Units and Unit Systems List

List of units, SI unit prefixes, and unit systems in Symbolic Math Toolbox™. For details, see Units of Measurement Tutorial. Common alternate names for units are supported and map to the names listed here. Plurals are not supported.

• Units List

• SI Unit Prefixes List

• Unit Systems List

• Defining Constants of SI Units

Units List

Length

• Ao - angstrom

• a_0 - Bohr radius

• au - astronomical unit

• ch - chain

• ft - foot

• ft_US - U.S. survey foot

• ftm - fathom

• fur - furlong

• gg - gauge

• hand - hand

• in - inch

• inm - international nautical mile

• land - league

• li - link

• line - line

• ly - light-year

• m - meter (SI)

• mi - mile

• mi_US - U.S. survey mile

• mil - mil

• nmile - British imperial nautical mile

• pc - parsec

• pica - pica

• pica_US - U.S. customary pica

• pt - point

• pt_US - U.S. customary point

• rod - rod

• span - span

• xu - x unit

• xu_Cu - x unit (copper)

• xu_Mo - x unit (molybdenum)

• yd - yard

Mass

• Mt - metric megaton

• ct - carat

• cwt - U.S. customary short hundredweight

• cwt_UK - British imperial short hundredweight

• dalton - atomic mass constant

• dr - dram

• g - gram (SI)

• gr - grain

• hyl - hyl

• kt - metric kiloton

• lbm - pound mass

• m_e - electron mass

• m_p - proton mass

• m_u - atomic mass constant

• oz - ounce

• quarter - quarter

• slug - slug

• stone - stone

• t - metric ton

• tn - U.S. customary short ton

• ton_UK - British imperial ton

Time

• d - day

• fortnight - 14 days

• h - hour

• min - minute

• month_30 - 30-day month

• s - second (SI)

• week - 7-day week

• year_360 - 360-day year

• year_Julian - Julian year

• year_Gregorian - Gregorian year

Absorbed Dose or Dose Equivalent

• Gy - gray (SI)

• Rad - absorbed radiation dose

• Sv - sievert (SI)

• rem - roentgen equivalent man

Acceleration

• Gal - gal

• g_n - earth gravitational acceleration

Activity

• Bq - becquerel (SI)

• Ci - curie

Amount of Substance

• item - number of items

• mol - mole (SI)

• molecule - number of molecules

Angular Momentum

• Nms - newton meter second

• h_bar - reduced Planck constant

• h_c - Planck constant

Area

• a - are

• ac - acre

• ac_US - U.S. survey acre

• barn - barn

• circ_mil - circular mil

• circ_inch - circular inch

• ha - metric hectare

• ha_US - U.S. survey hectare

• ro - rood

• twp - township

Capacitance

• F - farad (SI)

• abF - abfarad

• statF - statfarad

Capacitance Per Length

• e_0 - vacuum electric permittivity or electric constant

Catalytic Activity

• kat - katal (SI)

Conductance

• G_0 - conductance quantum

• S - siemens (SI)

• abS - absiemens

• statS - statsiemens

Data Transfer Rate

• Bd - baud

• bps - bit per second

Digital Information

• B - byte

• bit - basic unit of information

Dose Equivalent

• Sv - sievert (SI)

Dynamic Viscosity

• P - poise

• reyn - reynolds

Electric Charge

• C - coulomb (SI)

• Fr - franklin

• abC - abcoulomb

• e - elementary charge

• statC - statcoulomb

Electric Charge Per Mole of Electrons

• F_c - Faraday constant

Electric Current

• A - ampere (SI)

• Bi - biot

• abA - abampere

• statA - statampere

Electric Dipole Moment

• debye - debye

Electric Potential or Electromotive Force

• V - volt (SI)

• abV - abvolt

• statV - statvolt

Energy or Work or Heat

• Btu_IT - British thermal unit (International Table)

• Btu_th - British thermal unit (thermochemical)

