Water structure and science
(http://www1.lsbu.ac.uk/water/constants.html)

Extended data list for water

Important constants and conversion factors

link  Greek letters and symbols

V  SI units


Values for some useful physical constants and units
Constant Value
Absolute zero
temperature; zero kelvin (= 0 K, exactly); (at -273.15 °C, or at -459.67 °F)
Amount of a substance;

= mol

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
Astronomical unit, au
length (not an SI unit); one au = 149,597,870,700 m (exactly)
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)

Standard pressure is now defined as 100 kPa exactly.

Atomic mass of 12C 11.999 999 9958 g ˣ mol−1
Atomic mass unit (u, amu) = Dalton (Da) = 12C atom/12 = 1.660 539 066 60 ˣ 10−27 kg [934]
Atomic unit of action = reduced Planck's constant = h/2π = ħ
Atomic unit of charge = elementary charge
Atomic unit of energy = Eh = Hartree
Atomic unit of force = Eh/a0 = 8.238 723 4983 ˣ 10−8 N
Atomic unit of length = a0 = 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 5697 ˣ 1013 Pa [934]
Atomic unit of temperature = Eh/kB = 3.157 750 248 ˣ105 K [934]
Atomic unit of time = h/2πEh = 2.418 884 326 5857 ˣ 10−17 s [934]
Avogadro constant (NA) NA = 6.022 140 76 ˣ 1023 mol−1 [2395] (exactly)
Avogadro number dimensionless; = 6.022 140 76 ˣ 1023 [2395]
Bar (not an SI unit) pressure; 1 bar = 100,000 Pa (exactly) = 0.986 9233 atm = 14.695 9487 7551 psi
Barrel (bbl) (not an SI unit) volume of oil; 1 bbl = 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 (this is the US 'billion)
Boltzmann constant (kB)

relates temperature to energy; 1.380 649 ˣ 10−23 J ˣ K−1 (exactly) [2395] ;

kB ˣ T/e = 25.692 579 12 mV (at 25 °C)

Bohr radius (a0, atomic unit of length)
length; a0 = 5.291 772 109 03 ˣ 10−11 m [934] (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 ( °C) (centigrade)

0ne °C = one kelvin; TK = T°C + 273.15; T°C = TK - 273.15

Celsius zero point (0 °C exactly)

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

Standard temperature is now defined as 273.15 K exactly.

Centipoise, (cP; not an SI unit)

dynamic viscosity; one cP = mPa

Charge density

1 C ˣ m−2 = 6.241 5094 e ˣ nm−2

1 e ˣ nm−2 = 0.1602177 C ˣ m−2

Concentration
= mol ˣ m−3
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) (not an SI unit)
unit of radioactivity; 1 Ci = 3.7 ˣ 1010 Bq (exactly)
Dalton (Da)
mass; = atomic mass unit, 12C atom/12 = 1.660 539 040 ˣ 10−27 kg [934]
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''
Mass 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)
2.718 281 828 459 045 235 360 287 471 352 662 497 757 247 093 699 95.. ...
Electric conductance = 1/Ω; see siemens
Electric field strength V ˣ m−1 = N/C = kg ˣ m ˣ s−3 ˣ A−1
Electric resistance = Ω; see ohm
Electromagnetic radiation
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) [2395]
Electron mass (me, atomic unit of mass)
me = 9.109 383 7015 ˣ 10−31 kg [934]; 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 (exactly) [934]

1 eV ≡ 96.485 332 12 kJ ˣ mol−1

1 eV ≡  8,065.543 937  cm−1 ≡ 241.798 924 208 492 THz (≡ 1,239.841 984 39 nm)

1 eV ≡ 11,604.518 121 5501 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)
Energy conversion factors

mass (m) to energy (E); E = m ˣ c2

frequency (ω) to energy (E); E = ħ ˣ ω

temperature (T) to energy (E); E = kB ˣ T

Enthalpy
sensible heat; 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) [2395]

Faraday constant (F)

96,485.332 123 310 0184 C ˣ mol−1 exactly [2395];

(96,485.332 123 310 0184 J ˣ V−1 ˣ mol−1)

Foot (ft, ') (not an SI unit) length; the international foot = 30.48 cm (exactly)
Foot candle (fc) (not an SI unit) illuminance; 1 fc = lm ˣ ft−2 (1 fc ≈ 10.763 91 lux)
Frequency, 133Cs hyperfine transition frequency (ΔνCs) ΔνCs = 9,192,631,770 s−1 exactly
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; J ˣ mol−1 ˣ K−1) [2395]

