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This appendix is broken into several tables.

  • [link] , Important Constants
  • [link] , Submicroscopic Masses
  • [link] , Solar System Data
  • [link] , Metric Prefixes for Powers of Ten and Their Symbols
  • [link] , The Greek Alphabet
  • [link] , SI units
  • [link] , Selected British Units
  • [link] , Other Units
  • [link] , Useful Formulae
Important constants 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.
Symbol Meaning Best Value Approximate Value
c size 12{c} {} Speed of light in vacuum 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 size 12{3 "." "00" times "10" rSup { size 8{8} } ` {m} slash {s} } {}
G size 12{G} {} Gravitational constant 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 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 size 12{N rSub { size 8{A} } } {} Avogadro’s number 6 . 02214129 ( 27 ) × 10 23 size 12{6 "." "02214129" \( "27" \) times "10" rSup { size 8{"23"} } } {} 6 . 02 × 10 23 size 12{6 "." "02" times "10" rSup { size 8{"23"} } } {}
k size 12{k} {} Boltzmann’s constant 1 . 3806488 ( 13 ) × 10 − 23 J / K size 12{1 "." "3806488" \( "13" \) times "10" rSup { size 8{ - "23"} } ` {J} slash {K} } {} 1 . 38 × 10 − 23 J / K size 12{1 "." "38" times "10" rSup { size 8{ - "23"} } ` {J} slash {K} } {}
R size 12{R} {} Gas constant 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 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 size 12{σ} {} Stefan-Boltzmann constant 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 size 12{5 "." "67" times "10" rSup { size 8{ - 8} } ` {W} slash {m rSup { size 8{2} } cdot K} } {}
k size 12{k} {} Coulomb force constant 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 size 12{9 times "10" rSup { size 8{9} } ` {N cdot m rSup { size 8{2} } } slash {C rSup { size 8{2} } } } {}
q e size 12{q rSub { size 8{e} } } {} Charge on electron − 1 . 602176565 ( 35 ) × 10 − 19 C size 12{ - 1 "." "602176565" \( "35" \) times "10" rSup { size 8{ - "19"} } `C} {} − 1 . 60 × 10 − 19 C size 12{ - 1 "." "60" times "10" rSup { size 8{ - "19"} } `C} {}
ε 0 size 12{ε rSub { size 8{0} } } {} Permittivity of free space 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 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 size 12{μ rSub { size 8{0} } } {} Permeability of free space 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 size 12{1 "." "26" times "10" rSup { size 8{ - 6} } ` {T cdot m} slash {A} } {}
h size 12{h} {} Planck’s constant 6 . 62606957 ( 29 ) × 10 − 34 J ⋅ s size 12{6 "." "62606957" \( "29" \) times "10" rSup { size 8{ - "34"} } `J cdot s} {} 6 . 63 × 10 − 34 J ⋅ s size 12{6 "." "63" times "10" rSup { size 8{ - "34"} } `J cdot s} {}
Submicroscopic masses 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.
Symbol Meaning Best Value Approximate Value
m e size 12{m rSub { size 8{e} } } {} Electron mass 9 . 10938291 ( 40 ) × 10 − 31 kg size 12{9 "." "10938291" \( "40" \) times "10" rSup { size 8{ - "31"} } `"kg"} {} 9 . 11 × 10 − 31 kg size 12{9 "." "11" times "10" rSup { size 8{ - "31"} } `"kg"} {}
m p size 12{m rSub { size 8{p} } } {} Proton mass 1 . 672621777 ( 74 ) × 10 − 27 kg size 12{1 "." "672621777" \( "74" \) times "10" rSup { size 8{ - "27"} } `"kg"} {} 1 . 6726 × 10 − 27 kg size 12{1 "." "6726" times "10" rSup { size 8{ - "27"} } `"kg"} {}
m n size 12{m rSub { size 8{n} } } {} Neutron mass 1 . 674927351 ( 74 ) × 10 − 27 kg size 12{1 "." "674927351" \( "74" \) times "10" rSup { size 8{ - "27"} } `"kg"} {} 1 . 6749 × 10 − 27 kg size 12{1 "." "6749" times "10" rSup { size 8{ - "27"} } `"kg"} {}
u size 12{u} {} Atomic mass unit 1 . 660538921 ( 73 ) × 10 − 27 kg size 12{1 "." "660538921" \( "73" \) times "10" rSup { size 8{ - "27"} } `"kg"} {} 1 . 6605 × 10 − 27 kg size 12{1 "." "6605" times "10" rSup { size 8{ - "27"} } `"kg"} {}
Solar system data
