# C | Useful Information

### C | Useful Information

This appendix is broken into several tables.

Symbol Meaning Best Value Approximate Value
$cc size 12{c} {}$ Speed of light in vacuum $2.99792458×108m/s2.99792458×108m/s size 12{2 "." "99792458" times "10" rSup { size 8{8} }  {m} slash {s} } {}$ $3.00×108m/s3.00×108m/s size 12{3 "." "00" times "10" rSup { size 8{8} }  {m} slash {s} } {}$
$GG size 12{G} {}$ Gravitational constant $6.67408(31)×10−11N⋅m2/kg26.67408(31)×10−11N⋅m2/kg2 size 12{6 "." "67384" $$"80"$$ times "10" rSup { size 8{ - "11"} }  {N cdot m rSup { size 8{2} } } slash {"kg" rSup { size 8{2} } } } {}$ $6.67×10−11N⋅m2/kg26.67×10−11N⋅m2/kg2 size 12{6 "." "67" times "10" rSup { size 8{ - "11"} }  {N cdot m rSup { size 8{2} } } slash {"kg" rSup { size 8{2} } } } {}$
$NANA size 12{N rSub { size 8{A} } } {}$ Avogadro’s number $6.02214129(27)×10236.02214129(27)×1023 size 12{6 "." "02214129" $$"27"$$ times "10" rSup { size 8{"23"} } } {}$ $6.02×10236.02×1023 size 12{6 "." "02" times "10" rSup { size 8{"23"} } } {}$
$kk size 12{k} {}$ Boltzmann’s constant $1.3806488(13)×10−23J/K1.3806488(13)×10−23J/K size 12{1 "." "3806488" $$"13"$$ times "10" rSup { size 8{ - "23"} }  {J} slash {K} } {}$ $1.38×10−23J/K1.38×10−23J/K size 12{1 "." "38" times "10" rSup { size 8{ - "23"} }  {J} slash {K} } {}$
$RR size 12{R} {}$ Gas constant $8.3144621(75)J/mol⋅K8.3144621(75)J/mol⋅K size 12{8 "." "3144621" $$"75"$$  {J} slash {"mol" cdot K} } {}$ $8.31J/mol⋅K=1.99cal/mol⋅K=0.0821atm⋅L/mol⋅K8.31J/mol⋅K=1.99cal/mol⋅K=0.0821atm⋅L/mol⋅K size 12{8 "." "31" {J} slash {"mol" cdot K=1 "." "99" {"cal"} slash {"mol" cdot K=0 "." "0821" {"atm" cdot L} slash {"mol" cdot K} } } } {}$
$σσ size 12{σ} {}$ Stefan-Boltzmann constant $5.670373(21)×10−8W/m2⋅K5.670373(21)×10−8W/m2⋅K size 12{5 "." "670373" $$"21"$$ times "10" rSup { size 8{ - 8} }  {W} slash {m rSup { size 8{2} } cdot K} } {}$ $5.67×10−8W/m2⋅K5.67×10−8W/m2⋅K size 12{5 "." "67" times "10" rSup { size 8{ - 8} }  {W} slash {m rSup { size 8{2} } cdot K} } {}$
$kk size 12{k} {}$ Coulomb force constant $8.987551788...×109N⋅m2/C28.987551788...×109N⋅m2/C2 size 12{8 "." "987551788" "." "." "."  times "10" rSup { size 8{9} }  {N cdot m rSup { size 8{2} } } slash {C rSup { size 8{2} } } } {}$ $8.99×109N⋅m2/C28.99×109N⋅m2/C2 size 12{9 times "10" rSup { size 8{9} }  {N cdot m rSup { size 8{2} } } slash {C rSup { size 8{2} } } } {}$
$qeqe size 12{q rSub { size 8{e} } } {}$ Charge on electron $−1.602176565(35)×10−19C−1.602176565(35)×10−19C size 12{ - 1 "." "602176565" $$"35"$$ times "10" rSup { size 8{ - "19"} } C} {}$ $−1.60×10−19C−1.60×10−19C size 12{ - 1 "." "60" times "10" rSup { size 8{ - "19"} } C} {}$
$ε0ε0 size 12{ε rSub { size 8{0} } } {}$ Permittivity of free space $8.854187817...×10−12C2/N⋅m28.854187817...×10−12C2/N⋅m2 size 12{8 "." "854187817" "." "." "."  times "10" rSup { size 8{ - "12"} }  {C rSup { size 8{2} } } slash {N cdot m rSup { size 8{2} } } } {}$ $8.85×10−12C2/N⋅m28.85×10−12C2/N⋅m2 size 12{8 "." "85" times "10" rSup { size 8{ - "12"} }  {C rSup { size 8{2} } } slash {N cdot m rSup { size 8{2} } } } {}$
$μ0μ0 size 12{μ rSub { size 8{0} } } {}$ Permeability of free space $4π×10−7T⋅m/A4π×10−7T⋅m/A size 12{4π times "10" rSup { size 8{ - 7} }  {T cdot m} slash {A} } {}$ $1.26×10−6T⋅m/A1.26×10−6T⋅m/A size 12{1 "." "26" times "10" rSup { size 8{ - 6} }  {T cdot m} slash {A} } {}$
$hh size 12{h} {}$ Planck’s constant $6.62606957(29)×10−34J⋅s6.62606957(29)×10−34J⋅s size 12{6 "." "62606957" $$"29"$$ times "10" rSup { size 8{ - "34"} } J cdot s} {}$ $6.63×10−34J⋅s6.63×10−34J⋅s size 12{6 "." "63" times "10" rSup { size 8{ - "34"} } J cdot s} {}$
Table C1

