College Physics

# C | Useful Information

College PhysicsC | Useful Information

This appendix is broken into several tables.

Symbol Meaning Best Value Approximate Value
$c c size 12{c} {}$ Speed of light in vacuum $2 . 99792458 × 10 8 m / s 2 . 99792458 × 10 8 m / s size 12{2 "." "99792458" times "10" rSup { size 8{8} }  {m} slash {s} } {}$ $3 . 00 × 10 8 m / s 3 . 00 × 10 8 m / s size 12{3 "." "00" times "10" rSup { size 8{8} }  {m} slash {s} } {}$
$G G size 12{G} {}$ Gravitational constant $6 . 67408 ( 31 ) × 10 − 11 N ⋅ m 2 / kg 2 6 . 67408 ( 31 ) × 10 − 11 N ⋅ m 2 / kg 2 size 12{6 "." "67384" $$"80"$$ times "10" rSup { size 8{ - "11"} }  {N cdot m rSup { size 8{2} } } slash {"kg" rSup { size 8{2} } } } {}$ $6 . 67 × 10 − 11 N ⋅ m 2 / kg 2 6 . 67 × 10 − 11 N ⋅ m 2 / kg 2 size 12{6 "." "67" times "10" rSup { size 8{ - "11"} }  {N cdot m rSup { size 8{2} } } slash {"kg" rSup { size 8{2} } } } {}$
$N A N A size 12{N rSub { size 8{A} } } {}$ Avogadro’s number $6.02214076 × 10 23 6.02214076 × 10 23 size 12{6 "." "02214129" $$"27"$$ times "10" rSup { size 8{"23"} } } {}$ $6 . 02 × 10 23 6 . 02 × 10 23 size 12{6 "." "02" times "10" rSup { size 8{"23"} } } {}$
$k k size 12{k} {}$ Boltzmann’s constant $1.380649 × 10 − 23 J / K 1.380649 × 10 − 23 J / K size 12{1 "." "3806488" $$"13"$$ times "10" rSup { size 8{ - "23"} }  {J} slash {K} } {}$ $1 . 38 × 10 − 23 J / K 1 . 38 × 10 − 23 J / K size 12{1 "." "38" times "10" rSup { size 8{ - "23"} }  {J} slash {K} } {}$
$R R size 12{R} {}$ Gas constant $8 . 3144621 ( 75 ) J / mol ⋅ K 8 . 3144621 ( 75 ) J / mol ⋅ K size 12{8 "." "3144621" $$"75"$$  {J} slash {"mol" cdot K} } {}$ $8 . 31 J / mol ⋅ K = 1 . 99 cal / mol ⋅ K = 0 . 0821 atm ⋅ L / mol ⋅ K 8 . 31 J / mol ⋅ K = 1 . 99 cal / mol ⋅ K = 0 . 0821 atm ⋅ L / mol ⋅ K size 12{8 "." "31" {J} slash {"mol" cdot K=1 "." "99" {"cal"} slash {"mol" cdot K=0 "." "0821" {"atm" cdot L} slash {"mol" cdot K} } } } {}$
$σ σ size 12{σ} {}$ Stefan-Boltzmann constant $5 . 670373 ( 21 ) × 10 − 8 W / m 2 ⋅ K 5 . 670373 ( 21 ) × 10 − 8 W / m 2 ⋅ K size 12{5 "." "670373" $$"21"$$ times "10" rSup { size 8{ - 8} }  {W} slash {m rSup { size 8{2} } cdot K} } {}$ $5 . 67 × 10 − 8 W / m 2 ⋅ K 5 . 67 × 10 − 8 W / m 2 ⋅ K size 12{5 "." "67" times "10" rSup { size 8{ - 8} }  {W} slash {m rSup { size 8{2} } cdot K} } {}$
$k k size 12{k} {}$ Coulomb force constant $8 . 987551788 . . . × 10 9 N ⋅ m 2 / C 2 8 . 987551788 . . . × 10 9 N ⋅ m 2 / C 2 size 12{8 "." "987551788" "." "." "."  times "10" rSup { size 8{9} }  {N cdot m rSup { size 8{2} } } slash {C rSup { size 8{2} } } } {}$ $8.99 × 10 9 N ⋅ m 2 / C 2 8.99 × 10 9 N ⋅ m 2 / C 2 size 12{9 times "10" rSup { size 8{9} }  {N cdot m rSup { size 8{2} } } slash {C rSup { size 8{2} } } } {}$
