Appendix A Useful Information – Constants, Units, Formulae

Department of Physics and Astronomy at Douglas College; OpenStax

Appendix A Useful Information – Constants, Units, Formulae

This appendix is broken into several tables.

Table 3, Important Constants
Table 4, Submicroscopic Masses
Table 5, Solar System Data
Table 6, Metric Prefixes for Powers of Ten and Their Symbols
Table 7, The Greek Alphabet
Table 8, SI units
Table 9, Selected British Units
Table 10, Other Units
Table 11, Useful Formulae

Table 3. Important Constants^¹

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 Masses^²

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 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 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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