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Note

This is one of 199 standalone projects, maintained as part of the @thi.ng/umbrella monorepo and anti-framework.

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About
- Unit definitions
- Predefined units
  - Acceleration
  - Angle
  - Area
  - Data
  - Density
  - Electric current
  - Energy
  - Force
  - Frequency
  - Length
  - Luminous intensity
  - Mass
  - Parts per notation
  - Power
  - Pressure
  - Speed
  - Substance
  - Temperature
  - Time
  - Volume
- Creating & deriving units
  - Using standard metric prefixes
  - Unit combinators
- Unit conversions
- Quantities
  - Constants
Status
Installation
Dependencies
API
Authors
License

About

Extensible SI unit creation, conversions, quantities & calculations (incl. ~170 predefined units & constants).

All unit definitions, quantities & conversions are based on the SI unit system & concepts described here:

The overall conversion approach is inspired & partially based on:

Unit definitions

Each unit is defined via a 7-dimensional vector representing individual exponents for each of the SI base unit dimensions, in order:

id	SI dimension	Base unit	Base unit symbol
0	mass	kilogram	kg
1	length	meter	m
2	time	second	s
3	current	ampere	A
4	temperature	kelvin	K
5	amount of substance	mole	mol
6	luminous intensity	candela	cd

Dimensionless units (e.g. radian, byte) are supported too and represented by a vector with all dimensions set to zero.

Additionally, we also define a scale factor and zero offset for each unit, with most dimensions' base units usually using a factor of 1 and no offset.

For example, here's how we can define kilograms and meters:

import { coherent, unit } from "@thi.ng/units";

// kilogram, SI dimension 0
const KG = coherent(0);
// { dim: [ 1, 0, 0, 0, 0, 0, 0 ], scale: 1, offset: 0, coherent: true }

// meters, SI dimension 1
const M = coherent(1);
// { dim: [ 0, 1, 0, 0, 0, 0, 0 ], scale: 1, offset: 0, coherent: true }

// kelvin, SI dimension 4 (here without syntax sugar)
const K = unit(4, 1, 0, true);
// { dim: [ 0, 0, 0, 0, 1, 0, 0 ], scale: 1, offset: 0, coherent: true }

// fahrenheit, SI dim 4 with custom scale factor and zero offset
const F = unit(4, 1 / 1.8, 459.67 / 1.8);
// { dim: [ 0, 0, 0, 0, 1, 0, 0 ],  scale: 0.5555, offset: 255.3722, coherent: false }

More complex units like electrical resistance (e.g. ohm) are based on more than a single dimension:

import { div, A, V } from "@thi.ng/units";

// ohm = volt / ampere
div(V, A)
// { dim: [ 1, 2, -3, -2, 0, 0,  0 ], scale: 1, offset: 0, coherent: true }

This dimension vector represents the unit definition for (see SI derived units):

Ω = kg⋅m²⋅s⁻³⋅A⁻²

Btw. The formatSI() function can be used to format a unit's dimension vector:

import { div, formatSI, A, V } from "@thi.ng/units";

formatSI(div(V, A));
// "kg·m2·s-3·A-2"

Predefined units

The following units are provided as "builtins", here grouped by dimension:

Acceleration

Unit name	Variable name	Description
`m/s2`	`m_s2`	meter per second squared
`ft/s2`	`ft_s2`	foot per second squared
`rad/s2`	`rad_s2`	radian per second squared
`g0`	`g0`	standard gravity

Angle

Unit name	Variable name	Description
`arcmin`	`arcmin`	arc minute
`arcsec`	`arcsec`	arc second
`deg`	`deg`	degree
`gon`	`gon`	gradian
`rad`	`rad`	radian
`sr`	`sr`	steradian
`turn`	`turn`	turn

Area

Unit name	Variable name	Description
`m2`	`m2`	square meter
`cm2`	`cm2`	square centimeter
`mm2`	`mm2`	square millimeter
`km2`	`km2`	square kilometer
`ha`	`ha`	hectar
`ac`	`ac`	acre
`sqin`	`sqin`	square inch
`sqft`	`sqft`	square foot
`sqmi`	`sqmi`	square mile

