       # Important constants and conversion factors Greek letters and symbols

Values for some useful physical constants and units
Constant Value
Absolute zero
temperature; zero kelvin (0 K, exactly)
Amp (A), ampere

electric current; SI base unit. one A = one C ˣ s-1 = 6.241 509 744 607....ˣ 1018 e- ˣ s-1, based on the exact charge on the electron.

Ångström (Å; A.U.)
length (commonly used but not an SI unit); one Å = 0.1 nm (exactly)
Angular momentum (L)
L = kg ˣ m2 ˣ s-1 ˣ rad
Angular velocity (ω)
ω = frequency ˣ rad ; sometimes as = 2 π ˣ frequency ˣ rad
Standard atmosphere (that is, 1 atm)

101.325 kPa (exactly) =1.013 25 bar (exactly) = 760 Torr (exactly)
= 1.033 23 kgF ˣ cm-2 = 760.001 mm Hg (0 °C) 10.3629 m H2O (25 °C)

Atomic mass of 12C 12 g ˣ mol-1 (exactly)
Atomic mass unit (u, amu) = Dalton (Da) 12C atom/12 = 1.660 538 921 ˣ 10-27 kg 
Atomic unit of action = reduced Planck's constant
Atomic unit of charge = elementary charge
Atomic unit of energy = Hartree
Atomic unit of force = Eh/a0 8.238 722 78 ˣ 10-8 N (under revision)
Atomic unit of length = Bohr radius
Atomic unit of mass = electron rest mass in the atomic units system. Not to be confused with the unified atomic mass unit which is the Dalton
Atomic unit of pressure = Eh/a03 2.942 101 31 ˣ 1013 Pa  (under revision)
Atomic unit of temperature = Eh/kB 3.157 775 04 ˣ105 K  (under revision)
Atomic unit of time = h/Eh 2.418 884 326 502 ˣ 10-17 s  (under revision)
Avogadro constant (NA) 6.022 140 76 ˣ 1023 mol-1  (exactly)
Avogadro number dimensionless; 6.022 140 76 ˣ 1023 
Bar (commonly used but not an SI unit) pressure; 1 bar = 100,000 Pa (exactly) = 0.986 9233 atm = 14.695 9487 7551 psi
Barrel (bbl, oil volume; not an SI unit) = 42 US gallons = 158.987 294 928 L (exactly)
Barn (b) cross-sectional area; 1 b = 100 fm2 = 10-28 m2
Barye (Ba) (not an SI unit) pressure; 1 Ba = 0.1 Pa (exactly)
Becquerel (Bq)
unit of radioactivity; = one nuclear disintegration ˣ s-1, 1 Bq = 27.0270  pCi
Billion
number; 1000,000,000; 109
Boltzmann constant (kB)
1.380 649 ˣ 10-23 J ˣ K-1 (exactly)  ; kB ˣ T/e = 25.692 58 mV
Bohr radius (a0, atomic unit of length)
length; 0.529 177 210 92 ˣ 10-10 m  (under revision)
British Thermal Unit (Btu) (not an SI unit)
heat energy; 1 Btu = 1.054 3503 kJ; 1 Btu ˣ hr-1 = 0.292 875 J (power)
calorie (cal, obsolete)
energy; one cal = 4.1868 J (exactly)
Calorie (nutrition only, Cal)
energy; one Cal = 1 kcal = 4.1868 kJ (exactly)
Candela (cd)
luminous intensity; SI base unit; cd = lm/sr; A lit candle emits light of ≈ 1 cd
Celsius zero point (0 °C exactly)

273.15 K (exactly; one degree Celsius has the same size as one kelvin);

Charge density

1 C m-2 = 6.241 5094 e- nm-2

1 e- nm-2 = 0.1602177 C m-2

Coulomb (C)
electric charge; = NA/F electrons = 6.241 509 074 460 76 ˣ 1018 e-
Cubic foot (customary unit)

volume; = 0.028 316 846 592 m3 = 28.316 846 592 L (exactly)

