units

The Price of Unitless Arithmetic

On September 23, 1999, flight controllers expected NASA's Mars Climate Orbiter to pass behind Mars, fire its engine, and come back into radio contact after orbit insertion. It never came back. When engineers reviewed the final hours of flight data, the trajectory was not where the navigation system thought it was: the spacecraft had approached Mars far lower than planned. The investigation traced the loss to a unit boundary that software had failed to defend. One side of the system handled "small forces" data in English units; the navigation side expected metric units.

That is the kind of bug this package is meant to stop. Without units, the mistake is just arithmetic:

# A navigation routine expects impulse in newton-seconds.
expected_impulse_ns = 120

# A supplier routine accidentally sends a value in a different force unit.
# The number is still just a number, so Python accepts it.
reported_impulse_other_units = 120

trajectory_impulse = expected_impulse_ns + reported_impulse_other_units
print(trajectory_impulse)  # 240

There is nothing in 240 that tells you a spacecraft trajectory may now be wrong. With units attached, the mismatch stops at the boundary:

from units import CustomUnitBase
from units.dimension import DimensionSystem
from units.si import newton, second

class EnglishImpulseUnit(CustomUnitBase):
    dimension_system = DimensionSystem("english-impulse", ("lbf_s",))

pound_force_second = EnglishImpulseUnit.define("lbf_s")

expected_impulse = 120 * newton * second
reported_impulse = 120 * pound_force_second

trajectory_impulse = expected_impulse + reported_impulse
# UnitCompatibilityError: units mismatch: m·kg·s^-1 and lbf_s

That failure is the feature. A bug that would otherwise move through a program as an ordinary number is stopped before it contaminates mission-critical calculations.

Background: NASA/JPL describe the Mars Climate Orbiter loss as a navigation error caused by a failure to translate English units to metric, sending the spacecraft too close to Mars.

Source: https://en.wikipedia.org/wiki/Mars_Climate_Orbiter

About

python-units is a Python package for unit-aware arithmetic. It provides:

• a Quantity type that combines numeric values with unit information
• a registry of SI base and derived units
• algebraic unit manipulation and compatibility checks
• explicit multiplicative and affine conversions between compatible units
• common imperial and US customary units in units.imperial
• a public API that prioritizes scalar-by-unit construction and SI unit imports
• a migration path from the legacy Unit constructor and compatibility helpers
• a Python 3-only codebase with no Python 2 compatibility shims
• a project structure that separates public API, core logic, data models, and utilities
• comprehensive unit tests and documentation

Supported Python versions: 3.10+

Python 2 is not supported.

Project layout:

• public facade: src/units
• API exports: src/api
• business logic: src/core
• data models: src/models
• utilities: src/utils
• tests: tests/unit and tests/integration

Preferred API:

from units import Quantity
from units.si import metre, second, newton

distance = 10 * metre
time = 2 * second
speed = distance / time
force = 5 * newton
print(distance)
print(speed)
print(force)

The preferred construction style is scalar-by-unit multiplication:

from units.si import metre, second

length = 3 * metre
time = 2 * second
speed = length / time
volume = 5 * metre ** 3

Because ** binds more tightly than *, 5 * metre ** 3 is interpreted as 5 * (metre ** 3), which is the intended geometric-unit behavior.

The explicit constructor remains supported and is still the right low-level form when you want to be fully explicit:

from units import Quantity
from units.si import metre

length = Quantity(3, metre)

Legacy API compatibility:

import units as u
print(u.Unit(1, u.metre))

The legacy Unit constructor remains available as a compatibility alias for Quantity during the migration period. It is deprecated and scheduled for removal in 1.0.0, but it remains a true alias until then so existing type checks keep working. New code should prefer from units import Quantity and from units.si import ....

The package is Python 3-only. Python 2 compatibility behavior is not part of the supported interface.