$q e q e size 12{q rSub { size 8{e} } } {}$ Charge on electron $− 1.602176634 × 10 − 19 C − 1.602176634 × 10 − 19 C size 12{ - 1 "." "602176565" $$"35"$$ times "10" rSup { size 8{ - "19"} } C} {}$ $− 1 . 60 × 10 − 19 C − 1 . 60 × 10 − 19 C size 12{ - 1 "." "60" times "10" rSup { size 8{ - "19"} } C} {}$
$ε 0 ε 0 size 12{ε rSub { size 8{0} } } {}$ Permittivity of free space $8 . 854187817 . . . × 10 − 12 C 2 / N ⋅ m 2 8 . 854187817 . . . × 10 − 12 C 2 / N ⋅ m 2 size 12{8 "." "854187817" "." "." "."  times "10" rSup { size 8{ - "12"} }  {C rSup { size 8{2} } } slash {N cdot m rSup { size 8{2} } } } {}$ $8 . 85 × 10 − 12 C 2 / N ⋅ m 2 8 . 85 × 10 − 12 C 2 / N ⋅ m 2 size 12{8 "." "85" times "10" rSup { size 8{ - "12"} }  {C rSup { size 8{2} } } slash {N cdot m rSup { size 8{2} } } } {}$
$μ 0 μ 0 size 12{μ rSub { size 8{0} } } {}$ Permeability of free space $4π × 10 − 7 T ⋅ m / A 4π × 10 − 7 T ⋅ m / A size 12{4π times "10" rSup { size 8{ - 7} }  {T cdot m} slash {A} } {}$ $1 . 26 × 10 − 6 T ⋅ m / A 1 . 26 × 10 − 6 T ⋅ m / A size 12{1 "." "26" times "10" rSup { size 8{ - 6} }  {T cdot m} slash {A} } {}$
$h h size 12{h} {}$ Planck’s constant $6.62607015 × 10 − 34 J ⋅ s 6.62607015 × 10 − 34 J ⋅ s size 12{6 "." "62606957" $$"29"$$ times "10" rSup { size 8{ - "34"} } J cdot s} {}$ $6 . 63 × 10 − 34 J ⋅ s 6 . 63 × 10 − 34 J ⋅ s size 12{6 "." "63" times "10" rSup { size 8{ - "34"} } J cdot s} {}$
Table C1 Important Constants1
Symbol Meaning Best Value Approximate Value
$m e m e size 12{m rSub { size 8{e} } } {}$ Electron mass $9 . 10938291 ( 40 ) × 10 − 31 kg 9 . 10938291 ( 40 ) × 10 − 31 kg size 12{9 "." "10938291" $$"40"$$ times "10" rSup { size 8{ - "31"} } "kg"} {}$ $9 . 11 × 10 − 31 kg 9 . 11 × 10 − 31 kg size 12{9 "." "11" times "10" rSup { size 8{ - "31"} } "kg"} {}$
$m p m p size 12{m rSub { size 8{p} } } {}$ Proton mass $1 . 672621777 ( 74 ) × 10 − 27 kg 1 . 672621777 ( 74 ) × 10 − 27 kg size 12{1 "." "672621777" $$"74"$$ times "10" rSup { size 8{ - "27"} } "kg"} {}$ $1 . 6726 × 10 − 27 kg 1 . 6726 × 10 − 27 kg size 12{1 "." "6726" times "10" rSup { size 8{ - "27"} } "kg"} {}$
$m n m n size 12{m rSub { size 8{n} } } {}$ Neutron mass $1 . 674927351 ( 74 ) × 10 − 27 kg 1 . 674927351 ( 74 ) × 10 − 27 kg size 12{1 "." "674927351" $$"74"$$ times "10" rSup { size 8{ - "27"} } "kg"} {}$ $1 . 6749 × 10 − 27 kg 1 . 6749 × 10 − 27 kg size 12{1 "." "6749" times "10" rSup { size 8{ - "27"} } "kg"} {}$