1 m3 = 35.314 666 7215 cubic feet

Curie (Ci)
unit of radioactivity, not an SI unit, ; 3.7 ˣ 1010 Bq (exactly)
Dalton (Da)
mass; = atomic mass unit, 12C atom/12 = 1.660 538 921 ˣ 10-27 kg 
Day (d)
time: 86,400 seconds (exactly)
Debye (D) (not an SI unit)
3.335 640 95 ˣ 10-30 C ˣ m (= -0.208 194 35 e- ˣ Å)
Degree (°)
plane angle; 1° = π/180 rad (a circle 360° = 2π rad ); 1° = 60' = 3600''
Density (ρ)
= mass/volume, kg ˣ m-3
Dyne (dyn) (not an SI unit)
force; 1 dyn = 10-5 N
e (base for natural logarithms)
Electric field strength V ˣ m-1 ; kg ˣ m ˣ s-3 ˣ A-1
100 cm-1 105 nm 1.197 kJ ˣ mol-1 ≈ 3 THz
Electron charge (e, atomic unit of charge)
(-ve) 1.602 176 634 ˣ 10-19 C (exactly) 
Electron mass (me, atomic unit of mass)
9.109 382 91 ˣ 10-31 kg  (under revision); me = 0.511 MeV ˣ c-2
Electron volt (eV, electronvolt)

energy, 1 eV = 1 ˣ e ˣ V = 1.602 176 634 ˣ 10-19 J (96.485 332 12 kJ ˣ mol-1) 

1 eV 8,065.544 29  cm-1 241.798 9348 THz ( 1,239.841 93 nm)

1 eV 11,604.518 12 K

Electrostatic constant (ke) = coulomb force constant
ke=1/(4πε0) = c2 ˣ !0-7 H ˣ m-1 =  8.987 551 787 368 1764 ˣ 109 N ˣ m2 ˣ C-2 (exactly)
Enthalpy
a measure of the heat content of the system; usual units = J ˣ mol-1
Entropy
a measure of disorder and chaos of the system; usual units = J ˣ mol-1 ˣ K-1
Erg (erg) (not an SI unit)
energy; 1 erg = 10-7 J
Electrostatic unit of charge (esu) (not an SI unit)
electrical charge; 1 esu = 1 statC = dyn½ ˣ cm = cm3/2 ˣ g½ ˣ s-1 = 3.335 641×10-10 C. = 2.081 944 ˣ 1011 e-
Fahrenheit temperature scale (°F, customary unit in US)

(Fahrenheit temperature) = (Kelvin temperature) ˣ 9⁄5 − 459.67
(Kelvin temperature) = (Fahrenheit temperature + 459.67) ˣ 5⁄9

(Fahrenheit temperature) = (Celsius temperature) ˣ 9⁄5 + 32
(Celsius temperature) = (Fahrenheit temperature - 32) ˣ 5⁄9

One degree Fahrenheit has the same size as 5/9 kelvin and 5/9 °C

Farad (F) electric capacitance, = C/V = s4 ˣ A2 ˣ m-2 ˣ kg-1
Faraday electrical charge: 96,485.332 123 310 0184 C (exactly) one mole of electrons ( = e ˣ NA) 
Faraday constant (F) 96,485.332 123 310 0184 C ˣ mol-1 exactly (96,485.332 123 310 0184 J ˣ V-1 ˣ mol-1) ;
Foot (ft, ') (not an SI unit) length; 30.48 cm (exactly)
Foot candle (fc) (not an SI unit) illuminance; 1 fc = lm ˣ ft-2 (1 fc ≈ 10.763 91 lux)
Gallon (liquid volume; not an SI unit))

Imperial (UK) = 4.546 09 L (exactly)

US            = 3.785 411 784 L (exactly)

Gas constant, molar; R

(R = kB ˣ NA)

R = 8.314 462 618 153 24 Pa ˣ m3 ˣ mol-1 ˣ K-1 (exactly)  (= 0.082 057 46 L ˣ atm ˣ mol-1 ˣ K-1)
RT, Gas constant ˣ temperature (25 °C)
2,478.957 03 Pa ˣ m3 ˣ mol-1; (= 2.478 957 03 kJ ˣ mol-1)
RT/F, Gas constant ˣ temperature/Faraday (25 °C)
RT/F = 25.692 579 12 mV, Ln(10) ˣ RT/F = 59.159 349 685 mV
Gauss (G) (not an SI unit) magnetic flux density; 1 G = 1 Mx ˣ cm-2 = 10-4 T
Giga anna (Ga, Gyr) (not an SI unit)
time passed; 1000,000,000 years ago
Gram molecule mass; relative molecular mass (molecular weight) in grams = mol
Gray (Gy) Absorbed dose of radiation; Gy = J ˣ kg-1
Acceleration due to gravity (g, standard)
9.806 65 m s-2 (exactly) (≈ 32.1740 ft s-2 )
Hartree (Eh, atomic unit of energy)

4.359 744 34 ˣ 10-18 J  (under revision)

Henry (H)

inductance; 1 H = 1 V ˣ s ˣ A-1 = kg ˣ m2 ˣ s-2 ˣ A-2

Hertz (Hz)

Horsepower (hp) (not an SI unit)

power; 746 W (no single definition)

Hour (hr)

time; 3600 s

Standard Hydrogen Electrode

Absolute value 4.44 eV below vacuum; A relative value of 0.00 eV is the standard value.