### Important Constants1

Symbol Meaning Best Value Approximate Value
$meme size 12{m rSub { size 8{e} } } {}$ Electron mass $9.10938291(40)×10−31kg9.10938291(40)×10−31kg size 12{9 "." "10938291" $$"40"$$ times "10" rSup { size 8{ - "31"} } "kg"} {}$ $9.11×10−31kg9.11×10−31kg size 12{9 "." "11" times "10" rSup { size 8{ - "31"} } "kg"} {}$
$mpmp size 12{m rSub { size 8{p} } } {}$ Proton mass $1.672621777(74)×10−27kg1.672621777(74)×10−27kg size 12{1 "." "672621777" $$"74"$$ times "10" rSup { size 8{ - "27"} } "kg"} {}$ $1.6726×10−27kg1.6726×10−27kg size 12{1 "." "6726" times "10" rSup { size 8{ - "27"} } "kg"} {}$
$mnmn size 12{m rSub { size 8{n} } } {}$ Neutron mass $1.674927351(74)×10−27kg1.674927351(74)×10−27kg size 12{1 "." "674927351" $$"74"$$ times "10" rSup { size 8{ - "27"} } "kg"} {}$ $1.6749×10−27kg1.6749×10−27kg size 12{1 "." "6749" times "10" rSup { size 8{ - "27"} } "kg"} {}$
$uu size 12{u} {}$ Atomic mass unit $1.660538921(73)×10−27kg1.660538921(73)×10−27kg size 12{1 "." "660538921" $$"73"$$ times "10" rSup { size 8{ - "27"} } "kg"} {}$ $1.6605×10−27kg1.6605×10−27kg size 12{1 "." "6605" times "10" rSup { size 8{ - "27"} } "kg"} {}$
Table C2

### Submicroscopic Masses2

 Sun mass $1.99×1030kg1.99×1030kg size 12{1 "." "99" times "10" rSup { size 8{"30"} } "kg"} {}$ average radius $6.96×108m6.96×108m size 12{6 "." "96" times "10" rSup { size 8{8} } m} {}$ Earth-sun distance (average) $1.496×1011 m1.496×1011 m size 12{1 "." "496" times "10" rSup { size 8{"11"} } " m"} {}$ Earth mass $5.9736×1024kg5.9736×1024kg size 12{5 "." "9736" times "10" rSup { size 8{"24"} } "kg"} {}$ average radius $6.376×106m6.376×106m size 12{6 "." "376" times "10" rSup { size 8{6} } m} {}$${}$ orbital period $3.16×107 s 3.16×107 s size 12{3 "." "16" times "10" rSup { size 8{7} } " s "} {}$ Moon mass $7.35×1022kg7.35×1022kg size 12{7 "." "35" times "10" rSup { size 8{"22"} } "kg"} {}$ average radius $1.74×106m1.74×106m size 12{1 "." "74" times "10" rSup { size 8{6} } m} {}$ orbital period (average) $2.36×106 s2.36×106 s size 12{2 "." "36" times "10" rSup { size 8{6} } " s"} {}$ Earth-moon distance (average) $3.84×108 m3.84×108 m size 12{3 "." "84" times "10" rSup { size 8{8} } " m"} {}$
Table C3

