unitx

Write Python formulas with ready-to-use units and physical constants. unitx handles scalar quantities, unit conversion, and dimensional analysis, with exact rational unit scales and exponents.

unitx is in early development. Public APIs may change during the 0.x series.

Installation

Requires Python 3.12 or later, with no mandatory runtime dependencies.

Install a published release:

python -m pip install unitx

To use the current development version, run this from the repository root:

python -m pip install -e .

This README describes the current source tree, including unreleased changes. For a published release, consult the README at its matching Git tag.

Quick start

Start with the two namespaces in unitx.si: lowercase si provides units, and uppercase SI provides physical constants. Their members are ready to use in ordinary Python formulas:

>>> from unitx.si import SI, si
>>> distance = 3 * si.m
>>> elapsed = 2 * si.s
>>> speed = distance / elapsed
>>> print(speed)
1.5 m/s
>>> print(speed.to(si.cm / si.s))
150.0 cm/s
>>> print(SI.c)
299792458 m/s

Multiplying a scalar by a unit constructs a quantity. Divide quantities to compute rates, multiply them to combine physical quantities, and call .to() with the unit you want. A quantity's .value and .unit expose its magnitude and unit separately.

Units and constants with SI

Use the same import for both namespaces:

from unitx.si import SI, si

Common prefixed units and units such as hours, litres, electronvolts, and astronomical units are included. Units and constants can be combined directly:

>>> rest_energy = (SI.me * SI.c**2).to(si.MeV)
>>> round(float(rest_energy.value), 6)
0.510999
>>> (2 * si.h).to(si.s).value
7200
>>> (1 * si.us).to(si.ns).value
1000

Both namespaces are read-only and do not need to be instantiated. si exposes a selection of convenient attributes; other registered prefix combinations remain available through Unit, for example Unit('Tm'). Importing unitx initializes the predefined unit catalogue. Defining a custom unit registers its text spellings without adding an attribute to si.

SI defining constants retain their exact decimal values. Measured constants are stored nominal values; measurement uncertainties are not propagated. Derived Decimal constants are evaluated in the Decimal context active at import. Formulas involving pi use Decimal(str(math.pi)) as an approximation; additional Decimal precision does not add precision to pi.

Constructing units and quantities

For unit expressions and explicit construction, import the classes:

>>> from unitx.factor import Factor
>>> from unitx.quantity import Quantity
>>> from unitx.unit import Unit
>>> Quantity(50, 'cm') == 50 * si.cm
True
>>> Unit('astronomical unit') == si.au
True

Quantity(value, unit) accepts a unit expression or an existing Unit object. value * unit constructs a quantity, and value / unit constructs a quantity with the reciprocal unit. Construction preserves the original magnitude and its type.

Multiplication is symmetric: unit * value and value * unit both construct Quantity objects and preserve the magnitude's type. Dividing a unit by an int, Fraction, or finite Decimal constructs a quantity with an exact Fraction reciprocal, so degree / 60 loses no precision. Float divisors use native floating-point division without Factor's denominator limit. Booleans are not accepted as right-hand numeric operands. A Factor or SymbolicConstant on either side of a unit instead produces a ScaledUnit.

>>> metre = Unit('m')
>>> metre * 2 == 2 * metre
True
>>> (metre * 2).value
2
>>> double_metre = metre * Factor(2)
>>> print(double_metre)
2⋅m
>>> (3 * double_metre).to('m').value
6
>>> arcmin = si.deg / 60
>>> arcmin.value
Fraction(1, 60)
>>> arcmin.to(si.arcmin).value
Fraction(1, 1)

Multiplying a ScaledUnit by an ordinary number also constructs a quantity, keeping the exact scale in its unit and preserving the supplied magnitude. Combining a Unit with a Quantity continues to return a Quantity.

Quantities also accept Factor and SymbolicConstant operands on either side of multiplication or division. Multiplication and right-hand division preserve the magnitude and its type, combining the exact factor with the unit instead. Left-hand division takes the reciprocal magnitude and unit. Ordinary numeric operands continue to act on the magnitude: q * 2 and q * Factor(2) represent equal physical quantities but can have different .value and .unit pairs.

>>> from unitx.factor import PI
>>> hbar = SI.h / (2 * PI)
>>> print(hbar)
6.62607015E-34 J⋅s/(2⋅π)
>>> hbar.value == SI.h.value
True
>>> hbar * (2 * PI) == SI.h
True
>>> round(float(hbar.to('J*s').value) / 1e-34, 8)
1.05457182

The local hbar above retains the exact scale, whereas predefined SI.hbar provides its numerical value in ordinary J*s units. .value is always the magnitude paired with .unit, including its exact scale. Use .to('J*s').value to evaluate the local expression in joule seconds; conversion involving an irrational factor evaluates it approximately. String output combines the scale and formal units into one product, with grouped denominator factors and multiplication dots between adjacent numbers.

