This release is a pre-release and may not be stable for production use.
ucon
Pronounced: yoo · cahn A lightweight, unit-aware computation library for Python — built on first-principles.
Overview
ucon helps Python understand the physical meaning of your numbers.
It combines units, scales, and dimensions into a composable algebra that supports:
- Dimensional analysis through
NumberandRatio - Scale-aware arithmetic and conversions
- Metric and binary prefixes (
kilo,kibi,micro,mebi, ect.) - A clean foundation for physics, chemistry, data modeling, and beyond
Think of it as decimal.Decimal for the physical world — precise, predictable, and type-safe.
Introduction
The crux of this tiny library is to provide abstractions that simplify the answering of questions like:
"If given two milliliters of bromine (liquid Br2), how many grams of bromine does one have?"
To best answer this question, we turn to an age-old technique (dimensional analysis) which essentially allows for the solution to be written as a product of ratios. ucon comes equipped with some useful primitives:
| Type | Defined In | Purpose | Typical Use Cases |
|---|---|---|---|
Vector |
ucon.dimension |
Represents the exponent tuple of a physical quantity’s base dimensions (e.g., T, L, M, I, Θ, J, N). | Internal representation of dimensional algebra; building derived quantities (e.g., area, velocity, force). |
Dimension |
ucon.dimension |
Encapsulates physical dimensions (e.g., length, time, mass) as algebraic combinations of vectors. | Enforcing dimensional consistency; defining relationships between quantities (e.g., length / time = velocity). |
Unit |
ucon.unit |
Represents a named, dimensioned measurement unit (e.g., meter, second, joule). | Attaching human-readable units to quantities; defining or composing new units (newton = kilogram * meter / second²). |
Scale |
ucon.core |
Encodes powers of base magnitudes (binary or decimal prefixes like kilo-, milli-, mebi-). | Adjusting numeric scale without changing dimension (e.g., kilometer ↔ meter, byte ↔ kibibyte). |
Exponent |
ucon.core |
Represents base-power pairs (e.g., 10³, 2¹⁰) used by Scale. |
Performing arithmetic on powers and bases; normalizing scales across conversions. |
Number |
ucon.core |
Combines a numeric quantity with a unit and scale; the primary measurable type. | Performing arithmetic with units; converting between compatible units; representing physical quantities like 5 m/s. |
Ratio |
ucon.core |
Represents the division of two Number objects; captures relationships between quantities. |
Expressing rates, densities, efficiencies (e.g., energy / time = power, length / time = velocity). |
units module |
ucon.units |
Defines canonical unit instances (SI and common derived units). | Quick access to standard physical units (units.meter, units.second, units.newton, etc.). |
Under the Hood
ucon models unit math through a hierarchy where each layer builds on the last:
---
config:
layout: elk
elk:
mergeEdges: true # Combines parallel edges
nodePlacementStrategy: SIMPLE # Other options: SIMPLE, NETWORK_SIMPLEX, BRANDES_KOEPF (default)
---
flowchart LR
%% --- Algebraic substrate ---
subgraph "Algebraic Substrate"
A[Exponent] --> B[Scale]
end
%% --- Physical ontology ---
subgraph "Physical Ontology"
D[Dimension] --> E[Unit]
end
%% --- Value layer ---
subgraph "Value Layer"
F[Number]
G[Ratio]
end
%% --- Cross-layer relationships ---
E --> F
B --> F
%% Ratio composes Numbers and also evaluates to a Number
F --> G
G --> F
Why ucon?
Python already has mature libraries for handling units and physical quantities — Pint, SymPy, and Unum — each solving part of the same problem from different angles:
| Library | Focus | Limitation |
|---|---|---|
| Pint | Runtime unit conversion and compatibility checking | Treats quantities as decorated numbers — conversions work, but the algebra behind them isn’t inspectable or type-safe. |
| SymPy | Symbolic algebra and simplification of unit expressions | Excellent for symbolic reasoning, but not designed for runtime validation, conversion, or serialization. |
| Unum | Unit-aware arithmetic and unit propagation | Tracks units through arithmetic but lacks explicit dimensional algebra, conversion taxonomy, or runtime introspection. |
Together, these tools can use units, but none can explicitly represent and verify the relationships between units and dimensions.
That’s the gap ucon fills.
It treats units, dimensions, and scales as first-class objects and builds a composable algebra around them. This allows you to:
- Represent dimensional meaning explicitly (
Dimension,Vector); - Compose and compute with type-safe, introspectable quantities (
Unit,Number); - Perform reversible, declarative conversions (standard, linear, affine, nonlinear);
- Serialize and validate measurements with Pydantic integration;
- Extend the system with custom unit registries and conversion families.
Where Pint, Unum, and SymPy focus on how to compute with units,
ucon focuses on why those computations make sense. Every operation checks the dimensional structure, not just the unit labels. This means ucon doesn’t just track names: it enforces physics:
from ucon import Number, units
length = Number(quantity=5, unit=units.meter)
time = Number(quantity=2, unit=units.second)
speed = length / time # ✅ valid: L / T = velocity
invalid = length + time # ❌ raises: incompatible dimensions
Setup
Simple:
pip install ucon
Usage
This sort of dimensional analysis:
2 mL bromine | 3.119 g bromine
--------------x----------------- #=> 6.238 g bromine
1 | 1 mL bromine
becomes straightforward when you define a measurement:
from ucon import Number, Scale, Units, Ratio
# Two milliliters of bromine
two_mL_bromine = Number(unit=Units.liter, scale=Scale.milli, quantity=2)
# Density of bromine: 3.119 g/mL
bromine_density = Ratio(
numerator=Number(unit=Units.gram, quantity=3.119),
denominator=Number(unit=Units.liter, scale=Scale.milli),
)
# Multiply to find mass
grams_bromine = two_mL_bromine * bromine_density
print(grams_bromine) # <6.238 gram>
Scale conversion is automatic and precise:
grams_bromine.to(Scale.milli) # <6238.0 milligram>
grams_bromine.to(Scale.kibi) # <0.006091796875 kibigram>
Roadmap Highlights
| Version | Theme | Focus |
|---|---|---|
| 0.3.x | Primitive Type Refinement | Unified algebraic foundation |
| 0.4.x | Conversion System | Linear & affine conversions |
| 0.6.x | Nonlinear / Specialized Units | Decibel, Percent, pH |
| 0.8.x | Pydantic Integration | Type-safe quantity validation |
See full roadmap: ROADMAP.md
Contributing
Contributions, issues, and pull requests are welcome!
Ensure nox is installed.
pip install -r requirements.txt
Then run the full test suite (agains all supported python versions) before committing:
nox -s test
“If it can be measured, it can be represented. If it can be represented, it can be validated. If it can be validated, it can be trusted.”
1 maintainer
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