$u u size 12{u} {}$ Atomic mass unit $1 . 660538921 ( 73 ) × 10 − 27 kg 1 . 660538921 ( 73 ) × 10 − 27 kg size 12{1 "." "660538921" $$"73"$$ times "10" rSup { size 8{ - "27"} } "kg"} {}$ $1 . 6605 × 10 − 27 kg 1 . 6605 × 10 − 27 kg size 12{1 "." "6605" times "10" rSup { size 8{ - "27"} } "kg"} {}$
Table C2 Submicroscopic Masses2
 Sun mass $1 . 99 × 10 30 kg 1 . 99 × 10 30 kg size 12{1 "." "99" times "10" rSup { size 8{"30"} } "kg"} {}$ average radius $6 . 96 × 10 8 m 6 . 96 × 10 8 m size 12{6 "." "96" times "10" rSup { size 8{8} } m} {}$ Earth-sun distance (average) $1 . 496 × 10 11 m 1 . 496 × 10 11 m size 12{1 "." "496" times "10" rSup { size 8{"11"} } " m"} {}$ Earth mass $5 . 9736 × 10 24 kg 5 . 9736 × 10 24 kg size 12{5 "." "9736" times "10" rSup { size 8{"24"} } "kg"} {}$ average radius $6 . 376 × 10 6 m 6 . 376 × 10 6 m size 12{6 "." "376" times "10" rSup { size 8{6} } m} {}$ ${}$ orbital period $3 . 16 × 10 7 s 3 . 16 × 10 7 s size 12{3 "." "16" times "10" rSup { size 8{7} } " s "} {}$ Moon mass $7 . 35 × 10 22 kg 7 . 35 × 10 22 kg size 12{7 "." "35" times "10" rSup { size 8{"22"} } "kg"} {}$ average radius $1 . 74 × 10 6 m 1 . 74 × 10 6 m size 12{1 "." "74" times "10" rSup { size 8{6} } m} {}$ orbital period (average) $2 . 36 × 10 6 s 2 . 36 × 10 6 s size 12{2 "." "36" times "10" rSup { size 8{6} } " s"} {}$ Earth-moon distance (average) $3 . 84 × 10 8 m 3 . 84 × 10 8 m size 12{3 "." "84" times "10" rSup { size 8{8} } " m"} {}$
Table C3 Solar System Data
Prefix Symbol Value Prefix Symbol Value
tera T $10 12 10 12 size 12{"10" rSup { size 8{"12"} } } {}$ deci d $10 − 1 10 − 1 size 12{"10" rSup { size 8{ - 1} } } {}$
giga G $10 9 10 9 size 12{"10" rSup { size 8{9} } } {}$ centi c $10 − 2 10 − 2 size 12{"10" rSup { size 8{ - 2} } } {}$
mega M $10 6 10 6 size 12{"10" rSup { size 8{6} } } {}$ milli m $10 − 3 10 − 3 size 12{"10" rSup { size 8{ - 3} } } {}$
kilo k $10 3 10 3 size 12{"10" rSup { size 8{3} } } {}$ micro $μ μ size 12{μ} {}$ $10 − 6 10 − 6 size 12{"10" rSup { size 8{ - 6} } } {}$
hecto h $10 2 10 2 size 12{"10" rSup { size 8{2} } } {}$ nano n $10 − 9 10 − 9 size 12{"10" rSup { size 8{ - 9} } } {}$
deka da $10 1 10 1 size 12{"10" rSup { size 8{1} } } {}$ pico p $10 − 12 10 − 12 size 12{"10" rSup { size 8{ - "12"} } } {}$
$10 0 ( = 1 ) 10 0 ( = 1 ) size 12{"10" rSup { size 8{0} } $$=1$$ } {}$ femto f $10 − 15 10 − 15 size 12{"10" rSup { size 8{ - "15"} } } {}$
Table C4 Metric Prefixes for Powers of Ten and Their Symbols