Conversion and arithmetic

Use .to() to obtain a new quantity in a unit with the same physical dimensions, or .value_in(unit) to obtain only its numerical value. The target unit is required and accepts a string or Unit, including ScaledUnit. .value_in(unit) returns the same value and concrete type as .to(unit).value, without constructing a temporary quantity. Both follow the conversion rules below. A conversion with scale one preserves the original magnitude; Decimal magnitudes stay Decimal and other conversions can change the numerical type. .value reads the original stored magnitude. Addition and subtraction convert the right operand to the left operand's unit:

>>> length = Quantity(1, 'm')
>>> print(length + Quantity(50, 'cm'))
3/2 m
>>> length.value_in('cm')
100
>>> Quantity(1, 'cm').value_in('m')
Fraction(1, 100)

Multiplication and division combine units. Powers apply to both the magnitude and the unit. Multiplication or division by a Unit alone preserves the magnitude unchanged.

Conversion, addition, subtraction, and ordering across incompatible dimensions raise unitx.exceptions.DimensionError. Equality across incompatible dimensions returns False.

For repeated conversions, reuse a target Unit object to avoid parsing the expression on every call.

Unit expressions

Expressions support registered symbols, singular English names, SI prefixes, multiplication, division, parentheses, and rational powers:

>>> Unit('kg m/s2') == Unit('kg*m/s**2')
True
>>> Unit('m^(1/2)') ** 2 == Unit('m')
True
>>> Unit('micrometre') == Unit('um')
True
>>> Unit('ms') == Unit('m s')
False

• Multiplication can use * or whitespace. Adjacent letters form one unit token: ms is a millisecond, while m s is metre times second.
• Powers can use adjacent numbers, ^, or **. Exponents written as ratios require parentheses, as in m^(1/2); decimal exponents such as m^0.5 are exact.
• Multiplication and division associate left to right. Use m/(s A) to put both s and A in the denominator; m/s A means (m/s)*A.
• Unit symbols and names are case-sensitive. u, µ, and μ are accepted micro prefixes. Use lowercase k for kilo; K denotes kelvin.
• A registered multiword name is recognized before implicit multiplication when it occupies the entire input. Whitespace between its words is treated as a single space. Inside products, parentheses, reciprocals, and powers, use its symbol or combine Unit objects instead.

The unit table contains s, m, g, A, K, mol, and cd, plus the dimensionless identity. Importing unitx also initializes the common units in unitx.si, including named derived units such as N. Mass scales are referenced to kilograms: g has factor 1/1000, and kg has factor 1.

Defining units

Call .define() on a Unit, ScaledUnit, or positive real Quantity to register a new unit and return it:

>>> newton = Unit('kg*m/s2').define('demoN', 'demo newton')
>>> minute = (60 * Unit('s')).define('demoMin', 'demo minute', prefixable=False)
>>> Quantity(2, minute).to('s').value
120
>>> from unitx.factor import PI
>>> degree = ((PI / 180) * Unit()).define('demoDeg', name='demo degree', prefixable=False)
>>> degree.factor == PI / 180
True
>>> Quantity(1, 'kN').to(newton).value
1000

Multiplying or dividing a unit by a Factor or SymbolicConstant creates a ScaledUnit, which preserves an exact additional scale through unit arithmetic. Its scale is relative to its formal unit product; its factor is the total scale to the coherent SI unit. An ordinary Unit has an implicit additional scale of one; only ScaledUnit stores that scale. Unit multiplication, division, and powers involving a ScaledUnit keep that type even when the scale cancels to one. A scale of one compares equal to the corresponding Unit and has the same hash. Calling .define() returns an ordinary Unit with its own formal identity, sharing the definition's dimension and exact SI factor.

ScaledUnit supports shallow copying, deep copying, and pickling while preserving its exact scale and formal units. Restoring custom units requires their definitions to be registered in the receiving process.

Definitions affect the current process and leave the source object unchanged. The symbol is positional-only. The primary name accepts positional or keyword input. Additional name aliases are optional positional arguments after name, such as Unit('m').define('span', 'spanunit', 'spanlength', 'spanmeasure'). Pass the primary name positionally when supplying name aliases; omitting the aliases gives an empty tuple. symbol_aliases accepts a string or tuple of strings; it and prefixable must be passed by keyword. Symbols and symbol aliases must each be a single printable unit token. Names and name aliases may contain multiple such tokens separated by single ASCII spaces, without leading or trailing spaces. Decimal digits and parser operators are not allowed in any token. The primary symbol and name are required and must be nonempty; empty aliases are ignored.