Migration guide

Old style:

import units as u
distance = u.Unit(3, u.metre)
time = u.Unit(2, u.second)
speed = distance / time

New style:

from units.si import metre, second

distance = 3 * metre
time = 2 * second
speed = distance / time
volume = 5 * metre ** 3

Still supported when you want the fully explicit constructor form:

from units import Quantity
from units.si import metre, second

distance = Quantity(3, metre)
time = Quantity(2, second)
speed = distance / time

Public API

Stable top-level imports:

• Quantity
• Unit (compatibility alias for Quantity)
• convert
• value
• unit
• multiplier
• UnitsError, InvalidUnitError, InvalidValueError, UnitCompatibilityError, UnitOperandError

Canonical unit imports:

• from units.si import metre, second, newton
• prefixed and scaled units such as kilometre, centimetre, gram, minute, hour, kilowatt, and millivolt
• from units.imperial import inch, foot, yard, mile, ounce, pound, fahrenheit

Legacy compatibility helpers:

• Unit
• long_quantity
• int_unit
• float_unit
• long_unit
• complex_unit

These names remain available during the migration period and emit DeprecationWarning when called. Unit remains a true alias for Quantity and does not emit a call-time warning, because preserving Unit is Quantity is part of the pre-1.0.0 compatibility contract. New code should prefer Quantity, scalar-by-unit construction, and the *_quantity conversion helpers. The deprecated compatibility paths are scheduled for removal in 1.0.0.

Notes on semantics

• Addition and subtraction require identical units.
• Multiplication and division combine units algebraically.
• Explicit conversions are available through quantity.to(unit) and convert(quantity, unit).
• Scale-only conversions cover prefixed SI and imperial units.
• Affine conversions cover Celsius, Fahrenheit, and kelvin.
• Integer powers of units and unit-bearing quantities are supported.
• Unitless quantities are supported explicitly.
• Affine units such as Celsius and Fahrenheit are blocked from multiplicative arithmetic because offsets make those operations ambiguous.
• The core quantity model allows signed values. Domain-specific constraints such as non-negative lengths should be enforced by higher-level types or validators.

Conversion foundations

0.4.0 adds explicit multiplicative conversions. Conversion never happens silently during addition or subtraction; you choose the target unit.

from units import convert, multiplier, unit, value
from units.si import gram, hour, kilogram, kilometre, metre, minute, second

distance = 1.5 * kilometre
print(distance.to(metre))           # 1500 m
print(convert(2500 * metre, kilometre))  # 2.5 km

duration = 2 * hour
print(duration.to(minute))          # 120 min
print((1500 * gram).to(kilogram))   # 1.5 kg

speed = (72 * kilometre) / (2 * hour)
print(speed)                        # 10.0 m·s^-1

print(value(distance))              # 1.5
print(unit(distance))               # km
print(multiplier(kilometre))        # 1000.0

0.5.0 extends conversion to affine temperature units and common imperial units. Conversion still never happens silently during addition or subtraction; you choose the target unit.

0.5.0 examples

The 0.5.0 release adds three practical conversion capabilities: affine temperature conversion, imperial units, and familiar composite display units.

from units import convert
from units.imperial import fahrenheit, foot, mile, pound
from units.si import (
    degree_celcius,
    gram,
    hour,
    kelvin,
    kilometre,
    metre,
    picometre,
)

# Affine conversions include the offset.
print(convert(0 * degree_celcius, kelvin))       # 273.15 K
print(convert(32 * fahrenheit, degree_celcius))  # 0 °C

# Imperial units convert explicitly into SI or familiar metric units.
print(convert(3 * foot, metre))                  # 0.9144 m
print(convert(1 * pound, gram))                  # 453.59237 g

# Composite target units preserve the display unit you ask for.
speed = 60 * mile / hour
print(convert(speed, kilometre / hour))          # 96.56064 km·h^-1

# Pico-prefixed units are part of the prefixed SI set.
print(convert(1000000000000 * picometre, metre)) # 1 m

The same strict arithmetic rules still apply. Compatible conversion is explicit; addition and subtraction still require identical units.

Affine temperature conversions

Temperature scales such as Celsius and Fahrenheit require an offset. These are supported through explicit conversion:

from units import convert
from units.imperial import fahrenheit
from units.si import degree_celcius, kelvin

print(convert(0 * degree_celcius, kelvin))       # 273.15 K
print(convert(32 * fahrenheit, degree_celcius))  # 0 °C
print((100 * degree_celcius).to(fahrenheit))     # 212 °F

Affine units are not allowed in multiplicative arithmetic:

from units.si import degree_celcius, second

temperature = 20 * degree_celcius
temperature * second
# UnitCompatibilityError: units cannot be combined multiplicatively: °C and s

This is deliberate. Absolute temperatures and temperature intervals are different semantic concepts; constrained semantic types are planned for a later release.