 Alpha $Α Α size 12{Α} {}$ $α α size 12{α} {}$ Eta $Η Η size 12{Η} {}$ $η η size 12{η} {}$ Nu $Ν Ν size 12{Ν} {}$ $ν ν size 12{ν} {}$ Tau $Τ Τ size 12{Τ} {}$ $τ τ size 12{τ} {}$ Beta $Β Β size 12{Β} {}$ $β β size 12{β} {}$ Theta $Θ Θ size 12{Θ} {}$ $θ θ size 12{θ} {}$ Xi $Ξ Ξ size 12{Ξ} {}$ $ξ ξ size 12{ξ} {}$ Upsilon $Υ Υ size 12{Υ} {}$ $υ υ size 12{υ} {}$ Gamma $Γ Γ size 12{Γ} {}$ $γ γ size 12{γ} {}$ Iota $Ι Ι size 12{Ι} {}$ $ι ι size 12{ι} {}$ Omicron $Ο Ο size 12{Ο} {}$ $ο ο size 12{ο} {}$ Phi $Φ Φ size 12{Φ} {}$ $ϕ ϕ size 12{ϕ} {}$ Delta $Δ Δ size 12{Δ} {}$ $δ δ size 12{δ} {}$ Kappa $Κ Κ size 12{Κ} {}$ $κ κ size 12{κ} {}$ Pi $Π Π size 12{Π} {}$ $π π size 12{π} {}$ Chi $Χ Χ size 12{Χ} {}$ $χ χ size 12{χ} {}$ Epsilon $Ε Ε size 12{Ε} {}$ $ε ε size 12{ε} {}$ Lambda $Λ Λ size 12{Λ} {}$ $λ λ size 12{λ} {}$ Rho $Ρ Ρ size 12{Ρ} {}$ $ρ ρ size 12{ρ} {}$ Psi $Ψ Ψ size 12{Ψ} {}$ $ψ ψ size 12{ψ} {}$ Zeta $Ζ Ζ size 12{Ζ} {}$ $ζ ζ size 12{ζ} {}$ Mu $Μ Μ size 12{Μ} {}$ $μ μ size 12{μ} {}$ Sigma $Σ Σ size 12{Σ} {}$ $σ σ size 12{σ} {}$ Omega $Ω Ω size 12{ %OMEGA } {}$ $ω ω size 12{ω} {}$
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 $N = kg ⋅ m / s 2 N = kg ⋅ m / s 2 size 12{N="kg" cdot {m} slash {s rSup { size 8{2} } } } {}$ newton
Energy $J = kg ⋅ m 2 / s 2 J = kg ⋅ m 2 / s 2 size 12{J="kg" cdot {m rSup { size 8{2} } } slash {s rSup { size 8{2} } } } {}$ joule
Power $W = J / s W = J / s size 12{W= {J} slash {s} } {}$ watt
Pressure $Pa = N / m 2 Pa = N / m 2 size 12{"Pa"= {N} slash {m rSup { size 8{2} } } } {}$ pascal
Frequency $Hz = 1 / s Hz = 1 / s size 12{"Hz"= {1} slash {s} } {}$ hertz
Electronic potential $V = J / C V = J / C size 12{V= {J} slash {C} } {}$ volt
Capacitance $F = C / V F = C / V size 12{F= {C} slash {V} } {}$ farad
Charge $C = s ⋅ A C = s ⋅ A size 12{C=s cdot A} {}$ coulomb
Resistance $Ω = V / A Ω = V / A size 12{ %OMEGA = {V} slash {A} } {}$ ohm
Magnetic field $T = N / A ⋅ m T = N / A ⋅ m size 12{T= {N} slash { left (A cdot m right )} } {}$ tesla
Nuclear decay rate $Bq = 1 / s Bq = 1 / s size 12{"Bq"= {1} slash {s} } {}$ becquerel
Table C6 SI Units
 Length $1 inch ( in . ) = 2 . 54 cm ( exactly ) 1 inch ( in . ) = 2 . 54 cm ( exactly ) size 12{1" inch " $$"in" "."$$ =2 "." "54"" cm " $$"exactly"$$ } {}$ $1 foot ( ft ) = 0 . 3048 m 1 foot ( ft ) = 0 . 3048 m size 12{1" foot " $$"ft"$$ =0 "." "3048"" m"} {}$ $1 mile ( mi ) = 1 . 609 km 1 mile ( mi ) = 1 . 609 km size 12{1" mile " $$"mi"$$ =1 "." "609"" km"} {}$ Force $1 pound ( lb ) = 4 . 448 N 1 pound ( lb ) = 4 . 448 N size 12{1" pound " $$"lb"$$ =4 "." "448"" N"} {}$ Energy $1 British thermal unit ( Btu ) = 1 . 