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# `unit`

Units of measurement

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

For units in MATLAB®, see Units of Measurement Tutorial.

## Syntax

```unit::n
```

## Description

`unit::n` represents the unit of measurement `n`, where `n` follows commonly used names. For example, the units `unit::m`, `unit::meter`, and `unit::metre` all represent the physical unit meter. These `unit` objects are domain objects of domain type `unit`. You can use these units in arithmetical expressions as symbolic identifiers. For example, `3*unit::m^2`. You must use units consistently in expressions, and you must specify units for unknown variables so that the variables themselves are dimensionless. For details, see Example 3.

Expressions containing units are not combined or simplified automatically. Use `simplify` or `Simplify` to simplify expressions containing units. Use `unit::convert` to convert between units.

For a list of all implemented units, see List of Units.

## Examples

### Example 1

Create an expression using different units of length. The common names of units work as expected.

`27*unit::cm + 30*unit::mm`

Because MuPAD® does not simplify this expression automatically, use the `simplify` function to simplify the expression.

`simplify(%)`

Simplify an expression involving several different units.

`simplify(1234*unit::g + 1.234*unit::kg*unit::m^2/unit::inch^2)`

### Example 2

Convert between any two units using `unit::convert`.

Convert ounce to kilograms. `unit::convert` returns an exact conversion. Use `float` to obtain a floating-point result.

`unit::convert(unit::ounce, unit::kilogram)`

`float(%)`

Use `unit::convert` to convert between units that are not of the same type. For example, convert Newton-meter, which is a unit of torque, to Watts, which is a unit of power.

`unit::convert(1.23*unit::Nm, unit::W)`

Rewrite the target unit, Newton-meter, in terms of a composite expression in grams, centimeters, and milliseconds.

`unit::convert(unit::Nm, unit::g*unit::cm^2/unit::ms^2)`

Try to convert kg inch2/mm to cm. `unit::convert` has no effect on units it cannot convert.

`unit::convert(1.23*unit::kg*unit::inch^2/unit::mm, unit::cm)`

### Example 3

For numerical computations, explicitly specify units such that the variables themselves are dimensionless. If you apply units inconsistently, you might not get the desired result.

Demonstrate this issue by omitting the unit for an unknown variable in an expression. Substitute for the variable with a number and evaluate the expression using `float`. The `float` function cannot evaluate the expression.

```L := 1*unit::m: y := 0.1*unit::m: f := y - x*cos(L/x): float(subs(f, x = 1/PI))```

Evaluate the expression by specifying units consistently. Now, the unknown variable `x` is dimensionless.

```f := y - x*unit::m*cos(L/(x*unit::m)): float(subs(f, x = 1/PI))```

### Example 4

Add new units using `unit::newUnit`.

Add a velocity unit to the `unit` domain.

`unit::newUnit(SpeedOfLight = 300000*unit::km/unit::s)`

You can use the unit `unit::SpeedOfLight` like any other unit. Use `unit::SpeedofLight` to define another velocity unit.

`unit::newUnit(Warp9 = 1.516*unit::SpeedOfLight)`

Convert 123.4 miles per hour into the new speed units.

`unit::convert(123.4*unit::mile/unit::hour, unit::SpeedOfLight)`

`unit::convert(123.4*unit::mile/unit::hour, unit::Warp9)`

### Example 5

Use the conversion methods to convert between different systems of units.

Use `unit::convert2SIunits` to convert a mass expressed in non-metric units to SI units.

`mass := 2*unit::cal*unit::ms^2/unit::inch^2 - 45*unit::carat`

`unit::convert2SIunits(mass)`

`delete mass:`

Convert a temperature of `20` degrees Celsius into the Fahrenheit temperature scale using `unit::Celsius2Fahrenheit`.

`unit::Celsius2Fahrenheit(20)`

### Example 6

You can use most functions such as `diff`, `factor`, and `normal` with `unit`. These functions treat units like ordinary symbolic identifiers.

Use `diff`, `factor`, and `normal` with `unit`.