• E_h - Hartree energy

• J - joule (SI)

• Nm - newton meter

• Wh - watt hour

• Ws - watt second

• cal_4 - calorie (4 degree Celsius)

• cal_20 - calorie (20 degree Celsius)

• cal_15 - calorie (15 degree Celsius)

• cal_IT - calorie (International Table)

• cal_th - calorie (thermochemical)

• cal_mean - calorie (mean)

• eV - electronvolt

• erg - erg

• kcal_4 - kilocalorie (4 degree Celsius)

• kcal_20 - kilocalorie (20 degree Celsius)

• kcal_15 - kilocalorie (15 degree Celsius)

• kcal_IT - kilocalorie (International Table)

• kcal_th - kilocalorie (thermochemical)

• kcal_mean - kilocalorie (mean)

• kpm - kilopond meter

• therm - therm

Energy Per Temperature

• k_B - Boltzmann constant

Energy Per Temperature Per Amount of Substance

• R_c - molar gas constant

European Currency

• Cent - cent

• EUR - Euro

Flow Rate

• gpm - U.S. customary gallon per minute

• gpm_UK - British imperial gallon per minute

• lpm - liter per minute

Force

• N - newton (SI)

• dyn - dyne

• kgf - kilogram force

• kip - kip

• kp - kilopond

• lbf - pound force

• ozf - ounce force

• p - pond

• pdl - poundal

• sn - sthene

• tonf - short ton force

Former European Currency

• ATS - Austrian Schilling

• BEF - Belgian Franc

• DM - German Mark

• ESP - Spanish Peseta

• FIM - Finnish Markka

• FRF - French Franc

• IEP - Irish Pound

• ITL - Italian Lire

• LUF - Luxembourgian Franc

• NLG - Dutch Gulden

• PTE - Portuguese Escudo

Frequency

• Hz - hertz (SI)

• dv_Cs - caesium hyperfine transition frequency

Frequency of Rotation

• rpm - revolution per minute

• rps - revolution per second

Fuel Consumption

• l_100km - liter per 100 km

Fuel Economy

• mpg - mile per gallon

Gravity

• G_c - Newtonian constant of gravitation

Illuminance

• lx - lux (SI)

• nx - nox

• ph - phot

Inductance

• H - henry (SI)

• abH - abhenry

• statH - stathenry

Inductance Per Length

• mu_0 - vacuum magnetic permeability

Intensity Per Fourth Power of Absolute Temperature

• sigma - Stefan–Boltzmann constant

Ionising Dosage

• R - roentgen

Kinematic Viscosity

• St - stokes

• newt - newt

Luminance

• asb - apostilb

• sb - stilb

Luminous Efficacy

• K_cd - luminous efficacy of a defined visible radiation

Luminous Flux

• lm - lumen (SI)

Luminous Intensity

• cd - candela (SI)

• cp - candlepower

Magnetic Field Strength

• Oe - oersted

Magnetic Flux

• Mx - maxwell

• Wb - weber (SI)

• abWb - abweber

• statWb - statweber

• phi_0 - magnetic flux quantum

Magnetic Flux Density

• G - gauss

• T - tesla (SI)

• abT - abtesla

• statT - stattesla

Magnetic Force

• Gb - gilbert

Mass Per Length

• den - denier

• tex - filament tex

Particle Per Amount of Substance

• N_A - Avogadro constant

Plane Angle

• arcsec - arcsecond

• arcmin - arcminute

• deg - degree

• rad - radian (SI)

• rev - revolution

Power or Heat Flow Rate

• HP_E - electrical horsepower

• HP_I - mechanical horsepower

• HP_UK - British imperial horsepower

• HP_DIN - metric horsepower (DIN 66036)

• PS_SAE - net horsepower (SAE J1349)

• PS_DIN - horsepower (DIN 70020)

• W - watt (SI)

