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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:


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


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


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


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)


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
/ kohm kiloohm
/ Mohm megaohm
/ Gohm gigaohm
S S siemens
Wb Wb weber
T T tesla
H H henry


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


Unit Variable name Description
N N newton


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


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


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


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


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


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


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


Unit Variable name Description
mol mol mole


Unit Variable name Description
K K kelvin
celsius degree celsius
fahrenheit degree fahrenheit


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)


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


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");

// 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, quantity(300, "dpi")), NONE)
// [ 2480.314960629921, 3507.8740157480315 ]

// alternatively, dimensionless units can be deref'd directly
mul(A4, quantity(300, "dpi")).deref()
// [ 2480.314960629921, 3507.8740157480315 ]

When combining different quantities, their units do not need to be the same:

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


The following constants are provided (more to come):

Var name Unit Comment
DIN_A0 ... DIN_A8 2d vector of mm Paper sizes(1)
GRAVITATION kg-1·m3·s-2 Gravitational constant
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
COPPER kg/m3
GLASS kg/m3
GOLD kg/m3
ICE kg/m3
IRON kg/m3
NYLON kg/m3
SAND kg/m3
SILVER kg/m3
STEEL kg/m3
WATER kg/m3
WOOD kg/m3


BETA - possibly breaking changes forthcoming

Search or submit any issues for this package


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: 4.77 KB



Generated API docs


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

  title = "@thi.ng/units",
  author = "Karsten Schmidt",
  note = "https://thi.ng/units",
  year = 2021


© 2021 - 2024 Karsten Schmidt // Apache License 2.0

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