055 × 10 3 J 1 British thermal unit ( Btu ) = 1 . 055 × 10 3 J size 12{1" British thermal unit " $$"Btu"$$ =1 "." "055" times "10" rSup { size 8{3} } " J"} {}$ Power $1 horsepower ( hp ) = 746 W 1 horsepower ( hp ) = 746 W size 12{1" horsepower " $$"hp"$$ ="746"" W"} {}$ Pressure $1 lb / in 2 = 6 . 895 × 10 3 Pa 1 lb / in 2 = 6 . 895 × 10 3 Pa size 12{1 {"lb"} slash {"in" rSup { size 8{2} } } =6 "." "895" times "10" rSup { size 8{3} } " Pa"} {}$
Table C7 Selected British Units
 Length $1 light year ( ly ) = 9 . 46 × 10 15 m 1 light year ( ly ) = 9 . 46 × 10 15 m size 12{1" light"" year" $$"ly"$$  =9 "." "46" times "10" rSup { size 8{"15"} } " m"} {}$ $1 astronomical unit ( au ) = 1 . 50 × 10 11 m 1 astronomical unit ( au ) = 1 . 50 × 10 11 m size 12{1" astronomical"" unit" $$"au"$$  =1 "." "50" times "10" rSup { size 8{"11"} } " m"} {}$ $1 nautical mile = 1 . 852 km 1 nautical mile = 1 . 852 km size 12{1" nautical"" mile" =1 "." "852"" km"} {}$ $1 angstrom ( Å ) = 10 − 10 m 1 angstrom ( Å ) = 10 − 10 m size 12{1" angstrom" $$Å$$  ="10" rSup { size 8{ - "10"} } " m"} {}$ Area $1 acre ( ac ) = 4 . 05 × 10 3 m 2 1 acre ( ac ) = 4 . 05 × 10 3 m 2 size 12{1" acre" $$"ac"$$  =4 "." "05" times "10" rSup { size 8{3} } " m" rSup { size 8{2} } } {}$ $1 square foot ( ft 2 ) = 9 . 29 × 10 − 2 m 2 1 square foot ( ft 2 ) = 9 . 29 × 10 − 2 m 2 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 m 2 1 barn ( b ) = 10 − 28 m 2 size 12{1" barn" $$b$$  ="10" rSup { size 8{ - "28"} } " m" rSup { size 8{2} } } {}$ Volume $1 liter ( L ) = 10 − 3 m 3 1 liter ( L ) = 10 − 3 m 3 size 12{1" liter" $$L$$  ="10" rSup { size 8{ - 3} } " m" rSup { size 8{3} } } {}$ $1 U.S. gallon ( gal ) = 3 . 785 × 10 − 3 m 3 1 U.S. gallon ( gal ) = 3 . 785 × 10 − 3 m 3 size 12{1" U" "." S "." " gallon" $$"gal"$$  =3 "." "785" times "10" rSup { size 8{ - 3} } " m" rSup { size 8{3} } } {}$ Mass $1 solar mass = 1 . 99 × 10 30 kg 1 solar mass = 1 . 99 × 10 30 kg size 12{1" solar"" mass" =1 "." "99" times "10" rSup { size 8{"30"} } " kg"} {}$ $1 metric ton = 10 3 kg 1 metric ton = 10 3 kg size 12{1" metric"" ton" ="10" rSup { size 8{3} } " kg"} {}$ $1 atomic mass unit ( u ) = 1 . 6605 × 10 − 27 kg 1 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 × 10 7 s 1 year ( y ) = 3 . 16 × 10 7 s size 12{1" year" $$y$$  =3 "." "16" times "10" rSup { size 8{7} } " s"} {}$ $1 day ( d ) = 86 , 400 s 1 day ( d ) = 86 , 400 s size 12{1" day" $$d$$  ="86","400"" s"} {}$ Speed $1 mile per hour ( mph ) = 1 . 609 km / h 1 mile per hour ( mph ) = 1 . 609 km / h size 12{1" mile""per""hour" $$"mph"$$ =1 "." "609" {"km"} slash {h} } {}$ $1 nautical mile per hour ( naut ) = 1 . 