mathjs/docs/units.md

Units

Math.js supports units. Units can be used to do calculations and to perform conversions.

API

Units can be created using the function math.unit. This function accepts either a single string argument containing a value and unit, or two arguments, the first being a numeric value and the second a string containing a unit. Most units support prefixes like k or kilo, and many units have both a full name and an abbreviation. The returned object is a Unit.

Syntax:

math.unit(value: number, plainUnit: string) : Unit
math.unit(unit: string) : Unit
math.unit(unit: Unit) : Unit

Example usage:

var a = math.unit(45, 'cm');        // Unit 450 mm
var b = math.unit('0.1 kilogram');  // Unit 100 gram
var c = math.unit('2 inch');        // Unit 2 inch

A Unit contains the following functions:

• clone(). Clone the unit, returns a new unit with the same parameters.
• equalBase(unit). Test whether a unit has the same base as an other unit: length, mass, etc.
• equals(unit). Test whether a unit equals an other unit. Units are equal when they have the same base and same value when normalized to SI units.
• in(plainUnit). Convert the unit to a specific prefix and unit. Returns a clone of the unit with a fixed prefix and unit.
• toNumber(plainUnit). Get the value of a unit when converted to the specified plain unit (a unit with optional prefix but without value).
• toString(). Get a string representation of the unit. The function will determine the best fitting prefix for the unit. The units value is rounded to a fixed precision. The precision is defined in the option math.options.precision.

var a = math.unit(55, 'cm');        // Unit 550 mm
var b = math.unit('0.1 kilogram');  // Unit 100 gram
var c = math.unit('2 inch');        // Unit 100 millimeter

var d = c.in('cm');                 // Unit 5.08 cm
b.toNumber('gram');                 // Number 100

c.equals(a);                        // false
c.equals(d);                        // true
c.equalBase(a);                     // true
c.equalBase(b);                     // false

d.toString();                       // String "5.08 cm"

Calculations

Basic operations add, subtract, multiply, and divide can be performed on units. Trigonometric functions like sin support units with an angle as argument.

var a = math.unit(45, 'cm');        // Unit 450 mm
var b = math.unit('0.1m');          // Unit 100 mm
math.add(a, b);                     // Unit 0.65 m
math.multiply(b, 2);                // Unit 200 mm

var c = math.unit(45, 'deg');       // Unit 45 deg
math.cos(c);                        // Number 0.7071067811865476

Reference

Units

Math.js comes with the following built-in units.

Base	Unit
Length	meter (m), inch (in), foot (ft), yard (yd), mile (mi), link (li), rod (rd), chain (ch), angstrom, mil
Surface	m2, sqin, sqft, sqyd, sqmi, sqrd, sqch, sqmil
Volume	m3, litre (L), cuin, cuft, cuyd, teaspoon, tablespoon
Liquid	volume minim (min), fluiddram (fldr), fluidounce (fldz), gill (gi), cup (cp), pint (pt), quart (qt), gallon (gal), beerbarrel (bbl), oilbarrel (obl), hogshead
Angles	rad, deg, grad, cycle
Time	second (s), seconds, minute, minutes, hour (h), hours, day, days
Mass	gram(g), tonne, ton, grain (gr), dram(dr), ounce (oz), poundmass (lbm), hundredweight (cwt), stick
Electric current	ampere (A)
Temperature	kelvin (K), celsius (degC), fahrenheit (degF), rankine (degR)
Amount of substance	mole (mol)
Luminous	intensity candela (cd)
Force	newton (N), poundforce (lbf)
Binary	bit (b), byte (B)

Prefixes

The following decimal prefixes are available.

Name	Abbreviation	Value
deca	da	1e1
hecto	h	1e2
kilo	k	1e3
mega	M	1e6
giga	G	1e9
tera	T	1e12
peta	P	1e15
exa	E	1e18
zetta	Z	1e21
yotta	Y	1e24

Name	Abbreviation	Value
deci	d	1e-1
centi	c	1e-2
milli	m	1e-3
micro	u	1e-6
nano	n	1e-9
pico	p	1e-12
femto	f	1e-15
atto	a	1e-18
zepto	z	1e-21
yocto	y	1e-24

The following binary prefixes are available. They can be used with units bit (b) and byte (B).

Name	Abbreviation	Value
kilo, kibi	k, Ki	1024
mega, mebi	M, Mi	1024^2
giga, gibi	G, Gi	1024^3
tera, tebi	T, Ti	1024^4
peta, pebi	P, Pi	1024^5
exa, exi	E, Ei	1024^6
zetta, zebi	Z, Zi	1024^7
yotta, yobi	Y, Yi	1024^8