`diff(x/unit::m*exp(-x^2/unit::m^2), x)`

`factor(%)`

`normal((4*unit::m^2 - a^2*unit::m^2)/(2*unit::m - a*unit::m))`

## Parameters

 `n` The name of the physical unit. Expand the following list for all implemented units. You can represent a unit by multiple names. For example, you can represent a meter by `unit::m`, `unit::meter`, and `unit::metre`.

## List of Units

expand all

• `am`, `f` (= `Fermi` = `fermi`), `XU` (= `Xu` = `xu` = `XE`), `pm`

• `Ao` (= `Angstroem` = `angstroem` = `Angstrom` = `angstrom`)

• `nm` (= `nanometer`)

• `My` (= `micron` = `micrometer`)

• `mm` (= `millimeter`), `cm` (= `centimeter`)

• `dm` (= `decimeter`), `m` (= `meter`)

• `dam`, `hm`, `km` (= `kilometer`), `Mm`, `Gm`, `Tm`, `Pm`, `Em`

• `pt` (= `point`), `inch`

• `ft` (= `foot`), `ft_US` (= `foot_US`)

• `yd` (= `yard`), `mile`, `nmile`, `inm` (= `INM`)

• `AU` (= `AE`), `ly` (= `lightyear` = `Lj` = `lj`), `pc` (= `parsec`)

• `ch`, `fm` (= `fathom`), `fur` (= `furlong`), `gg`, `hand`

• `li` (= `link`), `line`, `mil`, `rod` (= `perch` = `pole`), `span`

• `ag`, `fg`, `pg`, `ng`, `mcg` (= `mcgram` = `microgram`)

• `mg` (= `milligram`), `cg`, `dg`, `g` (= `gram`), `hg`

• `kg` (= `kilogram`), `Mg`, `Gg`, `Tg`, `Pg`, `Eg`

• `t`, `kt`, `Mt`, `ct` (= `carat` = `Kt` = `Karat` = `karat`)

• `oz` (= `ounce`)

• `lb` (= `pound`), `stone`, `cwt` (= `sh_cwt`)

• `cwt_UK` (= `long_cwt` = `gross_cwt`), `tn` (= `ton` = `short_ton`), `ton_UK`

• `long_ton` (= `gross_ton`), `slug`, `gr`, `dr`, `quarter`, `cental`

• `as`, `fs`, `ps`, `ns` (= `nsec` = `nanosec` = `nanosecond`)

• `mcsec` (= `mcsecond` = `microsec` = `microsecond`)

• `ms` (= `msec` = `millisec` = `millisecond`), `cs`, `ds`

• `s` (= `sec` = `second`), `das`, `hs`, `ks`

• `Ms`, `Gs`, `Ts`, `Es`, `Ps`, `min` (= `minute` = `Minute`)

• `h` (= `hour`), `d` (= `day`)

• `week`, `month`

• `year`

• `K` (= `kelvin` = `Kelvin`), `Fahrenheit` (= `fahrenheit`), `Celsius` (= `celsius`)

• `Rankine` (= `rankine`), `Reaumur` (= `reaumur`)

• `degree` , `rad` (= `radian`)

• `sr` (= `steradian`)

• `bit` (= `Bit`), `kbit` (= `kBit`), `Mbit` (= `MBit`), `Gbit` (= `GBit`), `Tbit` (= `TBit`)

• `byte` (= `Byte`), `kbyte` (= `kByte`), `Mbyte` (= `MByte`), `Gbyte` (= `GByte`)

• `Tbyte` (= `TByte`)

• `bps`

• `Bd` (= `Baud` = `baud`)

• `knot`, `knot_UK`, `mach`

• `Gal`, `gn`

• `aN`, `fN`, `nN`, `pN`, `mcN`, `mN`, `cN`, `dN`, `N` (= `Newton` = `newton`), `daN`, `hN`, `kN`, `MN`, `GN`

• `TN`, `PN`, `EN`, `p` (= `pond` = `Pond`), `kp` (= `kilopond` = `Kilopond`), `dyn`, `pdl`, `lbf`