Data

Unit name	Variable name	Description
`bit`	`bit`	bit
`kbit`	`kbit`	kilobit
`Mbit`	`Mbit`	megabit
`Gbit`	`Gbit`	gigabit
`Tbit`	`Tbit`	terabit
`kibit`	`kibit`	kibibit (1024)
`Mibit`	`Mibit`	mebibit (1024)
`Gibit`	`Gibit`	gibibit (1024)
`Tibit`	`Tibit`	tebibit (1024)
`B`	`B`	byte (8 bit)
`kB`	`kB`	kilobyte (metric)
`MB`	`MB`	megabyte (metric)
`GB`	`GB`	gigabyte (metric)
`TB`	`TB`	terabyte (metric)
`PB`	`PB`	petabyte (metric)
`EB`	`EB`	exabyte (metric)
`KiB`	`KiB`	kibibyte (1024)
`MiB`	`MiB`	mebibyte (1024)
`GiB`	`GiB`	gibibyte (1024)
`TiB`	`TiB`	tebibyte (1024)
`PiB`	`PiB`	pebibyte (1024)
`EiB`	`EiB`	exbibyte (1024)

Density

Unit	Variable name	Description
`kg/m3`	`kg_m3`	density
`1/inch`	`dpi`	dots per inch

Electric current

Unit	Variable name	Description
`A`	`A`	ampere
`mA`	`mA`	milliampere
`mAh`	`mAh`	milliampere-hours
`C`	`C`	coulomb
`V`	`V`	volt
`mV`	`mV`	millivolt
`kV`	`kV`	kilovolt
`MV`	`MV`	megavolt
`F`	`F`	farad
`pF`	`pF`	picofarad
`µF`	`µF`	microfarad
`Ω`	`Ω` / `ohm`	ohm
`kΩ`	`kΩ` / `kohm`	kiloohm
`MΩ`	`MΩ` / `Mohm`	megaohm
`GΩ`	`GΩ` / `Gohm`	gigaohm
`S`	`S`	siemens
`Wb`	`Wb`	weber
`T`	`T`	tesla
`H`	`H`	henry

Energy

Unit	Variable name	Description
`J`	`J`	joule
`kJ`	`kJ`	kilojoule
`MJ`	`MJ`	megajoule
`GJ`	`GJ`	gigajoule
`cal`	`cal`	calorie
`kcal`	`kcal`	kilocalorie

Force

Unit	Variable name	Description
`N`	`N`	newton

Frequency

Unit	Variable name	Description
`Hz`	`Hz`	hertz
`kHz`	`KHz`	kilohertz
`MHz`	`MHz`	megahertz
`GHz`	`GHz`	gigahertz
`THz`	`THz`	terahertz
`rpm`	`rpm`	rotation per minute
`ω`	`ω` / `omega`	radian per second

Length

Unit name	Variable name	Description
`m`	`m`	meter
`Å`	`angstrom`	angstrom
`nm`	`nm`	nanometer
`µm`	`µm`	micrometer
`mm`	`mm`	millimeter
`cm`	`cm`	centimeter
`km`	`km`	kilometer
`au`	`au`	astronomical unit
`pc`	`pc`	parsec
`ly`	`ly`	light year
`in`	`in`	inch
`mil`	`mil` / `thou`	1/1000th inch
`ft`	`ft`	foot
`yd`	`yd`	yard
`mi`	`mi`	mile
`nmi`	`nmi`	nautical mile
`pica`	`pica`	pica
`point`	`point`	point

Luminous intensity

Unit	Variable name	Description
`cd`	`cd`	candela
`lm`	`lm`	lumen
`lx`	`lx`	lux

Mass

Unit name	Variable name	Description
`µg`	`µg`	microgram
`mg`	`mg`	milligram
`g`	`g`	gram
`kg`	`kg`	kilogram
`t`	`t`	tonne
`kt`	`kt`	kilotonne
`Mt`	`Mt`	megatonne
`Gt`	`Gt`	gigatonne
`lb`	`lb`	imperial pound
`st`	`st`	stone

Parts per notation

https://en.wikipedia.org/wiki/Parts-per_notation

Unit name	Variable name	Description
`%`	`percent`	part per hundred
`‰`	`permille`	part per thousand
`‱`	`permyriad`	part per ten thousand
`pcm`	`pcm`	part per hundred thousand
`ppm`	`ppm`	part per million
`ppb`	`ppb`	part per billion
`ppt`	`ppt`	part per trillion

Power

Unit name	Variable name	Description
`W`	`W`	watt
`mW`	`mW`	milliwatt
`kW`	`kW`	kilowatt
`MW`	`MW`	megawatt
`GW`	`GW`	gigawatt
`TW`	`TW`	terawatt
`Wh`	`Wh`	watt-hour
`kWh`	`kWh`	kilowatt-hour

Pressure

Unit name	Variable name	Description
`Pa`	`Pa`	pascal
`kPa`	`KPa`	kilopascal
`MPa`	`MPa`	megapascal
`GPa`	`GPa`	gigapascal
`at`	`at`	technical atmosphere
`atm`	`atm`	atmosphere
`bar`	`bar`	bar
`psi`	`psi`	pound per square inch

