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Units & Dimensions

Complete reference of built-in units grouped by physical dimension.

Base Dimensions

These are the fundamental SI base dimensions.

Length

Unit Shorthand Aliases Scalable
meter m m Yes
foot ft ft, feet No
inch in in, inches No
yard yd yd, yards No
mile mi mi, miles No

Mass

Unit Shorthand Aliases Scalable
gram g g Yes
kilogram kg kg No
pound lb lb, lbs No
ounce oz oz, ounces No

Time

Unit Shorthand Aliases Scalable
second s s, sec Yes
minute min min No
hour h h, hr No
day d d No

Temperature

Unit Shorthand Aliases Scalable
kelvin K K Yes
celsius degC degC No
fahrenheit degF degF No
rankine degR degR, R No
reaumur °Ré °Ré, degRe No

Electric Current

Unit Shorthand Aliases Scalable
ampere A A, I, amp Yes

Amount of Substance

Unit Shorthand Aliases Scalable
mole mol mol, n Yes

Luminous Intensity

Unit Shorthand Aliases Scalable
candela cd cd Yes
lumen lm lm Yes

Information

Unit Shorthand Aliases Scalable
bit b b, bits Yes
byte B B, bytes Yes

Derived Dimensions

Force

Unit Shorthand Aliases Scalable
newton N N Yes
pound_force lbf lbf No
kilogram_force kgf kgf No
dyne dyn dyn No

Energy

Unit Shorthand Aliases Scalable
joule J J Yes
calorie cal cal, calories No
btu BTU BTU No
watt_hour Wh Wh No
gray Gy Gy Yes
sievert Sv Sv Yes

Power

Unit Shorthand Aliases Scalable
watt W W Yes
horsepower hp hp No

Pressure

Unit Shorthand Aliases Scalable
pascal Pa Pa Yes
bar bar bar No
psi psi psi, lbf/in No
atmosphere atm atm No
torr Torr Torr No
millimeter_mercury mmHg mmHg No
inch_mercury inHg inHg No

Volume

Unit Shorthand Aliases Scalable
liter L L, l Yes
gallon gal gal, gallons No

Frequency

Unit Shorthand Aliases Scalable
hertz Hz Hz Yes
becquerel Bq Bq Yes

Radiation Exposure

Unit Shorthand Aliases Scalable
coulomb_per_kilogram C/kg C/kg No
roentgen R_exp R_exp No

Electrical

Unit Shorthand Aliases Dimension Scalable
volt V V voltage Yes
ohm ohm ohm resistance Yes
farad F F capacitance Yes
coulomb C C charge Yes
siemens S S conductance Yes
henry H H inductance Yes
weber Wb Wb magnetic_flux Yes
tesla T T magnetic_flux_density Yes
international_ampere A_int A_int current No
international_volt V_int V_int voltage No
international_ohm ohm_int ohm_int resistance No

Illuminance

Unit Shorthand Aliases Scalable
lux lx lx Yes

Catalytic Activity

Unit Shorthand Aliases Scalable
katal kat kat Yes

Entropy

Unit Shorthand Aliases Scalable
joule_per_kelvin J/K J/K No

Viscosity

Unit Shorthand Aliases Dimension Scalable
poise P P dynamic_viscosity No
stokes St St kinematic_viscosity No

Pseudo-Dimensions

These share a zero-vector but are semantically distinct.

Angle

Unit Shorthand Aliases Scalable
radian rad rad No
degree deg deg No
gradian grad grad, gon No
arcminute arcmin arcmin, ' No
arcsecond arcsec arcsec, " No
turn rev rev, revolution No

Solid Angle

Unit Shorthand Aliases Scalable
steradian sr sr No
square_degree sq_deg sq_deg No

Ratio (Dimensionless)

Unit Shorthand Aliases Notes
fraction frac frac, 1 0.0 to 1.0
percent % % 0.0 to 100.0
permille permille permille Parts per thousand
ppm ppm - Parts per million
ppb ppb - Parts per billion
basis_point bp bp, bps 1 bp = 0.01%
nines 9s 9s Reliability notation

Count

Unit Shorthand Aliases Notes
each ea ea, item, ct Discrete items

Logarithmic Units

Units that use logarithmic scales for representing ratios or absolute values relative to a reference.

Pure Ratio (Dimensionless)

These express power or amplitude ratios without a fixed reference level.

Unit Shorthand Aliases Formula Notes
bel - - log₁₀(ratio) Rarely used directly
decibel dB dB 10·log₁₀(ratio) 1 bel = 10 dB
neper Np Np ln(ratio) Natural log scale 
from ucon import units

# Power ratio to decibels
ratio = units.fraction(100)
db = ratio.to(units.decibel)  # <20.0 dB>

# Amplitude ratio to nepers
import math
ratio = units.fraction(math.e ** 2)
np = ratio.to(units.neper)  # <2.0 Np>

Reference-Level Units

These express absolute values on a logarithmic scale relative to a defined reference.