### Solar System Data

Prefix Symbol Value Prefix Symbol Value
tera T $10121012 size 12{"10" rSup { size 8{"12"} } } {}$ deci d $10−110−1 size 12{"10" rSup { size 8{ - 1} } } {}$
giga G $109109 size 12{"10" rSup { size 8{9} } } {}$ centi c $10−210−2 size 12{"10" rSup { size 8{ - 2} } } {}$
mega M $106106 size 12{"10" rSup { size 8{6} } } {}$ milli m $10−310−3 size 12{"10" rSup { size 8{ - 3} } } {}$
kilo k $103103 size 12{"10" rSup { size 8{3} } } {}$ micro $μμ size 12{μ} {}$ $10−610−6 size 12{"10" rSup { size 8{ - 6} } } {}$
hecto h $102102 size 12{"10" rSup { size 8{2} } } {}$ nano n $10−910−9 size 12{"10" rSup { size 8{ - 9} } } {}$
deka da $101101 size 12{"10" rSup { size 8{1} } } {}$ pico p $10−1210−12 size 12{"10" rSup { size 8{ - "12"} } } {}$
$100(=1)100(=1) size 12{"10" rSup { size 8{0} } $$=1$$ } {}$ femto f $10−1510−15 size 12{"10" rSup { size 8{ - "15"} } } {}$
Table C4

### Metric Prefixes for Powers of Ten and Their Symbols

 Alpha $ΑΑ size 12{Α} {}$ $αα size 12{α} {}$ Eta $ΗΗ size 12{Η} {}$ $ηη size 12{η} {}$ Nu $ΝΝ size 12{Ν} {}$ $νν size 12{ν} {}$ Tau $ΤΤ size 12{Τ} {}$ $ττ size 12{τ} {}$ Beta $ΒΒ size 12{Β} {}$ $ββ size 12{β} {}$ Theta $ΘΘ size 12{Θ} {}$ $θθ size 12{θ} {}$ Xi $ΞΞ size 12{Ξ} {}$ $ξξ size 12{ξ} {}$ Upsilon $ΥΥ size 12{Υ} {}$ $υυ size 12{υ} {}$ Gamma $ΓΓ size 12{Γ} {}$ $γγ size 12{γ} {}$ Iota $ΙΙ size 12{Ι} {}$ $ιι size 12{ι} {}$ Omicron $ΟΟ size 12{Ο} {}$ $οο size 12{ο} {}$ Phi $ΦΦ size 12{Φ} {}$ $ϕϕ size 12{ϕ} {}$ Delta $ΔΔ size 12{Δ} {}$ $δδ size 12{δ} {}$ Kappa $ΚΚ size 12{Κ} {}$ $κκ size 12{κ} {}$ Pi $ΠΠ size 12{Π} {}$ $ππ size 12{π} {}$ Chi $ΧΧ size 12{Χ} {}$ $χχ size 12{χ} {}$ Epsilon $ΕΕ size 12{Ε} {}$ $εε size 12{ε} {}$ Lambda $ΛΛ size 12{Λ} {}$ $λλ size 12{λ} {}$ Rho $ΡΡ size 12{Ρ} {}$ $ρρ size 12{ρ} {}$ Psi $ΨΨ size 12{Ψ} {}$ $ψψ size 12{ψ} {}$ Zeta $ΖΖ size 12{Ζ} {}$ $ζζ size 12{ζ} {}$ Mu $ΜΜ size 12{Μ} {}$ $μμ size 12{μ} {}$ Sigma $ΣΣ size 12{Σ} {}$ $σσ size 12{σ} {}$ Omega $ΩΩ size 12{ %OMEGA } {}$ $ωω size 12{ω} {}$
Table C5

### The Greek Alphabet

Entity Abbreviation Name
Fundamental units Length m meter
Mass kg kilogram
Time s second
Current A ampere
Derived units Force $N=kg⋅m/s2N=kg⋅m/s2 size 12{N="kg" cdot {m} slash {s rSup { size 8{2} } } } {}$ newton
Energy $J=kg⋅m2/s2J=kg⋅m2/s2 size 12{J="kg" cdot {m rSup { size 8{2} } } slash {s rSup { size 8{2} } } } {}$ joule
Power $W=J/sW=J/s size 12{W= {J} slash {s} } {}$ watt
Pressure $Pa=N/m2Pa=N/m2 size 12{"Pa"= {N} slash {m rSup { size 8{2} } } } {}$ pascal
Frequency $Hz=1/sHz=1/s size 12{"Hz"= {1} slash {s} } {}$ hertz
Electronic potential $V=J/CV=J/C size 12{V= {J} slash {C} } {}$ volt
Capacitance $F=C/VF=C/V size 12{F= {C} slash {V} } {}$ farad
Charge $C=s⋅AC=s⋅A size 12{C=s cdot A} {}$ coulomb
Resistance $Ω=V/AΩ=V/A size 12{ %OMEGA = {V} slash {A} } {}$ ohm
Magnetic field $T=N/A⋅mT=N/A⋅m size 12{T= {N} slash { left (A cdot m right )} } {}$ tesla
Nuclear decay rate $Bq=1/sBq=1/s size 12{"Bq"= {1} slash {s} } {}$ becquerel
Table C6