>>> span = (2 * si.m).define('span', 'survey span', 'survey distance')
>>> Unit('survey span') == span
True
>>> Unit('kilosurvey distance') == Unit('kspan')
True
>>> Unit('survey span') / si.s == Unit('span / s')
True

Multiword names are recognized only as complete inputs. For example, Unit('astronomical unit / arcsec') does not recognize astronomical unit as a factor; use one of the two compound forms above instead.

SI prefixes are enabled by default; set prefixable=False to disable them. Prefix names attach directly to the first word of a multiword name, as in kiloastronomical unit; a separate kilo astronomical unit is not accepted. Registration raises UnitRegistryError if a new spelling, including a generated prefixed form, already resolves to a unit or conflicts with another spelling in the same definition. A multiword spelling must not replace an existing implicit product such as metre second. Validation finishes before the registry changes.

Quantity definitions require positive finite int, Fraction, Decimal, or float magnitudes. Prefer Fraction or Decimal for exact scales. Floats use Factor's denominator limit and can warn or round to zero and fail, for example with 1e-10. Defining a unit does not evaluate symbolic scales numerically.

Units, dimensions, and equality

A Unit retains its formal factors. A Quantity compares physical values across compatible units:

>>> Unit('m') == Unit('cm')
False
>>> Quantity(1, 'm') == Quantity(100, 'cm')
True
>>> len({Quantity(1, 'm'), Quantity(100, 'cm')})
1
>>> from unitx.dimension import Dimension
>>> speed.dimension == Dimension(L=1, T=-1)
True

Equal quantities have equal hashes when their magnitudes are hashable. Different formal unit expressions can have the same physical dimension and scale without being equal as Unit objects.

An expression can be dimensionless and still carry a scale. Plain numbers added to or subtracted from dimensionless quantities represent unscaled values:

>>> scaled = Quantity(1, 'km/m')
>>> scaled.is_dimensionless()
True
>>> scaled == 1000
True
>>> (scaled + 1).to('').value
Fraction(1001, 1)

Numerical behavior

Exact unit algebra and numerical magnitude evaluation have different rules:

• Formal exponents use one rule in Monomial, Dimension, Factor, Unit, and Quantity: int/Fraction/Decimal values stay exact; floats use their shortest decimal text without a denominator limit. Thus 0.1 means 1/10 and 1e-10 remains nonzero. Use Fraction(1, 3) for exactly one third: the float 1 / 3 means the decimal 0.3333333333333333 in formal exponents. Factor's numeric scale inputs retain their separate denominator-limit rules.
• Quantity handles units; the magnitudes determine numerical arithmetic. Operators use the magnitudes in operand order and preserve native promotion, rounding, signals, and exceptions. Decimal arithmetic returns Decimal and follows its active context. Mixing Decimal with float or Fraction raises TypeError, as it does for the bare numbers; choose a common numerical type explicitly when needed.
• Conversion with a rational scale keeps int/Fraction values exact. Decimal conversion combines the value and scale exactly internally, then rounds once to Decimal in the active context. Irrational unit scales are approximated as floats, using their shortest decimal representations for Decimal conversion. A scale of one preserves the magnitude without arithmetic or rounding. Direct Factor(value) retains its separate exact Fraction evaluation rules.
• Addition and subtraction align the right operand with the left quantity's unit before numerical arithmetic. Integers being aligned with a Decimal magnitude are scaled in the Decimal domain, so Decimal('1') * si.m + 50 * si.cm returns a Decimal magnitude of 1.5. Explicit Fraction/float operands keep their own numerical domains. Finite-precision conversion and arithmetic can round; changing the result unit can therefore change rounding errors.
• Unary + and - apply the magnitude's native operators and preserve the unit. Decimal results remain Decimal and follow its context precision, rounding, signals, and exceptions; unary + can therefore change the numerical value.
• Integer division produces a float; Fraction arithmetic remains rational. Use Fraction magnitudes explicitly for exact rational results. Powers pass the original exponent to the magnitude: 2 ** 2.0 returns float and 2 ** Decimal('0.5') returns Decimal. Decimal magnitudes require int or Decimal exponents, as in Python. The unit follows the common formal exponent rule above; numerical evaluation still uses the original exponent object. Exponents must be finite real scalars other than bool. Numerical powers can round or produce complex values, following the magnitude's rules.
• Truth values follow the magnitude, so zero quantities are false regardless of unit. Comparisons with equal unit factors use native magnitude operators, including independent !=, Decimal signals/exceptions and complex ordering errors. For different unit factors, builtin real values and complex components are aligned exactly to avoid rounding-dependent equality or hashes. Ordinary numeric subclasses use the same alignment as their base types. Decimal/float signals apply to native comparisons with equal factors; cross-factor alignment compares exact rational coefficients and does not perform an additional comparison merely to reproduce signals. Decimal/Fraction comparisons are supported natively.
• Equality is exact, without a tolerance. Finite floats are compared as their stored binary rational values. Floating-point conversions and irrational powers may round; use isclose() for approximate real scalar comparisons. It uses the symmetric condition abs(a - b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol) in coherent SI units, with defaults rel_tol=1e-9 and abs_tol=0. Swapping quantities preserves the result. Nonzero absolute tolerances for dimensional quantities must carry matching units; plain operands and plain absolute tolerances represent unscaled dimensionless values. Tolerances must be finite and nonnegative. Different dimensions raise DimensionError. NaNs are never close, and infinities are close only to infinities of the same sign. Finite rational coefficients stay exact; residual irrational unit factors are approximated. With both tolerances zero, isclose() uses exact equality.