R = 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 (g) (gramme) mass; g = 10−3 ˣ Kg
Gram molecule mass; relative molecular mass (molecular weight) in grams = mol
Gray (Gy) absorbed dose of radiation; Gy = J ˣ kg−1 = m2 ˣs−2
The golden ratio (φ)
1.618 033 988 749 894 848 204 586 834 365 638 117 720 309 179 805 76 ...
Acceleration due to gravity (g, standard)
g = 9.806 65 m ˣ s−2 (exactly) (≈ 32.1740 ft ˣ s−2 )
Hartree (Eh)

energy; Eh = atomic unit of energy = 4.359 744 722 2071 ˣ 10−18 J [934]

Hectare (ha)

area, 1 ha = 1 hm2 = 104 m2

Henry (H)

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

Hertz (Hz)

frequency (ν), cycles per second: = 1 s−1 (see also terahertz)

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, amount of heat; one J = one kg ˣ m2 ˣ s−2;

J = N ˣ m = Pa ˣ m3 = kPa ˣ L = C ˣ V

One joule ≡ 1.509 190 179 642 15 ˣ 1033 Hz; 5.034 116 567 542 71 ˣ 1022 cm−1;

6.241 509 074 460 76 ˣ 1018 eV

katal (kat)

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

Kelvin (K, kelvin)

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. [934]

1 K = 0.086 173 332 621 4518 meV = 0.695 034 8004 cm1 ( ≡ 8.314 4626 J ˣ mol−1)

Kilocalorie (kcal, not SI unit)
thermochemical energy; one kcal = 4.184 kJ (exactly)
Kilogram (kg)

mass; SI base unit. Defined in terms of the Planck constant (h), meter, and second [2395]; 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 = 1 dm3 = 103 ˣ cm3 = 10−3 ˣ m3 (exactly)
Ln( )
Natural logarithm; = Loge( ). Sometimes referred to as log in the literature
Loge(10); Ln(10)
2.302 585 092 994 045 684 017 991 454 684 364 207 601 101 488 628 77.....
Loschmidt constant (STP) (= PNA/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)
Luminous efficacy (Kcd) The luminous efficacy (Kcd) 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 lm ˣ m−2 = 1 cd ˣ sr ˣ m−2
Mass fraction
kg ˣ kg−1; but usually treated as dimensionless
Mega anna (Ma, Myr) (not an SI unit, see also mya)
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)
Mile per hour (mph) velocity; 1 mph = 1.609 344 km ˣ hr−1 = 0.447 04 m ˣ s−1 (exactly)
Millibar (mb) (not an SI unit) pressure; 1 mb = 100 Pa = 1 hPa
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 energy
J ˣ mol−1
Molar volume of ideal gas (at STP)

= R ˣ 273.15/100,000 m3 ˣ mol−1 = 22.710 954 64 L ˣ mol−1

(22.413 969 54 L ˣ mol−1 at 273.15 K and 101.325 kPa)

Mole (mol) amount; SI base unit. an Avogadro number of items; mol = (6.022 140 76 ˣ 1023)/NA
Moment of force = N ˣ m
Mya (not an SI unit) time passed; 1 Mya = 1,000,000 years ago
Nernst constant, = RT/F

25.692 579 12 mV (25 °C); Loge(10) ˣ RT/F = 0.059 159 349 685 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 = m ˣ kg ˣ s−2 ˣ A−2

Permeability of a vacuum (µ0) (Magnetic constant)

µ0 = 4π ˣ 10−7 N ˣ A−2 = 4π ˣ 10−7 T2 ˣ m3 ˣ J−1 (exactly)

µ0 = 1.256 637 062 12 µH ˣ m−1N ˣ A−2) [934]

Permittivity (ε)

the ability of a substance to store electrical energy in an electric field;

ε = F ˣ m−1 = m3 ˣ kg−1 ˣ s4 ˣ A2

Permittivity of a vacuum (ε0) (Electric constant)

ε0 = (μ0 c2)−1 in units C2 ˣ J−1 ˣ m−1 (exactly)

ε0 = 8.854 187 8128 pF ˣ m−1

Π (= circle circumference/diameter)
3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 10...
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) [2395]

Reduced Planck constant (h/2π = ħ )

relates frequency to energy; ħ = 1.054 571 817 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); may be divided into 20 fluid ounces (UK)

US                = 0.473 176 473 L (exactly); may be divided into 16 fluid ounces (US)

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 = 4.448 221 615 2605 N
ppb
parts per billion; 1 : 1000,000,000
Proton charge
(+ve) 1.602 176 634 ˣ 10−19 C (exactly)
Proton gyromagnetic ratio (γP)
γP = 2.675 152 55 ˣ 108 rad ˣ s−1 ˣ T−1
Proton mass
= 1.672 621 923 69  ˣ 10−27 kg [934]
Proton : electron mass ratio
= 1836.152 673 43 [934]
psi (pounds weight per square inch; customary unit)
pressure; 1 psi = 6,894.757 293 168 Pa; 1 atm = 101,325 Pa = 14.695 94 psi
psu (practical salinity unit) (not an SI unit)
The psu has no dimensional units; see elsewhere

Quadrillion

number; 1000,000,000,000,000; 1015
Rad (not an SI unit) absorbed dose of radiation; 1 rad = 0.01 Gy
Radian (rad)

SI unit of angle, the units are m ˣ m−1 but usually treated as dimensionless;

one 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
Rem (not an SI unit) Radiation dose equivalent; 1 rem = 0.01 Sv
Roentgen (R) (not an SI unit) Exposure of X-rays and gamma rays; 1 R = 2.580 ˣ 10−4 ˣ C ˣ kg−1 air at STP
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; The previously used units of mhos ˣ cm−1 are numerically equivalent to S ˣ cm−1.

