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))

External Websites

The International System of Units (SI)