Knudsen number calculator

This calculator accepts a molecular mean_free_path λ and a strictly positive characteristic_length L, returns knudsen_number equal to λ divided by L, and labels the usual continuum, slip, transitional, and free-molecular bands as an educational regime_hint. Zero or negative characteristic length is rejected as invalid_input because the ratio is then undefined. Successful API calls cost $0.002.

What Kn = λ/L means and which two lengths you must send

Delivering mean_free_path, characteristic_length, knudsen_number, Kn, formula, method, and regime_hint as JSON makes the result easy to paste into notes, diff in automated tests, or reuse across languages without reimplementing the division.

How this calculator validates input and applies Kn = λ/L

Numeric strings that parse to finite numbers are accepted so forms and CSV-style pipelines can pass values without an extra cast. Mean free path must not be negative: a negative collision length is unphysical, while a zero mean free path is allowed and yields Kn equals zero, the deep continuum limit. There is no unit-conversion service, no kinetic-theory solver, and no temperature-dependent collision table; this is the definitional ratio Kn equals λ over L from two known lengths. Send a JSON body with required fields mean_free_path and characteristic_length. Every field must be finite: missing fields, empty strings, non-numeric text, NaN, and Infinity all fail immediately with invalid_input before any result is returned, and failed validation is not charged. Aliases are supported: lambda, mfp, and molecular_mean_free_path for mean_free_path; length, L, char_length, hydraulic_diameter, and gap for characteristic_length. Characteristic length must be strictly positive: zero or negative L is always rejected as invalid_input because division by a non-positive length is undefined and the Knudsen model collapses. After validation, the engine divides mean free path by characteristic length and rounds to a stable twelve-decimal precision so the same input always yields the same JSON across JavaScript engines. A soft regime_hint labels common rarefied-gas bands — Kn below about 0.01 as continuum, from 0.01 up to 0.1 as slip, from 0.1 up to 10 as transitional, and 10 and above as free_molecular — purely as an educational convenience; it is not a substitute for a full Boltzmann solver and does not replace engineering judgment for complex geometries. The same pure function powers the free in-browser tool and the API path.

Practical use, limits, pricing, and delivery channels

Use the browser tool when you want an immediate Kn equals lambda over L check while grading a rarefied-gas homework, verifying a MEMS vacuum gap, sketching whether a vacuum duct is continuum or free-molecular, or sanity-checking the non-dimensional inputs of a DSMC simulation. There is no language model, no external collision-property service, and no randomness, so the capacity is safe to pin in continuous-integration checks and reproducible lesson materials. Each successful request is one billable item at $0.002; failed validation does not consume balance. Choose units consistently — if mean_free_path is in metres, characteristic_length must also be in metres so Kn is dimensionless and ready for textbook comparison. Results are fully deterministic: the same two inputs always yield the same knudsen_number, the same Kn alias, and the same formula and method labels. Wire the endpoint into gas-dynamics drills, contest answer checkers, MEMS sketch tools, or preprocessing steps where you already prefer explicit domain errors — such as rejecting zero or negative characteristic length — over opaque black-box widgets that cannot explain why a bad input was refused. Keep both lengths coherent, pin the rounded knudsen_number in tests, and you get a reproducible rarefied-gas dimensionless group without standing up kinetic-theory infrastructure of your own.