Hyperfine splitting frequency of the caesium-133 atom

Δν(133Cs)hfs is exactly 9,192,631,770 hertz (Hz) (defines the second)

Inch (in, ") (not an SI unit)

length; 2.54 cm (exactly)

Joule (J)

energy, work, heat; one J = one kg ˣ m2 ˣ s-2; J = N ˣ m = Pa ˣ m3 = kPa ˣ L = C ˣ V

katal (kat)

catalytic activity; one kat = one mol ˣ s-1

Kelvin (K)

Thermodynamic temperature; SI base unit. It was defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of set isotopic composition water; (Absolute zero, 0 K = −273.15 °C or −459.67 °F). Now it is defined in terms of the Boltzmann constant, the second, the meter, and the kilogram.

1 K = 0.086 217 38 meV = 0.695 cm1 ( 8.318 7129 J ˣ mol-1)

Kilocalorie (kcal, thermochemical)
one kcal = 4.1840 kJ (exactly)
Kilogram (kg)

mass; SI base unit. Defined in terms of the Planck constant (h), meter, and second ; kg = h / (6.626 070 15 ˣ 10-34 ) ˣ m-2 ˣ s

= (299,792,458)2/{(6.626 070 15 ˣ 10-34) ˣ ( 9,192,631,770)} ˣ ΔνCs ˣ h ˣ c-2 (exactly)

Kilogram-force (kgF)
force; 1 kgF = 9.806 65 N (exactly)
Kilowatt-hour (kWh)
work (= energy); 1 kWh = 3.6 MJ (exactly)
Lightyear length; one lightyear = 9,460,730,472,580.8 km (exactly)
Liter, (L, l; alternatively spelled litre in the UK) volume; commonly used but not an SI unit; one L = 10-3 ˣ m3 (exactly)
Ln( )
Natural logarithm; = Loge( ). Sometimes referred to as log in the literature
Loge(10); Ln(10)
Loschmidt constant (STP) (= P NA/RT)
2.651 6462 ˣ 1025 molecules of ideal gas ˣ m-3 (= 44.615 036 mol ˣ m-3)
Lumen, (lm) luminous flux; one lm = one cd ˣ sr; (= cd ˣ m2 ˣ m-2). The luminous efficacy of monochromatic radiation of frequency 540 ˣ 1012 Hz is exactly 683 lm ˣ W-1
Luminance, (Lv) one Lv = one cd ˣ m-2
Lux, (lx) illuminance; 1 lx = 1 cd ˣ sr ˣ m-2
time passed; 1 Ma = 1,000,000 years ago
Maxwell (Mx) (not an SI unit) magnetic flux; 1 Mx = 1 G ˣ cm2 = 10-8 Wb
Meter (m); alternatively spelled metre in the UK length; SI base unit. defined by the speed of light below
Micron (µ, µm), micrometer length: = 1 µm = 10-6 m
Mil (not an SI unit) length; easily confused as may mean either, m ˣ 10-3 or in ˣ 10-3
Mile (international, not an SI unit) length: 1,609.344 m (exactly)
Minute

(min) time; 1 min = 60 s

('), plane angle; 1' = π/10800 rad (a circle 360° = 2π rad ); 1' = 60''

mm-Hg (not an SI unit)
historical pressure unit; 133.322 387 415 Pa (exactly) (1.0 mm-Hg ≈ 1.0 torr)
Molal concentration (m)
1 m = 1 mol ˣ (kg solvent)-1 (see for conversion to molarity)
Molality, standard (m°)
m° = 1 mol ˣ (kg solvent)-1
Molar concentration (M)
1 mol ˣ (L solution)-1 = 103 mol ˣ m-3 (see for conversion to molality)
Molar volume of ideal gas (STP) = R ˣ 273.15/100,000 m3 ˣ mol-1 = 22.710 953 L ˣ mol-1 (22.414 L ˣ mol-1 at 101.325 kPa)
Mole (mol) amount; SI base unit. an Avogadro number of items
Mya (not an SI unit) time passed; 1 Mya = 1,000,000 years ago
Nernst constant, = RT/F 25.692576 mV (25 °C); Loge(10) ˣ RT/F = 0.059 159 243 V (25 °C)
Newton (N) force; N = 1 kg ˣ m ˣ s-2
Oersted (Oe) magnetic field; 1 Oe (103/4π) ˣ A ˣ m-1
Ohm (Ω) electric resistance; = V/A, 1 Ω = 1 kg ˣ m2 ˣ s-3 ˣ A-2
Osmole (Osm) (not an SI unit) amount; the number of moles of solute that contribute to the osmotic pressure of a solution. Ideally, 1 mole of NaCl in 1 Kg water is 2 Osm ˣ kg-1-water
Pascal (Pa) pressure, stress, 1 Pa = 1 N ˣ m-2 = 1 kg ˣ m-1 ˣ s-2
Parts per billion (ppb) ppb = parts per 1000,000,000; for example, 1 µg ˣ kg-1
Parts per million (ppm) ppm = parts per 1000,000; for example, 1 mg ˣ kg-1; also used in NMR