852 km / h 1 nautical mile per hour ( naut ) = 1 . 852 km / h size 12{1" nautical""mile""per""hour" $$"naut"$$ =1 "." "852" {"km"} slash {h} } {}$ Angle $1 degree ( ° ) = 1 . 745 × 10 − 2 rad 1 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 degree 1 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 arc 1 second of arc ( '' ) = 1 / 60 minute of arc size 12{1" second""of""arc" { { $$}} sup { '' }$$ = {1} slash {"60"} " minute of arc"} {}$ $1 grad = 1 . 571 × 10 − 2 rad 1 grad = 1 . 571 × 10 − 2 rad size 12{1" grad" =1 "." "571" times "10" rSup { size 8{ - 2} } " rad"} {}$ Energy $1 kiloton TNT ( kT ) = 4 . 2 × 10 12 J 1 kiloton TNT ( kT ) = 4 . 2 × 10 12 J size 12{1" kiloton"" TNT" $$"kT"$$  =4 "." 2 times "10" rSup { size 8{"12"} } " J"} {}$ $1 kilowatt hour ( kW ⋅ h ) = 3 . 60 × 10 6 J 1 kilowatt hour ( kW ⋅ h ) = 3 . 60 × 10 6 J size 12{1" kilowatt"" hour" $$"kW" cdot h$$  =3 "." "60" times "10" rSup { size 8{6} } " J"} {}$ $1 food calorie ( kcal ) = 4186 J 1 food calorie ( kcal ) = 4186 J size 12{1" food""calorie" $$"kcal"$$ ="4186"" J"} {}$ $1 calorie ( cal ) = 4 . 186 J 1 calorie ( cal ) = 4 . 186 J size 12{1" calorie" $$"cal"$$ =4 "." "186"" J"} {}$ $1 electron volt ( eV ) = 1 . 60 × 10 − 19 J 1 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 × 10 5 Pa 1 atmosphere ( atm ) = 1 . 013 × 10 5 Pa size 12{1" atmosphere" $$"atm"$$  =1 "." "013" times "10" rSup { size 8{5} } " Pa"} {}$ $1 millimeter of mercury ( mm Hg ) = 133 . 3 Pa 1 millimeter of mercury ( mm Hg ) = 133 . 3 Pa size 12{1" millimeter""of""mercury" $$"mm""Hg"$$ ="133" "." 3" Pa"} {}$ $1 torricelli ( torr ) = 1 mm Hg = 133 . 3 Pa 1 torricelli ( torr ) = 1 mm Hg = 133 . 3 Pa size 12{1" torricelli" $$"torr"$$ =1" mm""Hg "="133" "." 3" Pa"} {}$ Nuclear decay rate $1 curie ( Ci ) = 3 . 70 × 10 10 Bq 1 curie ( Ci ) = 3 . 70 × 10 10 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 $dd size 12{d} {}$ $C = 2 πr = πd C = 2 πr = πd size 12{C=2πr=πd} {}$ Area of a circle with radius $rr size 12{r} {}$ or diameter $dd size 12{d} {}$ $A = πr 2 = πd 2 / 4 A = πr 2 = πd 2 / 4 size 12{A=πr rSup { size 8{2} } = {πd rSup { size 8{2} } } slash {4} } {}$ Area of a sphere with radius $rr size 12{r} {}$ $A = 4 πr 2 A = 4 πr 2 size 12{A=4πr rSup { size 8{2} } } {}$ Volume of a sphere with radius $rr size 12{r} {}$ $V = 4 / 3 πr 3 V = 4 / 3 πr 3 size 12{V= left ( {4} slash {3} right ) left (πr rSup { size 8{3} } right )} {}$
Table C9 Useful Formulae

### 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.