Unit Shorthand Dimension Reference Formula
decibel_milliwatt dBm power 1 mW 10·log₁₀(P / 1 mW)
decibel_watt dBW power 1 W 10·log₁₀(P / 1 W)
decibel_volt dBV voltage 1 V 20·log₁₀(V / 1 V)
decibel_spl dBSPL pressure 20 µPa 20·log₁₀(P / 20 µPa) 
from ucon import units

# Power to dBm
power = units.watt(1.0)
dbm = power.to(units.decibel_milliwatt)  # <30.0 dBm>

# dBm back to watts
dbm = units.decibel_milliwatt(0.0)
power = dbm.to(units.watt)  # <0.001 W> (1 mW)

# Voltage to dBV
voltage = units.volt(10.0)
dbv = voltage.to(units.decibel_volt)  # <20.0 dBV>

# Sound pressure to dBSPL
pressure = units.pascal(1.0)
dbspl = pressure.to(units.decibel_spl)  # <~94 dBSPL>

Chemistry

Unit Shorthand Dimension Reference Formula
pH pH concentration 1 mol/L -log₁₀([H⁺] / 1 mol/L)

pH measures hydrogen ion concentration on a logarithmic scale. It has concentration dimension (amount_of_substance / volume), enabling direct conversion with mol/L.

from ucon import units

# Concentration to pH
mol_per_liter = units.mole / units.liter
conc = mol_per_liter(1e-7)
ph = conc.to(units.pH)  # <7.0 pH> (neutral)

# pH to concentration
ph = units.pH(4.0)
conc = ph.to(mol_per_liter)  # <1e-4 mol/L> (acidic)

# Common pH values
mol_per_liter(1e-1).to(units.pH)   # <1.0 pH>  (strong acid)
mol_per_liter(1e-7).to(units.pH)   # <7.0 pH>  (neutral)
mol_per_liter(1e-14).to(units.pH)  # <14.0 pH> (strong base)

CGS-EMU Units

Units in the CGS electromagnetic unit system. These use the CGS basis (L, M, T) with SI current mapping to L^(1/2)·M^(1/2)·T^(-1).

Unit Shorthand Aliases Dimension
biot Bi Bi, abampere, abA cgs_emu_current
abcoulomb abC abC cgs_emu_charge
abvolt abV abV cgs_emu_voltage
abohm abΩ abΩ cgs_emu_resistance
abfarad abF abF cgs_emu_capacitance
abhenry abH abH cgs_emu_inductance
gilbert Gb Gb, Gi cgs_emu_current

Cross-basis conversion factors (SI → CGS-EMU):

SI Unit CGS-EMU Unit Factor
ampere biot 0.1
coulomb abcoulomb 0.1
volt abvolt 1e8
ohm abohm 1e9
farad abfarad 1e-9
henry abhenry 1e9

Priority Aliases

Some aliases take precedence to prevent ambiguous parses:

Alias Resolves To Reason
min minute Not milli-inch
mcg microgram Medical convention
cc milliliter Cubic centimeter = 1 mL

Creating Custom Units

For units not in the built-in set, create them with Unit:

Python API

from ucon.core import Unit, Dimension

# Define a custom unit
drop = Unit(
    name="drop",
    dimension=Dimension.count,
    aliases=("gtt", "drop")
)

# Use immediately
drops = drop(15)  # <15 gtt>

With ConversionGraph

To enable conversions with custom units, register them in a graph:

from ucon import get_default_graph
from ucon.core import Unit, Dimension
from ucon.maps import LinearMap

# Create custom unit
slug = Unit(name="slug", dimension=Dimension.mass, aliases=("slug",))

# Get graph and register
graph = get_default_graph().copy()
graph.register_unit(slug)

# Add conversion edge
from ucon import units
graph.add_edge(slug, units.kilogram, LinearMap(14.5939))

# Now conversions work
from ucon.graph import using_graph
with using_graph(graph):
    mass = slug(1).to(units.kilogram)  # <14.5939 kg>

Via MCP Server

# Register unit for session
define_unit(name="slug", dimension="mass", aliases=["slug"])

# Add conversion edge
define_conversion(src="slug", dst="kg", factor=14.5939)

# Use in conversions
convert(value=1, from_unit="slug", to_unit="lb")

Common Custom Units

Domain Unit Dimension Aliases
Medical drop count gtt
Aerospace slug mass slug
Maritime nautical_mile length nmi, NM
Energy therm energy therm
Nuclear curie frequency Ci

All Dimensions
acceleration current information permittivity
angle density kinematic_viscosity power
angular_momentum dynamic_viscosity length pressure
area electric_field_strength luminous_intensity ratio
capacitance energy magnetic_flux resistance
catalytic_activity entropy magnetic_flux_density resistivity
cgs_emu_capacitance exposure magnetic_permeability solid_angle
cgs_emu_charge force mass specific_heat_capacity
cgs_emu_current frequency molar_mass temperature
cgs_emu_inductance gravitation molar_volume thermal_conductivity
cgs_emu_resistance illuminance momentum time
cgs_emu_voltage inductance none velocity
charge voltage
conductance volume
conductivity
count