = 1.60 \times 10^{-19} \;\text{J}[/latex] |
| Pressure |
[latex]1 \;\text{atmosphere} \;(\text{atm}) = 1.013 \times 10^5 \;\text{Pa}[/latex] |
|
[latex]1 \;\text{millimeter of mercury} \;(\text{mm Hg}) = 133.3 \;\text{Pa}[/latex] |
|
[latex]1 \;\text{torricelli} \;(\text{torr}) = 1 \;\text{mm Hg} = 133.3 \;\text{Pa}[/latex] |
| Nuclear decay rate |
[latex]1 \;\text{curie} \;(\text{Ci}) = 3.70 \times 10^{10} \; \text{Bq}[/latex] |
| Table 9. Other Units |
| [latex]\text{Circumference of a circle with radius} \; \text{r} \; \text{or diameter} \;\text{d}[/latex] |
[latex]C = 2 \pi r = \pi d[/latex] |
| [latex]\text{Area of a circle with radius} \; r \;\text{or diameter} d[/latex] |
[latex]A = \pi r^2 = \pi d^{2}/4[/latex] |
| [latex]\text{Area of a sphere with radius} \; r[/latex] |
[latex]A = 4 \pi r^2[/latex] |
| [latex]\text{Volume of a sphere with radius} \; r[/latex] |
[latex]V = (4/3)( \pi r^3)[/latex] |
| Table 10. Useful Formulae |
Footnotes
- 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.
- 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.