Imperial and US customary units

Common non-SI units live in units.imperial:

from units import convert
from units.imperial import foot, mile, pound
from units.si import gram, hour, kilometre, metre

print(convert(3 * foot, metre))              # 0.9144 m
print(convert(1 * mile, kilometre))          # 1.609344 km
print(convert(1 * pound, gram))              # 453.59237 g

speed = 60 * mile / hour
print(convert(speed, kilometre / hour))      # 96.56064 km·h^-1

Prefixed and scaled units

Common SI prefixes and practical time units are available from units.si:

from units.si import (
    centimetre,
    gram,
    hour,
    kiloampere,
    kilometre,
    kilovolt,
    kilowatt,
    megawatt,
    micrometre,
    microsecond,
    milliampere,
    milligram,
    millimetre,
    millisecond,
    millivolt,
    milliwatt,
    minute,
    nanometre,
    nanosecond,
    picogram,
    picometre,
    picosecond,
    tonne,
)

Scaled units participate correctly in multiplication, division, and powers:

from units.si import hour, kilometre, metre

area = (2 * kilometre) * (3 * metre)
print(area)                         # 6000 m^2

square = (2 * kilometre) ** 2
print(square)                       # 4000000 m^2

speed = (72 * kilometre) / (2 * hour)
print(speed)                        # 10.0 m·s^-1

Familiar composite units

Composite unit expressions such as kilometre / hour are algebraic unit definitions. Direct arithmetic renders in canonical SI base form:

from units.si import hour, kilometre

speed = 30 * kilometre / hour
print(speed)                        # 8.333333333333334 m·s^-1

When you want a semantically familiar display unit, convert to that composite unit or give it an explicit name:

from units import DerivedUnit, convert
from units.si import hour, kilometre

kilometres_per_hour = DerivedUnit.define("km·hr^-1", kilometre / hour)

speed = 30 * kilometre / hour
print(convert(speed, kilometre / hour))      # 30 km·h^-1
print(convert(speed, kilometres_per_hour))  # 30 km·hr^-1
print(30 * kilometres_per_hour)             # 30 km·hr^-1

This keeps the arithmetic deterministic while letting application code choose domain-specific display names such as km·hr^-1, N·m, or any other familiar derived unit form.

Real-world examples

Electrical engineering: from resistance to power dissipation

from units.si import ampere, ohm, volt, watt

current = 12 * ampere
resistance = 8 * ohm
voltage = current * resistance
power = voltage * current

print(voltage)  # 96 V
print(power)    # 1152 W

This works because the package canonicalizes unambiguous derived-unit assemblies:

• ampere * ohm -> volt
• volt * ampere -> watt

Pump sizing: hydraulic power from pressure rise and flow rate

from units.si import metre, second, kilogram, pascal, watt

density = 998 * (kilogram / metre ** 3)
flow_velocity = 2.5 * (metre / second)
pipe_area = 0.0314 * metre ** 2
pressure_rise = 180000 * pascal

volumetric_flow = flow_velocity * pipe_area
hydraulic_power = pressure_rise * volumetric_flow

print(volumetric_flow)   # m^3·s^-1
print(hydraulic_power)   # W

This is a good example of a multi-step engineering computation that still renders to intuitive derived units at the end of the chain.

Structural mechanics: work from force over distance

from units.si import metre, newton

force = 4200 * newton
displacement = 0.35 * metre
work = force * displacement

print(work)  # J

Geometric quantities: powers of units

from units.si import metre

volume = 5 * metre ** 3
area = (12 * metre) ** 2

print(volume)  # 5 m^3
print(area)    # 144 m^2

The unit form is also valid on its own:

from units.si import metre

area_unit = metre ** 2
volume_unit = metre ** 3

Fluid mechanics: dynamic pressure

from units.si import kilogram, metre, pascal, second

density = 1.225 * (kilogram / metre ** 3)
velocity = 68 * (metre / second)
dynamic_pressure = 0.5 * density * velocity * velocity

print(dynamic_pressure)  # Pa

Custom unit systems

Custom unit systems are supported, but they are intentionally separate from SI canonicalization. Use them when you want the same algebra and formatting behaviour without forcing your units into the SI registry.

from units import CustomUnitBase, DimensionSystem

class CommUnit(CustomUnitBase):
    dimension_system = DimensionSystem('comm', ('b', 's', 'B'))

bit = CommUnit.define('b')
second = CommUnit.define('s')

data = 32 * bit
duration = 4 * second
rate = data / duration

print(rate)  # 8.0 b·s^-1

Custom systems inherit useful behaviour:

• dimensional algebra
• string rendering
• incompatibility checks within a system

They do not automatically simplify into SI-derived names such as V, J, or Pa, and they cannot be mixed with SI units unless you build an explicit bridge.