• poncelet - poncelet

Pressure or Stress

• Ba - barye

• Pa - pascal (SI)

• Torr - torr

• at - technical atmosphere

• atm - standard atmosphere

• bar - bar

• cmHg - centimeter of mercury (conventional)

• cmH2O - centimeter of water (conventional)

• ftHg - foot of mercury (conventional)

• ftH2O - foot of water (conventional)

• inHg - inch of mercury (conventional)

• inH2O - inch of water (conventional)

• ksf - kip per square foot

• ksi - kip per square inch

• mH2O - meter of water (conventional)

• mHg - meter of mercury (conventional)

• mmHg - millimeter of mercury (conventional)

• mmH2O - millimeter of water (conventional)

• psf - pound force per square foot

• psi - pound force per square inch

• pz - pieze

Radiation

• lan - langley

Reciprocal Length

• kayser - kayser

• R_inf - Rydberg constant

Refractive Power of Lenses

• dpt - diopter

Resistance

• Ohm - ohm (SI)

• abOhm - abohm

• statOhm - statohm

Solid Angle

• sr - steradian (SI)

Substance Per Volume

• molarity - molarity

Temperature

• Celsius - degree Celsius (SI)

• Fahrenheit - degree Fahrenheit

• K - kelvin (SI)

• Rankine - degree Rankine

• Reaumur - degree Reaumur

Velocity

• Kyne - kyne

• c_0 - speed of light in vacuum

• fpm - foot per minute

• fps - foot per second

• kmh - kilometer per hour

• knot_UK - British imperial knot

• kts - international knot

• mach - speed of sound

• mph - mile per hour

Volume

• barrel - barrel

• bbl - U.S. customary dry barrel

• bu_UK - British imperial bushel

• chaldron - chaldron

• dry_bu - U.S. customary dry bushel

• dry_gal - U.S. customary dry gallon

• dry_pk - U.S. customary dry peck

• dry_pt - U.S. customary dry pint

• dry_qt - U.S. customary dry quart

• fldr - U.S. customary fluid dram

• fldr_UK - British imperial fluid drachm (dram)

• floz - U.S. customary fluid ounce

• floz_UK - British imperial fluid ounce

• gal - U.S. customary liquid gallon

• gal_UK - British imperial gallon

• gill - U.S. customary fluid gill

• gill_UK - British imperial gill

• igal - British imperial gallon

• l - liter

• liq_pt - U.S. customary liquid pint

• liq_qt - U.S. customary liquid quart

• minim - U.S. customary minim

• minim_UK - British imperial minim

• pint - U.S. customary liquid pint

• pint_UK - British imperial pint

• pk_UK - British imperial peck

• pottle - British imperial pottle

• qt_UK - British imperial quart

• quart - U.S. customary liquid quart

SI Unit Prefixes List

SI unit prefixes in Symbolic Math Toolbox. Every unit marked by SI in the units list accepts SI prefixes. For example, m accepts nm, mcm, mm, cm, km and so on.

Prefix	Input Forms	Example using meters u.m where u = symunit
Yotta 1024	Y, yotta	u.Ym, u.yottam
Zetta 1021	Z, zetta	u.Zm, u.zettam
Exa 1018	E, exa	u.Em, u.exam
Peta 1015	P, peta	u.Pm, u.petam
Tera 1012	T, tera	u.Tm, u.teram
Giga 109	G, giga	u.gigam, u.Gm
Mega 106	M, mega	u.Mm, u.megam
Kilo 103	k, kilo	u.km, u.kilom
Hecto 102	h, hecto	u.hm, u.hectom
Deka 101	da, deka, deca	u.dam, u.dekam, u.decam
Deci 10–1	d, deci	u.dm, u.decim
Centi 10–2	c, centi	u.cm, u.centim
Milli 10–3	m, milli	u.mm, u.millim
Micro 10–6	mc, micro, u	u.mcm, u.microm, u.um
Nano 10–9	n, nano	u.nm, u.nanom
Pico 10–12	p, pico	u.pm, u.picom
Femto 10–15	f, femto	u.fm, u.femtom
Atto 10–18	a, atto	u.am, u.attom
Zepto 10–21	z, zepto	u.zm, u.zeptom
Yocto 10–24	y, yocto	u.ym, u.yoctom

Unit Systems List

Available unit systems in Symbolic Math Toolbox are listed below. For details, see Unit Conversions and Unit Systems.