Speed

Unit	Variable name	Description
`m/s`	`m_s`	meter per second
`km/h`	`km_h`	kilometer per hour
`mph`	`mph`	mile per hour
`kn`	`kn`	knot

Substance

Unit	Variable name	Description
`mol`	`mol`	mole

Temperature

Unit	Variable name	Description
`K`	`K`	kelvin
`℃`	`celsius`	degree celsius
`℉`	`fahrenheit`	degree fahrenheit

Time

Unit	Variable name	Description
`s`	`s`	second
`ms`	`ms`	millisecond
`µs`	`µs`	microsecond
`ns`	`ns`	nanosecond
`min`	`min`	minute
`h`	`h`	hour
`d`	`d`	day
`week`	`week`	week
`month`	`month`	month (30 days)
`year`	`year`	year (365.25 days)

Volume

Unit	Variable name	Description
`m3`	`m3`	cubic meter
`mm3`	`mm3`	cubic millimeter
`cm3`	`cm3`	cubic centimeter
`km3`	`km3`	cubic kilometer
`l`	`l`	liter
`cl`	`cl`	centiliter
`ml`	`ml`	milliliter
`gal`	`gal`	imperial gallon
`pt`	`pt`	imperial pint
`fl oz`	`floz`	imperial fluid ounce
`us gal`	`us_gal`	US gallon
`us pt`	`us_pt`	US pint
`us cup`	`us_cup`	US cup
`us fl oz`	`us_floz`	US fluid ounce

Creating & deriving units

Using standard metric prefixes

Existing coherent units can be prefixed to produce derived versions:

import { prefix, Hz } from "@thi.ng/units";

// define micrometer (also available as preset)
prefix("µ", "m")
// { dim: [ 0, 1, 0, 0, 0, 0, 0 ], scale: 0.000001, offset: 0, coherent: false }

// define kKhz
prefix("k", Hz);
// { dim: [ 0, 0, -1, 0, 0, 0, 0 ], scale: 1000, offset: 0, coherent: false }

Unit combinators

The following combinators can be used to derive scaled and/or more complex units (or quantities) in multiple SI dimensions:

div(a, b): derives a new unit via the division of the given units
mul(a, b): derives a new unit as the product of the given units
pow(u, k): raises given unit to power k (e.g. meter ⇒ square meter)
reciprocal(u): Creates reciprocal of given unit (e.g. Hz ⇒ 1/second)

import { div, mul, pow, prefix, reciprocal, bit, m, s } from "@thi.ng/units";

// acceleration (meter per second squared)
const m_s2 = div(m, pow(s, 2));
// { dim: [ 0, 1, -2, 0, 0, 0,  0 ], scale: 1, offset: 0, coherent: false }

// define kilowatt-hour (also available as preset)
const kWh = mul(prefix("k","W"), "h");
// { dim: [ 1, 2, -2, 0, 0, 0, 0 ], scale: 3600000, offset: 0, coherent: false }

// define `word` as 16 bits
const word = mul(bit, 16);
// { dim: [ 0, 0, 0, 0, 0, 0, 0 ], scale: 16, offset: 0, coherent: false }

// Hz = 1/s
const Hz = reciprocal(s);
// { dim: [ 0, 0, -1, 0, 0, 0, 0 ], scale: 1, offset: 0, coherent: false }

Unit conversions

Units (and quantities) can be converted using convert(). Only units with compatible (incl. reciprocal) dimensions can be converted, otherwise an error will be thrown. On the other hand, all dimensionless units can be converted to other dimensionless units (even if it would be semantic nonsense).

Units can be specified in various ways:

import { convert, div, reciprocal, h, km_h, mph, yd } from "@thi.ng/units";

// convert from km/h to mph using unit names
convert(100, "km/h", "mph");
// 62.13711922373341

// or using predefined unit constants directly
convert(60, mph, km_h);
// 96.56063999999998

// or using anonymous units (meter/second ⇒ yard/hour)
convert(1, "m/s", div(yd, h));
// 3937.007874015749

// convert into opposite direction (meter/second  ⇒ second/meter)
convert(10, "m/s", reciprocal("m/s"));
// 0.1

Another example using dimensionless units (here angles, arc second ⇒ radian) to compute the distance of 10 arcsec on the earth surface (in meters):

import { convert, R } from "@thi.ng/units";

// earth radius in meters
// (also available as quantity EARTH_RADIUS, see section below)
const R = 6371000;

convert(10, "arcsec", "rad") * R;
// 308.87479623488537

Quantities

The library also supports defining quantities, i.e. certain finite amounts of a given unit. These can be a number or vector-based and can be used for calculations & conversions using the above mentioned polymorphic functions: div(), mul(), reciprocal() and convert().