• `ozf`, `tonf`

• `aNm`, `fNm`, `pNm`, `nNm`, `mcNm`, `mNm`, `cNm`, `dNm`, `Nm` (= `Newtonmeter` = `newtonmeter`)

• `daNm`, `hNm`, `kNm`, `MNm`, `GNm`, `TNm`, `PNm`, `ENm`, `kpm`

• `aNms`, `fNms`, `pNms`, `nNms`, `mcNms`, `mNms`, `cNms`, `dNms`

• `Nms` (= `Newtonmetersec` = `newtonmetersec`)

• `daNms`, `hNms`, `kNms`, `MNms`, `GNms`, `PNms`, `ENms`, `TNms`

• `aJ` (= `aWs`), `fJ` (= `fWs`), `pJ` (= `pWs`), `nJ` (= `nWs`), `mcJ` (= `mcWs` = `microWs`)

• `mJ` (= `mJoule` = `mjoule` = `mWs`), `cJ` (= `cWs`), `dJ` (= `dWs`)

• `J` (= `Joule` = `joule` = `Ws`), `daJ` (= `daWs`), `hJ` (= `hWs`)

• `kJ` (= `kJoule` = `kjoule` = `kWs`), `MJ` (= `MJoule` = `Mjoule` = `MWs`)

• `GJ` (= `GWs`), `TJ` (= `TWs`), `PJ` (= `PWs`), `EJ` (= `EWs`), `Wh`, `kWh`, `MWh`, `GWh`

• `cal` (= `Calory` = `calory`), `kcal`, `aeV`, `feV`, `peV`, `neV`, `mceV`, `meV`, `ceV`, `deV`, `eV`

• `daeV`, `heV`, `keV`, `MeV`, `GeV`, `TeV`, `PeV`, `EeV`, `PSh`, `erg`, `Btu`, `therm`

• `aW`, `fW`, `pW`, `nW`, `mcW` (= `mcWatt` = `mcwatt` = `microW` = `microWatt` = `microwatt`)

• `mW` (= `mWatt` = `mwatt`), `cW`, `dW`, `W` (= `Watt` = `watt`), `daW`, `hW`

• `kW` (= `kWatt` = `kwatt`), `MW` (= `MWatt` = `Mwatt`), `GW` (= `GWatt` = `Gwatt`)

• `TW`, `PW`, `EW`, `hp` (= `bhp`)

• `aHz`, `fHz`, `pHz`, `nHz`, `mcHz`, `mHz`, `cHz`, `dHz`, `Hz` (= `Hertz` = `hertz`), `daHz`, `hHz`

• `kHz` (= `kHertz` = `khertz`), `MHz` (= `MHertz` = `Mhertz`)

• `GHz` (= `GHertz` = `Ghertz`), `THz`, `PHz`, `EHz`

• `aPa`, `fPa`, `pPa`, `nPa`, `mcPa`, `mPa`, `cPa`, `dPa`, `Pa` (= `Pascal` = `pascal`)

• `daPa`, `hPa` (= `hPascal` = `hpascal`), `kPa`, `MPa`, `GPa`, `TPa`, `PPa`, `EPa`

• `mcbar` (= `mcBar` = `microbar` = `microBar`), `mbar` (= `mBar`), `bar` (= `Bar`)

• `kbar` (= `kBar`), `at` (= `ata` = `atu`), `atm`, `mmH2O` (= `mmWS`), `mH2O` (= `mWS`)

• `inH2O`, `ftH2O`, `mmHg`, `mHg`, `inHg`, `psi`, `Torr`

• `a` (= `are` = `Ar`), `ac` (= `acre`), `b` (= `barn`), `ha` (= `hectare`)

• `ro` (= `rood`), `township`, `circ_mil`, `circ_inch`

• `al`, `fl`, `pl`, `nl`, `mcl`, `ml`, `cl`, `dl`, `l` (= `Liter` = `liter` = `Litre` = `litre`), `dal`