### SI Units

 Length $1inch (in.)=2.54 cm (exactly)1inch (in.)=2.54 cm (exactly) size 12{1" inch " $$"in" "."$$ =2 "." "54"" cm " $$"exactly"$$ } {}$ $1 foot (ft)=0.3048 m1 foot (ft)=0.3048 m size 12{1" foot " $$"ft"$$ =0 "." "3048"" m"} {}$ $1 mile (mi)=1.609km1 mile (mi)=1.609km size 12{1" mile " $$"mi"$$ =1 "." "609"" km"} {}$ Force $1 pound (lb)=4.448 N1 pound (lb)=4.448 N size 12{1" pound " $$"lb"$$ =4 "." "448"" N"} {}$ Energy $1 British thermal unit (Btu)=1.055×103 J1 British thermal unit (Btu)=1.055×103 J size 12{1" British thermal unit " $$"Btu"$$ =1 "." "055" times "10" rSup { size 8{3} } " J"} {}$ Power $1 horsepower (hp)=746 W1 horsepower (hp)=746 W size 12{1" horsepower " $$"hp"$$ ="746"" W"} {}$ Pressure $1lb/in2=6.895×103 Pa1lb/in2=6.895×103 Pa size 12{1 {"lb"} slash {"in" rSup { size 8{2} } } =6 "." "895" times "10" rSup { size 8{3} } " Pa"} {}$
Table C7