Permeability

the degree of magnetization of a material in response to a magnetic field = H ˣ m-1

Permeability of a vacuum (µ0) (Magnetic constant)

4π ˣ 10-7 N ˣ A-2 = 4π ˣ 10-7 T2 ˣ m3 ˣ J-1 (exactly)

= 1.256 637 061 435 917 295 µH ˣ m-1N ˣ A-2) 

Permittivity

the ability of a substance to store electrical energy in an electric field = F ˣ m-1

Permittivity of a vacuum (ε0) (Electric constant)

= (μ0 c2)-1 in units C2 ˣ J-1 ˣ m-1 (exactly)

= 8.854 187 817 620 389 850 536 563 031 710 pF ˣ m-1

Π (= circle circumference/diameter)
Planck constant (h)

quantum of electromagnetic action; a photon's energy is equal to its frequency multiplied by the Planck constant.

h = 6.626 070 15 × 10-34 kg ˣ m2 ˣ s-1 (exactly; 6.626 070 15 × 10-34 J ˣ s) 

Reduced Planck constant (h/2π = ħ = atomic unit of action)
1.054 571 718 ˣ 10-34 J ˣ s; energy (J) =ħ ˣ ω
Pint (liquid volume; not an SI unit)

Imperial (UK) = 0.568 261 25 L (exactly)

US                = 0.473 176 473 L (exactly)

Poise (P) (not an SI unit)
dynamic viscosity; one P = one dyne ˣ s ˣ cm-2 = 0.1 N ˣ m-2 ˣ s = 0.1 Pa ˣ s

Pound (lb) (avoirdupois, US and UK) (not an SI unit)

mass = 0.453 592 37 kg (exactly)
Pound weight (lbf) (not an SI unit)
force = 4.448222 N
Proton charge
(+ve) 1.602 176 634 ˣ 10-19 C (exactly)
Proton gyromagnetic ratio (γP)
γP = 2.67515255 ˣ 108 rad ˣ s-1 ˣ T-1
psi (pounds weight per square inch; customary unit)
pressure; 1 psi = 6,894.757 293 168 Pa; 1 atm = 101,325 Pa = 14.6959 psi
psu (practical salinity unit) (not an SI unit)
The psu has no dimensional units; see elsewhere

number; 1000,000,000,000,000; 1015

SI unit of angle, the units are m ˣ m-1 but usually treated as dimensionless; 1 rad = 360°/2π = 57.295 779 513 082 320 876 798 154 814 105 170 3°; One revolution = 360° = 2π ˣ rad °

Radiance W ˣ sr-1 ˣ m-2 ; kg ˣ s-3
Second (s) time; SI base unit. The second is equal to the duration of exactly 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the unperturbed ground state of the 133Cs atom. ΔνCs = 9,192,631,770 s-1 exactly. This definition of the second may be updated in 2026.
Second ('') (''), Plane angle; 1'' = π/648,000 rad (a circle 360° = 2π rad )
Siemens (S) electric conductance; = A/V, 1 S = 1/Ω = 1 s3 ˣ A2 ˣ kg-1 ˣ m-2
Sievert (Sv) radiation dose equivalent; Sv = J ˣ kg-1
Specific heat
energy ˣ mol-1 ˣ K-1; = kg ˣ m2 ˣ s-2 ˣ mol-1 ˣ K-1
Spectral luminous efficiency (Kλ)
Kλ = Lm ˣ watt-1
Speed of light in a vacuum, (c)
299,792,458 m ˣ s-1 (exactly, also defines the meter) 
Standard conditions for dissolved activities

101.325 kPa, 273.15 K, concentration 1 mol ˣ L-1 (1000 mol ˣ m-3)

Standard temperature and pressure, for gases (STP)

100 kPa, 273.15 K (exactly) IUPAC

Statcoulomb (statC)

electrical charge; see esu

Standard state        (thermodynamic)

varies as stated, but often; pressure, 100 kPa; temperature, 25.00 °C

The solid angle of the sphere surface (area A, radius r) from the center, = (A/r2 ) ˣ sr

4π  ˣ sr = entire surface of a sphere radius r. The units of sr are m2 ˣ m-2 but usually treated as dimensionless;.