Sun mass 1 . 99 × 10 30 kg size 12{1 "." "99" times "10" rSup { size 8{"30"} } `"kg"} {}
average radius 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 size 12{1 "." "496" times "10" rSup { size 8{"11"} } " m"} {}
Earth mass 5 . 9736 × 10 24 kg size 12{5 "." "9736" times "10" rSup { size 8{"24"} } `"kg"} {}
average radius 6 . 376 × 10 6 m size 12{6 "." "376" times "10" rSup { size 8{6} } `m} {} {}
orbital period 3 . 16 × 10 7 s size 12{3 "." "16" times "10" rSup { size 8{7} } " s "} {}
Moon mass 7 . 35 × 10 22 kg size 12{7 "." "35" times "10" rSup { size 8{"22"} } `"kg"} {}
average radius 1 . 74 × 10 6 m size 12{1 "." "74" times "10" rSup { size 8{6} } `m} {}
orbital period (average) 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 size 12{3 "." "84" times "10" rSup { size 8{8} } " m"} {}
Metric prefixes for powers of ten and their symbols
Prefix Symbol Value Prefix Symbol Value
tera T 10 12 size 12{"10" rSup { size 8{"12"} } } {} deci d 10 − 1 size 12{"10" rSup { size 8{ - 1} } } {}
giga G 10 9 size 12{"10" rSup { size 8{9} } } {} centi c 10 − 2 size 12{"10" rSup { size 8{ - 2} } } {}
mega M 10 6 size 12{"10" rSup { size 8{6} } } {} milli m 10 − 3 size 12{"10" rSup { size 8{ - 3} } } {}
kilo k 10 3 size 12{"10" rSup { size 8{3} } } {} micro μ size 12{μ} {} 10 − 6 size 12{"10" rSup { size 8{ - 6} } } {}
hecto h 10 2 size 12{"10" rSup { size 8{2} } } {} nano n 10 − 9 size 12{"10" rSup { size 8{ - 9} } } {}
deka da 10 1 size 12{"10" rSup { size 8{1} } } {} pico p 10 − 12 size 12{"10" rSup { size 8{ - "12"} } } {}
— — 10 0 ( = 1 ) size 12{"10" rSup { size 8{0} } \( `=1` \) } {} femto f 10 − 15 size 12{"10" rSup { size 8{ - "15"} } } {}
The greek alphabet
Alpha Α size 12{Α} {} α size 12{α} {} Eta Η size 12{Η} {} η size 12{η} {} Nu Ν size 12{Ν} {} ν size 12{ν} {} Tau Τ size 12{Τ} {} τ size 12{τ} {}
Beta Β size 12{Β} {} β size 12{β} {} Theta Θ size 12{Θ} {} θ size 12{θ} {} Xi Ξ size 12{Ξ} {} ξ size 12{ξ} {} Upsilon Υ size 12{Υ} {} υ size 12{υ} {}
Gamma Γ size 12{Γ} {} γ size 12{γ} {} Iota Ι size 12{Ι} {} ι size 12{ι} {} Omicron Ο size 12{Ο} {} ο size 12{ο} {} Phi Φ size 12{Φ} {} ϕ size 12{ϕ} {}
Delta Δ size 12{Δ} {} δ size 12{δ} {} Kappa Κ size 12{Κ} {} κ size 12{κ} {} Pi Π size 12{Π} {} π size 12{π} {} Chi Χ size 12{Χ} {} χ size 12{χ} {}
Epsilon Ε size 12{Ε} {} ε size 12{ε} {} Lambda Λ size 12{Λ} {} λ size 12{λ} {} Rho Ρ size 12{Ρ} {} ρ size 12{ρ} {} Psi Ψ size 12{Ψ} {} ψ size 12{ψ} {}
Zeta Ζ size 12{Ζ} {} ζ size 12{ζ} {} Mu Μ size 12{Μ} {} μ size 12{μ} {} Sigma Σ size 12{Σ} {} σ size 12{σ} {} Omega Ω size 12{ %OMEGA } {} ω size 12{ω} {}
Si units
Entity Abbreviation Name
Fundamental units Length m meter
Mass kg kilogram
Time s second
Current A ampere
Supplementary unit Angle rad radian
Derived units Force 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 size 12{J="kg" cdot {m rSup { size 8{2} } } slash {s rSup { size 8{2} } } } {} joule
Power W = J / s size 12{W= {J} slash {s} } {} watt
Pressure Pa = N / m 2 size 12{"Pa"= {N} slash {m rSup { size 8{2} } } } {} pascal
Frequency Hz = 1 / s size 12{"Hz"= {1} slash {s} } {} hertz
Electronic potential V = J / C size 12{V= {J} slash {C} } {} volt
Capacitance F = C / V size 12{F= {C} slash {V} } {} farad
Charge C = s ⋅ A size 12{C=s cdot A} {} coulomb
Resistance Ω = V / A size 12{ %OMEGA = {V} slash {A} } {} ohm
Magnetic field T = N / A ⋅ m size 12{T= {N} slash { left (A cdot m right )} } {} tesla
Nuclear decay rate Bq = 1 / s size 12{"Bq"= {1} slash {s} } {} becquerel
Selected british units
Length 1 inch ( in . ) = 2 . 54 cm ( exactly ) size 12{1" inch " \( "in" "." \) =2 "." "54"" cm " \( "exactly" \) } {}
1 foot ( ft ) = 0 . 3048 m size 12{1" foot " \( "ft" \) =0 "." "3048"" m"} {}
1 mile ( mi ) = 1 . 609 km size 12{1" mile " \( "mi" \) =1 "." "609"" km"} {}
Force 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 size 12{1" British thermal unit " \( "Btu" \) =1 "." "055" times "10" rSup { size 8{3} } " J"} {}
