Froude number calculator

This capacity divides velocity by the square root of gravity times length, rejects a non-positive characteristic length with a clear invalid_input error, and returns structured JSON with Fr, the echoed inputs, formula, method, and a soft regime hint.

What Fr = V/√(gL) means and which quantities you need to send

Delivering velocity, gravity, length, froude_number, Fr, 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 square-root arithmetic.

How this calculator validates input and applies Fr = V/√(gL)

Numeric strings that parse to finite numbers are accepted so forms and CSV-style pipelines can pass values without an extra cast. Gravity must also be strictly positive so the radicand is a positive real number; a zero or negative g would collapse the definition. Velocity must be non-negative: a still fluid yields Fr equal to zero, which is a valid subcritical result, but a negative speed is not a characteristic flow speed in this convention. There is no unit-conversion service, no Saint-Venant solver, and no ship-resistance table; this is ideal constant-g Fr from three known quantities. Send a JSON body with required fields velocity, gravity, and 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: v, speed, flow_velocity for velocity; g, gravitational_acceleration for gravity; L, characteristic_length, depth for length. Characteristic length must be strictly positive: a zero or negative length is always rejected as invalid_input because the square root of g times L is undefined or imaginary for this model and the product contract names that failure explicitly. After validation, the engine computes the square root of gravity times length, divides velocity by that denominator, and rounds to a stable decimal precision so the same input always yields the same JSON across JavaScript engines. A soft regime_hint labels common free-surface bands—below one as subcritical, near one as critical, and above one as supercritical—purely as an educational convenience; it is not a densimetric, two-layer, or wave-breaking classifier and does not replace engineering judgment for compound channels or stratified flows. 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 Fr equals V over square root of g L check while grading homework, verifying an open-channel lab, sketching whether a spillway is supercritical, or sanity-checking the non-dimensional inputs of a shallow-water simulation. Choose units consistently—if velocity is in metres per second, gravity in metres per second squared, and length in metres, Fr is dimensionless and ready for textbook comparison. There is no language model, no external fluid-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. Results are fully deterministic: the same three inputs always yield the same froude_number, the same Fr alias, and the same formula and method labels. Wire the endpoint into open-channel drills, contest answer checkers, spillway sketch tools, or preprocessing steps where you already prefer explicit domain errors—such as rejecting a non-positive characteristic length—over opaque black-box widgets that cannot explain why a bad input was refused.