Stokes (St) (not an SI unit)
kinematic viscosity; 1 St = 1 cm2 ˣ s-1 = 10-4 m2 ˣ s-1
Sun
solar irradiation; 1 kW ˣ m-2
Surface tension N ˣ m-1 ; kg ˣ s-2
Terahertz (THz)

frequency in cycles per second:one THz = 1012 s-1 = 2π ˣ 1012 radian ˣ s-1 = one ps-1 33.355 640 952 cm-1 299.792 458 µm (exactly) 0.004 135 667 516 eV 399.031 27 J ˣ mol-1

Tesla (T)
magnetic field strength; = Wb ˣ m-2; 1 T = 1 kg ˣ s-2 ˣ A-1 = V ˣ s ˣ m-2
Thermal energy (kT at 25 °C)
2.478 957 kJ ˣ mol-1; 4.116405 J ˣ 10-21 ˣ molecule-1; 1.5 ˣ kT = 3.718 kJ ˣ mol-1
Ton (metric ton) (tonne, t) mass; = 103 kg (1 Mg)
Ton (UK; long ton)

mass; = 2,240 lb avoirdupois, UK; = 1016.046 908 80 kg (exactly)

Ton (US; short ton)

mass; = 2,000 lb avoirdupois, US; = 907.184 740 kg (exactly)

Torr (not an SI unit)

historical pressure unit; one torr = 101325⁄760 Pa (exactly; ≈ 133.322 368 4211  Pa )

≡ 1 mm Hg

Trillion
number; 1000,000,000,000; 1012
Units; metric prefixes

deci- d 10-1;centi- c 10-2; milli- m 10-3; micro- µ 10-6; nano- n 10-9; pico- p 10-12; femto- f 10-15; atto- a 10-18; zepto- z 10-21; yocto- y 10-24; ronto- r 10-27 a; quecto- q 10-30 a

deca- da 101; hecto- h 102; kilo- k 103; mega- M 106; giga- G 109; tera- T 1012; peta- P 1015; exa- E 1018; zetta- Z 1021; yotta- Y 1024; ronna- R 1027 a; quecca- Q 1030 a

Vacuum permeability
Viscosity, dynamic (η)

Pa ˣ s ( kg ˣ m-1 ˣ s-1); 10 poise = 1 Pa ˣ s

Viscosity, kinematic (ν)

= η/ρ (m2 ˣ s-1) = dynamic viscosity divided by the density of the liquid;

10,000 stokes = 1 m2 ˣ s-1

Volt (V) electrical potential; V = amps ˣ ohms (A ˣ Ω); V = power/current (W/A); V = energy/amount of charge (J/C); one V = one kg ˣ m2 ˣ s-3 ˣ A-1
Wavelength (nm)

one nm = 107/wavenumber (cm-1)

(electromagnetic; one nm 3.335 640 95 attosecond)

Wavenumber (m-1) (=1/wavelength)

one m-1 = 109/wavelength (nm), one m-1 0.119 626 57 J ˣ mol-1,

1000 cm-1 11.962 657 kJ ˣ mol-1

(one cm-1 0.029 979 2458 THz exactly)

Wavenumber, wavelength. frequency conversions Watt (W)

power, radiant flux; one W = one J ˣ s-1 = one kg ˣ m2 ˣ s-3

Weber (Wb)

magnetic flux; = T ˣ m2 = V ˣ s; 1 Wb = 1 kg ˣ m2 ˣ s-2 ˣ A-1

Year (a, yr)

One Gregorian year = 365.2425 days = 31,556,952 seconds

One Julian year = 365.25 days = 31,557,600 seconds

One mean Tropical year = 365.2422 days = 31,556,926 seconds

Note that the SI unit definitions  came into force on 20 May 2019 (see right).

s - defined using the frequency of the cesium hyperfine transition (ΔvCs),

kg - defined using the Planck constant (h),

mol -defined using the Avogadro constant (NA ),

cd - defined using the sensitivity of the human eye (luminous efficacy, Kcd),

K - defined using the Boltzmann constant (kB),

A - defined using the elementary electric charge (e),

m - defined using the speed of light (c) .

Generated from a Mathematica notebook at https://github.com/episanty/SI-unit-relations.

## Footnotes

a Prefixes awaiting approval, D. Adam, Metric prefixes sought for extreme numbers, Science, 363 (2019) 681. [Back]

This page was established in 2007 and last updated by Martin Chaplin on 1 November, 2019