Unit System	Base Units	Derived Units
SI units ('SI')	baseUnits('SI') ans = [ [kg], [s], [m], [A], [cd], [mol], [K]]	derivedUnits('SI') ans = [ [F], [C], [S], [H], [V], [J], [N], [lx], [lm], [Wb], [W],... [Pa], [Ohm], [T], [Gy], [Bq], [Sv], [Hz], [kat], [rad], [sr],... [Celsius]]
CGS units ('CGS')	baseUnits('CGS') ans = [ [cm], [g], [s], [K]]	derivedUnits('CGS') ans = [ [Gal], [dyn], [erg], [Ba], [P], [St], [Celsius]]
US units ('US')	baseUnits('US') ans = [ [lbm], [s], [ft], [A], [cd], [mol], [K]]	derivedUnits('US') ans = [ [F], [C], [S], [H], [V], [Btu_IT], [lbf], [lx], [lm], [Wb],... [W], [psf], [Ohm], [T], [Gy], [Bq], [Sv], [Hz], [kat], [rad],... [sr], [Fahrenheit], [gal]]
Electrostatic units ('ESU')	baseUnits('ESU') ans = [ [cm], [g], [s], [K], [statC]]	derivedUnits('ESU') ans = [ [Gal], [dyn], [erg], [Ba], [P], [St], [Celsius], [statA], [statF],... [statH], [statS], [statOhm], [statT], [statV], [statWb]]
Gaussian units ('GU')	baseUnits('GU') ans = [ [cm], [g], [s], [K], [Fr]]	derivedUnits('GU') ans = [ [Gal], [dyn], [erg], [Ba], [P], [St], [Celsius], [G],... [Bi], [Mx], [Oe], [debye]]
Electromagnetic units ('EMU')	baseUnits('EMU') ans = [ [cm], [g], [s], [K], [abA]]	derivedUnits('EMU') ans = [ [Gal], [dyn], [erg], [Ba], [P], [St], [Celsius], [abC],... [abF], [abH], [abS], [abOhm], [abT], [abV], [abWb]]

Defining Constants of SI Units

In 2019, the seven SI base units were redefined in terms of seven physical constants that have exact values. These constants are represented by symbolic units as listed below.

Physical Constants	Symbolic Values
Caesium-133 hyperfine transition frequency (dv_Cs)	u = symunit; unitConvert(u.dv_Cs,'SI') ans = 9192631770*(1/[s])
Speed of light (c_0)	u = symunit; unitConvert(u.c_0,'SI') ans = 299792458*([m]/[s])
Planck constant (h_c)	u = symunit; unitConvert(u.h_c,'SI') ans = (132521403/200000000000000000000000000000000000000000)*(([kg]*[m]^2)/[s])
Elementary charge (e)	u = symunit; unitConvert(u.e,'SI') ans = (801088317/5000000000000000000000000000)*[A]*[s]
Boltzmann constant (k_B)	u = symunit; unitConvert(u.k_B,'SI') ans = (1380649/100000000000000000000000000000)*(([kg]*[m]^2)/([K]*[s]^2))
Avogadro constant (N_A)	u = symunit; unitConvert(u.N_A,'SI') ans = 602214076000000000000000*(1/[mol])
Luminous efficacy of a 540 THz radiation (K_cd)	u = symunit; unitConvert(u.K_cd,'SI') ans = 683*(([cd]*[s]^3*[sr])/([kg]*[m]^2))