• `hl`, `kl`, `Ml`, `Gl`, `Tl`, `Pl`, `El`, `gal` (= `gallon`), `gal_UK`, `barrel`, `bu_UK`, `chaldron`

• `pottle`, `pint_UK`, `pk_UK`, `qt_UK`, `gill`, `gill_UK`, `floz`, `floz_UK`, `fldr`, `fldr_UK`

• `minim`, `minim_UK`, `liq_qt`, `liq_pt`, `dry_bu`, `dry_pk`, `bbl`, `dry_gal`, `dry_qt`, `dry_pt`

• `cent` (= `Cent`), `EUR` (= `EURO` = `Euro`), `ATS`, `DEM` (= `DM`), `BEF`, `ESP`, `FIM`, `FRF`, `LUF`

• `NLG`, `PTE`, `IEP`, `ITL`

• `fmol`, `amol`, `pmol`, `nmol`, `mcmol` (= `mcMol` = `micromol` = `microMol`)

• `mmol` (= `mMol`), `cmol`, `dmol`, `mol` (= `Mol`), `damol`, `hmol`, `kmol` (= `kMol`), `Mmol`

• `Gmol`, `Tmol`, `Pmol`, `Emol`

• `aA`, `fA`, `pA`, `nA` (= `nAmpere` = `nampere`)

• `mcA` (= `microA` = `microAmpere` = `microampere`), `mA` (= `mAmpere` = `mampere`)

• `cA`, `dA`, `A` (= `ampere` = `Ampere`), `daA`, `hA`, `kA` (= `kAmpere` = `kampere`), `MA`, `GA`

• `TA`, `PA`, `EA`, `Bi` (= `Biot` = `biot`), `Gb` (= `Gilbert` = `gilbert`)

• `aV`, `fV`, `pV`, `nV` (= `nanoV` = `nVolt` = `nvolt`)

• `mcV` (= `microV` = `mcVolt` = `mcvolt`), `mV` (= `mVolt` = `mvolt`), `cV`, `dV`

• `V` (= `Volt` = `volt`), `daV`, `hV`

• `kV` (= `kVolt` = `kvolt`)

• `MV` (= `MVolt` = `Mvolt`), `GV` (= `GVolt` = `Gvolt`), `TV`, `PV`, `EV`

• `aOhm` (= `aohm`), `fOhm` (= `fohm`), `pOhm` (= `pohm`), `nOhm` (= `nohm`)

• `mcOhm` (=`mcohm` = `microOhm` = `microohm`)

• `mOhm` (= `mohm` = `milliOhm` = `milliohm`), `dOhm` (= `dohm`), `cOhm` (= `cohm`)

• `Ohm` (= `ohm`), `daOhm` (= `daohm`), `hOhm` (= `hohm`), `kOhm` (= `kohm`), `MOhm` (= `Mohm`)

• `GOhm` (= `Gohm`), `TOhm` (= `Tohm`), `POhm` (= `Pohm`), `EOhm` (= `Eohm`)

• `aC`, `fC`, `pC`, `nC`, `mcC`, `mC`, `cC`, `dC`, `C` (= `Coulomb` = `coulomb`), `daC`, `hC`, `kC`, `MC`, `GC`, `TC`

• `PC`, `EC`

• `aF`, `fF`, `pF` (= `pFarad` = `pfarad`), `nF` (= `nFarad` = `nfarad`)

• `mcF` (= `mcFarad` = `mcfarad` = `microF` = `microFarad` = `microfarad`)

• `mF` (= `mFarad` = `mfarad`), `cF`, `dF`, `F` (= `Farad` = `farad`), `daF`, `hF`

• `kF` (= `kFarad` = `kfarad`) , `MF`, `GF`, `TF`, `PF`, `EF`

• `S` (= `Siemens` = `siemens`)

• `H` (= `Henry` = `henry`)

• `T` (= `Tesla` = `tesla`), `G` (= `Gauss` = `gauss`)

• `Wb` (= `Weber` = `weber`), `M` (= `Maxwell` = `maxwell`)