Sievert (Sv) radiation dose equivalent; Sv = J ˣ kg−1 = m2 ˣs−2
Specific gravity

relative density; for liquids, it is relative to water at 3.98 °C (~ 1000 kg ˣ m−3)

                         for gases, it is relative to air at 20 °C, 101.325 kPa (~ 1.205 kg ˣ m−3)

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)
c = 299,792,458 m ˣ s−1 (exactly; also defines the meter) [934]
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)

STP ≡ 100 kPa, 273.15 K (exactly) IUPAC

Statcoulomb (statC)

electrical charge; 1 statC = dyn½ ˣ cm = cm3/2 ˣ g½ ˣ s−1 ; not an SI unit; see esu

Standard state        (thermodynamic)

varies as stated, but often; pressure, 100 kPa; temperature, 25.00 °C (77 °F)

Stefan-Boltzmann constant (σ)

σ = π2kB4/(60ħ3c2) = 5.670 374 419 ˣ 10−8 W ˣ m−2 ˣ K−4

Steradian (sr)

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; measured in kWh ˣ m−2
Surface tension = N ˣ m−1 ; kg ˣ s−2
Tablespoon (Tbsp) Culinary measure, volume; standardised, Tbsp; 1 Tbsp = 15 mL = 3 tsp
Teaspoon (tsp) Culinary measure, volume;standardised, 1 tsp = 5 mL; = ⅓ tablespoon (Tbsp)
Terahertz (THz)

frequency in cycles per second: one THz = 1012 s−1 = 2π ˣ 1012 radian ˣ s−1 = one ps−1 ≡ 33.355 640 951 981 52 cm−1 ≡ 299.799 365 702 µm (exactly)

≡ 0.004 135 667 516 eV ≡ 6.626 070 15 ˣ 10−22 J ≡ 399.031 271 289 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 conductivity
= W ˣ m−1 ˣ K−1 = m ˣ kg ˣ s−3 ˣ K−1
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; one t = 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; binary prefixes

kibi (210)1 ; mebi (210)2 ; gibi (210)3 ; tebi (210)4 ; pebi (210)5 ; exbi(210)6; NIST e.g.,

1 gibibyte = 1 GiB = 1,073,741,824 byte; 1 gigabyte = 1 GB = 1,000,000,000 byte

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

see Permeability of a vacuum

Viscosity, dynamic (η)

η = Pa ˣ s = kg ˣ m−1 ˣ s−1;

10 poise = 1 Pa ˣ s

Viscosity, kinematic (ν)

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 5656 J ˣ mol−1;

1000 cm−1 ≡ 11.962 656 56 kJ ˣ mol−1

(one cm−1 ≡ 0.029 979 2458 THz exactly)

Wavenumber, wavelength. frequency conversions

The electromagnetic spectrum

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; one Wb = one kg ˣ m2 ˣ s−2 ˣ A−1

Weight

force which depends on terrestrial gravity = (1/9.806 65) ˣ kg ˣ m ˣ s−2 , = N

Year (a, yr) (not an SI unit)

(varies from year to year)

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

One Julian year (a) = 365.25 days = 31,557,600 seconds (exactly, fixed in astronomy)

One mean Tropical year = 365.24219 days = 31,556,925.216 seconds

 

The relationship between the SI units,

based on https://github.com/episanty/SI-unit-relations

The relationship between the SI units, from https://github.com/episanty/SI-unit-relations

SI units

Note that the SI unit definitions [1031] came into force on 20 May 2019 (see right). The Dimensions are given in red capitals; Mass, Length, Time, Substance, temperature as Theta Θ, luminosity in Joules per second, electric current (a) Intensity.

s - second defined using the frequency of the cesium hyperfine transition (ΔvCsT−1),

kg - kilogram defined using the Planck constant (hL2MT−1),

mol -mole defined using the Avogadro constant (NAS−1),

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

K - kelvin defined using the Boltzmann constant (kBL2MT−2Θ−1),

A - amp defined using the elementary electric charge  (eIT),

m - meter defined using the speed of light (cLT−1) .

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Footnotes

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

(c) Martin Chaplin 28 October, 2020
(printed 31 October 2020)