Quantities are created via quantity() which acts as factory function for a thin Quantity class wrapper. The latter also implements the standard IDeref interface to obtain the unwrapped amount (though it only should be used for dimensionless quantities). Use convert() otherwise!

import { convert, div, quantity } from "@thi.ng/units";

// (also available as preset)
const speedOfLight = quantity(299792458, "m/s");

// compute wavelength of a WiFi signal in millimeters
convert(div(speedOfLight, quantity(2.4,"GHz")), "mm");
// 124.9135

Some examples using vector quantities:

import { convert, mul, quantity, NONE } from "@thi.ng/units";

// DIN A4 paper size (also available as preset)
const A4 = quantity([210, 297], "mm");
// (also available as preset)
const DPI_300 = quantity(300, "dpi");

// convert paper size to inches
convert(A4, "in");
// [ 8.2677, 11.6929 ]

// or calculate pixel dimensions @ 300 dpi
// the result of this product is dimensionless,
// so we use the NONE preset as target unit...
convert(mul(A4, DPI_300), NONE)
// [ 2480.314960629921, 3507.8740157480315 ]

// alternatively, dimensionless units can be deref'd directly
mul(A4, DPI_300).deref()
// [ 2480.314960629921, 3507.8740157480315 ]

When combining different quantities, their units do not need to be the same (but compatible):

import { convert, mul, quantity } from "@thi.ng/units";

// compute 10 mm x 2 inch and convert to square centimeter
convert(mul(quantity(10, "mm"), quantity(2, "in")), "cm2")
// 5.08

Constants

The following constants are provided (more to come):

Var name	Unit	Comment
`DIN_A0` ... `DIN_A8`	2d vector of `mm`	Paper sizes⁽¹⁾
`DPI_72` / `DPI_150` / `DPI_300` / `DPI_600`	dots per inch	Screen/print resolutions
`EARTH_GRAVITY`	`m/s`
`EARTH_CIRCUMFERENCE`	`m`
`EARTH_MASS`	`kg`
`EARTH_RADIUS`	`m`
`GRAVITATION`	`kg-1·m3·s-2`	Gravitational constant
`SPEED_OF_LIGHT`	`m/s`
`SPEED_OF_SOUND_IN_AIR`	`m/s`	at 20 ℃
`SPEED_OF_SOUND_IN_WATER`	`m/s`	at 20 ℃
`US_ANSI_A` ... `US_ANSI_E`	2d vector of `inch`	Paper sizes⁽¹⁾
`US_ARCH_A` ... `US_ARCH_E`	2d vector of `inch`	Paper sizes⁽¹⁾
`US_LETTER` / `US_HALF_LETTER`	2d vector of `inch`	Paper sizes⁽¹⁾
`US_LEGAL` / `US_JUNIOR_LEGAL`	2d vector of `inch`	Paper sizes⁽¹⁾

⁽¹⁾ - all paper sizes are also available as landscape presets (using _LANDSCAPE as suffix).

Densities of selected materials:

Var name	Unit
`AIR`	`kg/m3`
`ALUMINIUM`	`kg/m3`
`CONCRETE`	`kg/m3`
`COPPER`	`kg/m3`
`DIAMOND`	`kg/m3`
`GLASS`	`kg/m3`
`GOLD`	`kg/m3`
`ICE`	`kg/m3`
`IRON`	`kg/m3`
`NYLON`	`kg/m3`
`PLASTIC`	`kg/m3`
`PLATINUM`	`kg/m3`
`SAND`	`kg/m3`
`SALT_WATER`	`kg/m3`
`SILICON`	`kg/m3`
`SILVER`	`kg/m3`
`STEEL`	`kg/m3`
`TITANIUM`	`kg/m3`
`WATER`	`kg/m3`
`WOOD`	`kg/m3`

Status

BETA - possibly breaking changes forthcoming

Search or submit any issues for this package

Installation

yarn add @thi.ng/units

ESM import:

import * as units from "@thi.ng/units";

Browser ESM import:

<script type="module" src="https://esm.run/@thi.ng/units"></script>

JSDelivr documentation

For Node.js REPL:

const units = await import("@thi.ng/units");

Package sizes (brotli'd, pre-treeshake): ESM: 4.78 KB

Dependencies

Note: @thi.ng/api is in most cases a type-only import (not used at runtime)

API

Generated API docs

Authors

Karsten Schmidt

If this project contributes to an academic publication, please cite it as:

@misc{thing-units,
  title = "@thi.ng/units",
  author = "Karsten Schmidt",
  note = "https://thi.ng/units",
  year = 2021
}

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