• `Oe` (= `Oersted` = `oersted`)

• `Gb` (= `Gilbert` = `gilbert`)

• `fcd`, `acd`, `pcd`, `ncd`, `mccd`, `mcd`, `ccd`, `dcd`, `cd` (= `candela` = `Candela`), `dacd`, `hcd`

• `kcd`, `Mcd`, `Gcd`, `Tcd`, `Pcd`, `Ecd`, `HK`, `IK`

• `sb` (= `stilb`), `asb` (= `apostilb`)

• `lm` (= `lumen`)

• `lx` (= `lux`), `ph` (= `phot`), `nx`

• `langley`

• `aBq`, `fBq`, `pBq`, `nBq`, `mcBq`, `mBq`, `cBq`, `dBq`, `Bq` (= `Becquerel` = `becquerel`), `daBq`

• `hBq`, `kBq`, `MBq`, `GBq`, `TBq`, `PBq`, `EBq`, `Ci` (= `Curie`)

• `aSv`, `fSv`, `pSv`, `nSv`, `mcSv`, `mSv`, `cSv`, `dSv`

• `Sv` (= `Sievert` = `sievert`), `daSv`, `hSv`, `kSv`, `MSv`, `GSv`, `TSv`, `PSv`, `ESv`

• `arem`, `frem`, `prem`, `nrem`, `mcrem`, `mrem`, `crem`, `drem`

• `rem` (= `Rem`), `darem`, `hrem`, `krem`, `Mrem`, `Grem`, `Trem`, `Prem`, `Erem`

• `aGy`, `fGy`, `pGy`, `nGy`, `mcGy`, `mGy`, `cGy`, `dGy`, `Gy` (= `Gray` = `gray`), `daGy`, `hGy`, `kGy`, `MGy`, `GGy`

• `TGy`, `PGy`, `EGy`, `rd`

• `R` (= `Roentgen`)

• `dpt` (= `diopter` = `dioptre`)

• `P` (= `Poise`)

• `St` (= `Stokes`)

• `tex`, `den` (= `denier`)

## Methods

expand all

`unit::convert(x, targetunit)` converts all units in the arithmetical expression `x` to the `targetunit` if possible. The `targetunit` can be a unit (such as `unit::m`) or an arithmetical expression (such as `unit::km/unit::s`). In the second case, `convert` rewrites `x` in terms of the units found in `targetunit`. See Example 2.

`unit::convert2SIunits(x)` rewrites all units in the arithmetical expression `x` in terms of corresponding SI base units. See Example 5.

`unit::display(x)` formats the displayed output of the arithmetical expression `x` such that the units appear as a separate factor at the end of each term.

`unit::findUnits(x)` returns the set of all units found in the arithmetical expression `x`.

`unit::newUnit(newname = f*oldunit)` creates a unit addressed by `unit::newname`. The name `newname` must be an identifier. The new unit is declared as a multiple `f` of one or more pre-existing units `oldunit`, where `f` is a number. See Example 4.

`unit::simplify(x)` combines all units of the same type in the arithmetical expression `x` to one unit of that type found in `x`. See Example 1.

The following methods convert a numeric temperature value to the same temperature in another temperature scale. The name of a method describes the temperature scales that the method converts between. For example, `Celsius2Fahrenheit` converts a temperature in Celsius to the same temperature in Fahrenheit. See Example 5.

• Celsius2Fahrenheit

• Celsius2Kelvin

• Celsius2Rankine

• Celsius2Reaumur

• Fahrenheit2Celsius

• Fahrenheit2Kelvin

• Fahrenheit2Rankine

• Fahrenheit2Reaumur

• Kelvin2Fahrenheit

• Kelvin2Celsius

• Kelvin2Rankine

• Kelvin2Reaumur

• Rankine2Fahrenheit

• Rankine2Kelvin

• Rankine2Celsius

• Rankine2Reaumur

• Reaumur2Fahrenheit

• Reaumur2Kelvin

• Reaumur2Rankine

• Reaumur2Celsius