SciEng Formulary

SciEng Formulary is a curated, machine-readable library of verified scientific and engineering formulas for humans, Python programs, and AI agents.

Every formula carries:

• its equation;
• input variables and the output variable, each with a dimension and a reference SI unit;
• assumptions and applicability limits, written so you can tell when not to use it;
• one or more authoritative references, rendered in IEEE style;
• an executable Python evaluator;
• numerical verification cases that the evaluator must reproduce.

It is meant for engineers, scientists and students, and for the programs, AI agents and CAD/CAE/analysis workflows that need a formula they can look up, check and evaluate:

scientific or engineering question
  -> search for a formula
  -> inspect its variables and assumptions
  -> inspect its authoritative references
  -> evaluate it
  -> use the result in any downstream workflow

The package uses only the Python standard library.

Installation

Once SciEng Formulary is published on PyPI (it has not been released yet):

pip install sciengformulary

Until then, install it from a clone; see Development.

Quick start

from sciengformulary import formulas

f = formulas.get("aerodynamics.dynamic_pressure")
print(f.equation)                    # q = 0.5 * rho * V^2
print(f.input_names)                 # ('rho', 'V')
print(f.assumptions[0])              # when the formula applies
print(f.references[0].format_ieee()) # verified source, IEEE style

result = f.evaluate(rho=1.225, V=120.0)  # 8820.0 (Pa, for SI inputs)

More of the API:

formulas.list()                       # every formula, sorted by id
formulas.search("normal shock")       # deterministic keyword search
f.verification_cases                  # known input/output cases
f.verify()                            # re-run them; raises ValueError on a mismatch
f.to_dict()                           # all metadata, including structured references
                                      # and verification cases, as JSON-ready data

A formula can also be imported directly:

from sciengformulary.catalog.aerodynamics import dynamic_pressure

What is in the catalog

The catalog contains 415 formulas in 18 knowledge domains, including 84 formulas contributed by @jwchin06 and 11 chemistry-related E3 formulas. See the contribution inventory and provenance review.

Only formulas that have been checked against an authoritative source are included. Candidates that could not be verified, or whose sources disagree, are left out rather than added with a weaker guarantee.

How formulas are verified

A formula is checked in two different ways.

References and human review establish that the formula is right.

• Every formula has at least one authoritative ReferenceSpec: a standards body or government technical organisation (NASA, NIST, NACA reports), an established textbook, a peer-reviewed paper, or official university teaching material. A FormulaSpec without one cannot be constructed.
• References are stored as structured fields (authors, organisation, title, year, URL, locator, ...). IEEE is the only citation style; format_ieee() renders it.
• Locators (section, equation, figure) point at where the relationship was checked. Reviewers open the source and confirm the equation, its notation and its assumptions.

Verification cases establish that the code is right.

• Every formula has at least one VerificationCase: inputs, an expected result determined independently of the evaluator (a published worked example or table, or an independent calculation from the published equation), and a tolerance.
• verify() checks that the evaluator reproduces every case. It runs when each formula is constructed and again in CI.
• A passing case shows that the Python code implements the declared equation. It does not show that the equation is scientifically correct or applies to your problem.

Check the whole installed catalog at any time:

python -m sciengformulary.validation

Units

• Evaluators do no unit conversion. You are responsible for passing every input in one consistent unit system; the result comes out in the matching unit of that system.
• Each variable's si_unit is its canonical reference SI representation, and dimension gives its base dimensions (M, L, T, Theta, N, I).
• Empirical formulas whose coefficients only hold in particular units say so in their assumptions.
• Formulas that need physical constants (Boltzmann, Planck, Stefan-Boltzmann, G, standard gravity) use the CODATA 2022 values in SI units, so their other inputs must be in SI units.

Development

git clone https://github.com/2ssunny/sciengformulary.git
cd sciengformulary
pip install -e .
python -m sciengformulary.validation

Repository structure

src/sciengformulary/
├─ __init__.py          # `formulas` registry instance
├─ validation.py        # whole-catalog checks (python -m sciengformulary.validation)
├─ core/
│  ├─ reference.py      # ReferenceSpec (structured source, IEEE rendering)
│  ├─ verification.py   # VerificationCase (known input/output case)
│  ├─ variable.py       # VariableSpec
│  ├─ spec.py           # FormulaSpec
│  └─ registry.py       # FormulaRegistry: get / list / search
└─ catalog/             # one package per knowledge domain, one file per formula
   ├─ _sources.py       # shared bibliographic records
   ├─ _constants.py     # CODATA constants with their NIST references
   ├─ aerodynamics/
   ├─ ...
   └─ thermodynamics/

Contributing

See CONTRIBUTING.md for the source-quality, anti-fabrication, verification-case and units rules, and RELEASING.md for how releases are published.

License

Licensed under the Apache License 2.0. See LICENSE.