>>> from decimal import Decimal, localcontext
>>> from fractions import Fraction
>>> with localcontext() as context:
...     context.prec = 2
...     q = Quantity(Decimal('1.2345'), 'm')
...     print((+q).value, (-q).value, (q * 2).value)
1.2 -1.2 2.5
>>> Quantity(Decimal('0.1'), 'm').to('cm').value
Decimal('10')
>>> (Quantity(Fraction(1), 'm') / Quantity(3, 's')).value
Fraction(1, 3)
>>> (Quantity(2, 'm') ** 2.0).value
4.0
>>> bool(Quantity(0, 'm'))
False
>>> Quantity(0.1, '') == Quantity(Fraction(1, 10), '')
False
>>> Quantity(0.1 + 0.2, 'm').isclose(Quantity(0.3, 'm'))
True
>>> a, b = Quantity(1, 'm'), Quantity(100.05, 'cm')
>>> a.isclose(b, rel_tol=0, abs_tol=Quantity(1, 'mm'))
True
>>> b.isclose(a, rel_tol=0, abs_tol=Quantity(1, 'mm'))
True

The built-in integer factorization backend is bounded. Unresolved factors emit IncompleteFactorWarning and can limit simplification and comparisons. SymPy is an optional, more capable factorization backend:

python -m pip install sympy

Current scope

• NumPy scalars, arrays, and NumPy operations are not supported yet. NumPy integration is planned. Structural compatibility with a magnitude protocol does not imply NumPy support.
• Custom magnitudes must support scalar arithmetic, return a Python bool from equality, and defer raw operations with Unit operands to its reflected operators.
• Scalar operations use the magnitude's supported operand types, including complex numbers and custom scalar magnitudes. Custom magnitudes must also defer operations with Quantity operands so that Quantity can handle units. Ordering follows the magnitude's native rules.
• Unit conversion is multiplicative. Offset temperature scales such as Celsius and Fahrenheit are not supported.

Building blocks

The package includes inline type annotations and a py.typed marker. Construction and operations with Unit preserve the magnitude type in type hints; conversion and numerical arithmetic use result unions where the concrete type depends on runtime values or units. Modules whose names start with _ are internal.

Upgrading from 0.3.0

Version 0.4.0 replaced the implementation previously published on PyPI as 0.3.0. It introduced incompatible changes:

• Python 3.12 or later is required; Python 3.11 is no longer supported.
• The former unitx.utils namespace was removed. Classes can be imported from their modules, as shown above; the current source tree also exports Unit, Quantity, and Dimension at the package root.
• Unit no longer defines len() or special truth-value behavior. Use unit == Unit('') to check the formal identity, or unit.is_dimensionless() to check physical dimensions.
• Conversion and arithmetic can produce different magnitude types, especially for Decimal inputs. Review the numerical behavior before relying on a result's concrete type or approximate equality.

Development

Install the development version and test dependencies:

python -m pip install -e ".[test]"
python -m pytest -q
python -m ruff check .
python -m ruff format --check .

The pytest suite includes doctests and Pyright checks for the typed API. CI runs the suite with both the built-in and SymPy factorization backends.

Releases

The release workflow validates the source, builds a wheel and source distribution, checks their metadata, and tests the installed wheel. Manual workflow runs store the distributions without uploading them to PyPI.

Publishing a GitHub release runs the same checks and uploads the distributions to PyPI. The release tag must match the project version, for example v0.4.0 for version 0.4.0. Configure a PyPI Trusted Publisher for the repository, workflow release.yml, and GitHub environment pypi before publishing.

See CHANGELOG.md for release history. Licensed under the MIT License.