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
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 \o 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 \text{m} meter
Mass \text{kg} kilogram
Time \text{s} second
Current \text{A} ampere
Supplementary unit Angle \text{rad} radian
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 1 \;\text{horsepower} \; (\text{hp}) = 746 \;\text{W}
Pressure 1 \;\text{lb} / \text{in}^2 = 6.895 \times 10^3 \;\text{Pa}
Table 9. Selected British Units
Length 1 \;\text{light year} \; (\text{ly}) = 9.46 \times 10^{15} \; \text{m}
1 \; \text{astronomical unit} \;(\text{au}) = 1.50 \times 10^{11} \; \text{m}
1 \;\text{nautical mile} = 1.852 \;\text{km}
1 \;\text{angstrom} ( \AA ) = 10^{-10} \text{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 \;\text{U.S. gallon} \;(\text{gal}) = 3.785 \times 10^{-3} \;\text{m}^3
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 9. 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 10. Useful Formulae

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.

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