Power 1 horsepower ( hp ) = 746 W size 12{1" horsepower " \( "hp" \) ="746"" W"} {}
Pressure 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"} {}
Other units
Length 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 size 12{1`" astronomical"`" unit"` \( "au" \) ` =1 "." "50" times "10" rSup { size 8{"11"} } " m"} {}
1 nautical mile = 1 . 852 km size 12{1`" nautical"`" mile"` =1 "." "852"`" km"} {}
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 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 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 size 12{1`" barn"` \( b \) ` ="10" rSup { size 8{ - "28"} } " m" rSup { size 8{2} } } {}
Volume 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 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 size 12{1`" solar"`" mass"` =1 "." "99" times "10" rSup { size 8{"30"} } " 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 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 size 12{1`" year"` \( y \) ` =3 "." "16" times "10" rSup { size 8{7} } " 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 size 12{1`" mile"`"per"`"hour"` \( "mph" \) `=1 "." "609"` {"km"} slash {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 size 12{1`" degree"` \( ° \) ` =1 "." "745" times "10" rSup { size 8{ - 2} } " rad"} {}
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 size 12{1`" second"`"of"`"arc"` { { \( }} sup { '' } \) `= {1} slash {"60"`} " minute of arc"} {}
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 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 size 12{1`" kilowatt"`" hour"` \( "kW" cdot h \) ` =3 "." "60" times "10" rSup { size 8{6} } " J"} {}
1 food calorie ( kcal ) = 4186 J size 12{1`" food"`"calorie"` \( "kcal" \) `="4186"`" J"} {}
1 calorie ( cal ) = 4 . 186 J size 12{1`" calorie"` \( "cal" \) `=4 "." "186"`" 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 size 12{1`" atmosphere"` \( "atm" \) ` =1 "." "013" times "10" rSup { size 8{5} } " 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 size 12{1`" torricelli"` \( "torr" \) `=1`" mm"``"Hg "="133" "." 3`" Pa"} {}
Nuclear decay rate 1 curie ( Ci ) = 3 . 70 × 10 10 Bq size 12{1`" curie"` \( "Ci" \) ` =3 "." "70" times "10" rSup { size 8{"10"} } " Bq"} {}
Useful formulae
Circumference of a circle with radius r size 12{r} {} or diameter d size 12{d} {} C = 2 πr = πd size 12{C=2πr=πd} {}
Area of a circle with radius r size 12{r} {} or diameter d size 12{d} {} 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 r size 12{r} {} A = 4 πr 2 size 12{A=4πr rSup { size 8{2} } } {}
Volume of a sphere with radius r size 12{r} {} V = 4 / 3 πr 3 size 12{V= left ( {4} slash {3} right ) left (πr rSup { size 8{3} } right )} {}

Questions & Answers

differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
what is labour ?
Lambiv
how will I do?
Venny Reply
how is the graph works?I don't fully understand
Rezat Reply
information
Eliyee
devaluation
Eliyee
t
WARKISA
hi guys good evening to all
Lambiv
multiple choice question
Aster Reply
appreciation
Eliyee
explain perfect market
Lindiwe Reply
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
yes,thank you
Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Lilia Reply
what is the difference between economic growth and development
Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
Abdisa Reply
any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
Feyisa Reply
Answer
Feyisa
c
Jabir
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
Gsbwnw Reply
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
types of unemployment
Yomi Reply
What is the difference between perfect competition and monopolistic competition?
Mohammed
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Source:  OpenStax, Physics 110 at une. OpenStax CNX. Aug 29, 2013 Download for free at http://legacy.cnx.org/content/col11566/1.1
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