### Selected British Units

 Length $1 light year(ly)=9.46×1015 m1 light year(ly)=9.46×1015 m size 12{1" light"" year" $$"ly"$$  =9 "." "46" times "10" rSup { size 8{"15"} } " m"} {}$ $1 astronomical unit(au)=1.50×1011 m1 astronomical unit(au)=1.50×1011 m size 12{1" astronomical"" unit" $$"au"$$  =1 "." "50" times "10" rSup { size 8{"11"} } " m"} {}$ $1 nautical mile=1.852 km1 nautical mile=1.852 km size 12{1" nautical"" mile" =1 "." "852"" km"} {}$ $1 angstrom(Å)=10−10 m1 angstrom(Å)=10−10 m size 12{1" angstrom" $$Å$$  ="10" rSup { size 8{ - "10"} } " m"} {}$ Area $1 acre(ac)=4.05×103 m21 acre(ac)=4.05×103 m2 size 12{1" acre" $$"ac"$$  =4 "." "05" times "10" rSup { size 8{3} } " m" rSup { size 8{2} } } {}$ $1square foot(ft2)=9.29×10−2 m21square foot(ft2)=9.29×10−2 m2 size 12{1"square""foot" $$"ft" rSup { size 8{2} }$$  =9 "." "29" times "10" rSup { size 8{ - 2} } " m" rSup { size 8{2} } } {}$ $1 barn(b)=10−28 m21 barn(b)=10−28 m2 size 12{1" barn" $$b$$  ="10" rSup { size 8{ - "28"} } " m" rSup { size 8{2} } } {}$ Volume $1 liter(L)=10−3 m31 liter(L)=10−3 m3 size 12{1" liter" $$L$$  ="10" rSup { size 8{ - 3} } " m" rSup { size 8{3} } } {}$ $1 U.S. gallon(gal)=3.785×10−3 m31 U.S. gallon(gal)=3.785×10−3 m3 size 12{1" U" "." S "." " gallon" $$"gal"$$  =3 "." "785" times "10" rSup { size 8{ - 3} } " m" rSup { size 8{3} } } {}$ Mass $1 solar mass=1.99×1030 kg1 solar mass=1.99×1030 kg size 12{1" solar"" mass" =1 "." "99" times "10" rSup { size 8{"30"} } " kg"} {}$ $1 metric ton=103 kg1 metric ton=103 kg size 12{1" metric"" ton" ="10" rSup { size 8{3} } " kg"} {}$ $1 atomic mass unit(u)=1.6605×10−27 kg1 atomic mass unit(u)=1.6605×10−27 kg size 12{1" atomic"" mass"" unit" $$u$$  =1 "." "6605" times "10" rSup { size 8{ - "27"} } " kg"} {}$ Time $1 year(y)=3.16×107 s1 year(y)=3.16×107 s size 12{1" year" $$y$$  =3 "." "16" times "10" rSup { size 8{7} } " s"} {}$ $1 day(d)=86,400 s1 day(d)=86,400 s size 12{1" day" $$d$$  ="86","400"" s"} {}$ Speed $1 mile per hour(mph)=1.609km/h1 mile per hour(mph)=1.609km/h size 12{1" mile""per""hour" $$"mph"$$ =1 "." "609" {"km"} slash {h} } {}$ $1 nautical mile per hour(naut)=1.852km/h1 nautical mile per hour(naut)=1.852km/h size 12{1" nautical""mile""per""hour" $$"naut"$$ =1 "." "852" {"km"} slash {h} } {}$ Angle $1 degree(°)=1.745×10−2 rad1 degree(°)=1.745×10−2 rad size 12{1" degree" $$°$$  =1 "." "745" times "10" rSup { size 8{ - 2} } " rad"} {}$ $1 minute of arc(')=1/60 degree1 minute of arc(')=1/60 degree size 12{1" minute""of""arc" { { $$}} sup { ' }$$ = {1} slash {"60"} " degree"} {}$ $1 second of arc('')=1/60 minute of arc1 second of arc('')=1/60 minute of arc size 12{1" second""of""arc" { { $$}} sup { '' }$$ = {1} slash {"60"} " minute of arc"} {}$ $1 grad=1.571×10−2 rad1 grad=1.571×10−2 rad size 12{1" grad" =1 "." "571" times "10" rSup { size 8{ - 2} } " rad"} {}$ Energy $1 kiloton TNT(kT)=4.2×1012 J1 kiloton TNT(kT)=4.2×1012 J size 12{1" kiloton"" TNT" $$"kT"$$  =4 "." 2 times "10" rSup { size 8{"12"} } " J"} {}$ $1 kilowatt hour(kW⋅h)=3.60×106 J1 kilowatt hour(kW⋅h)=3.60×106 J size 12{1" kilowatt"" hour" $$"kW" cdot h$$  =3 "." "60" times "10" rSup { size 8{6} } " J"} {}$ $1 food calorie(kcal)=4186 J1 food calorie(kcal)=4186 J size 12{1" food""calorie" $$"kcal"$$ ="4186"" J"} {}$ $1 calorie(cal)=4.186 J1 calorie(cal)=4.186 J size 12{1" calorie" $$"cal"$$ =4 "." "186"" J"} {}$ $1 electron volt(eV)=1.60×10−19 J1 electron volt(eV)=1.60×10−19 J size 12{1" electron"" volt" $$"eV"$$  =1 "." "60" times "10" rSup { size 8{ - "19"} } " J"} {}$ Pressure $1 atmosphere(atm)=1.013×105 Pa1 atmosphere(atm)=1.013×105 Pa size 12{1" atmosphere" $$"atm"$$  =1 "." "013" times "10" rSup { size 8{5} } " Pa"} {}$ $1 millimeter of mercury(mmHg)=133.3 Pa1 millimeter of mercury(mmHg)=133.3 Pa size 12{1" millimeter""of""mercury" $$"mm""Hg"$$ ="133" "." 3" Pa"} {}$ $1 torricelli(torr)=1mmHg =133.3 Pa1 torricelli(torr)=1mmHg =133.3 Pa size 12{1" torricelli" $$"torr"$$ =1" mm""Hg "="133" "." 3" Pa"} {}$ Nuclear decay rate $1 curie(Ci)=3.70×1010 Bq1 curie(Ci)=3.70×1010 Bq size 12{1" curie" $$"Ci"$$  =3 "." "70" times "10" rSup { size 8{"10"} } " Bq"} {}$
Table C8

### Other Units

 Circumference of a circle with radius $rr size 12{r} {}$ or diameter $dd size 12{d} {}$ $C=2πr=πdC=2πr=πd size 12{C=2πr=πd} {}$ Area of a circle with radius $rr size 12{r} {}$ or diameter $dd size 12{d} {}$ $A=πr2=πd2/4A=πr2=πd2/4 size 12{A=πr rSup { size 8{2} } = {πd rSup { size 8{2} } } slash {4} } {}$ Area of a sphere with radius $rr size 12{r} {}$ $A=4πr2A=4πr2 size 12{A=4πr rSup { size 8{2} } } {}$ Volume of a sphere with radius $rr size 12{r} {}$ $V=4/3πr3V=4/3πr3 size 12{V= left ( {4} slash {3} right ) left (πr rSup { size 8{3} } right )} {}$
Table C9

### 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.