Physics calculator

Froude Number Calculator

Compute the open-channel Froude number Fr = v / √(g L). Default g=9.80665 m/s². Runs locally. Not Reynolds, not Manning, not Chezy, and not Q=Av.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary Engine tested · Source checked · 17/17 tests · Production surface contract 3/3 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
Model: Open-channel Froude number Fr = v / √(g L). Invert v or L. Default g=9.80665. Reports subcritical, critical, or supercritical.
Scope: Froude Fr = v / √(g L); default g=9.80665 m/s²
Verification: Engine tested · 17/17 tests · Production surface contract 3/3 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: ISO 80000-11 — Characteristic numbers — Froude number Fr
ISO 80000-4 — Mechanics — Velocity, length, acceleration
Sources
Evidence: 2 golden · 10 boundary · 5 property · Production surface contract 3/3 · Artifact integrity PASS
Production: Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 163 CURRENT) @ 2026-09-17T09:03:11.906Z
Semantic contract: PASS

Formulas

Core equations used by this calculator.

Froude numberFr = v / √(g L)

Velocityv = Fr √(g L)

LengthL = v² / (g Fr²)

iSI. v in m/s, L in m (characteristic length, often hydraulic depth), g in m/s². Default g=9.80665. This page is not Reynolds Re=ρvL/μ, not Manning, not Chezy, and not Q=Av.

How to use

Enter speed v

Mean flow speed in m/s. Invert for v on the v tab. URL field is v_m_s.

Enter length L

Characteristic length, typically hydraulic depth, in metres.

Optional g

Leave blank for standard gravity 9.80665 m/s².

Read Fr and regime

Fr = v / √(g L). Fr<1 subcritical, Fr=1 critical, Fr>1 supercritical.

Example calculations

Common configurations with formula and result.

v=1 m/s, L=1 m

Default g=9.80665 m/s²

Fr = 1 / √9.80665

Fr ≈ 0.31933 · subcritical

Critical, L=1 m

v = √g

Fr = √g / √(g · 1) = 1

Fr = 1 · critical

Froude Number calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 17/17 tests · Production surface contract 3/3
Named expert review Not performed
Calculation version 1.0.0

Review policy · Evidence

Definition: Froude number Fr = v / √(g L). Free-surface: Fr<1 subcritical, Fr=1 critical, Fr>1 supercritical. Default g = 9.80665 m/s².
What it calculates: Open-channel Froude number Fr = v / √(g L). Invert v or L. Default g=9.80665. Reports subcritical, critical, or supercritical.
Inputs: mode?
v|Fr
L|Fr
g?
Outputs: Fr
v
L
g
regime
mode
model
Formula: Fr = v / √(g L)
Assumptions: Froude Fr = v / √(g L); default g=9.80665 m/s²
Free-surface: Fr<1 subcritical, Fr=1 critical, Fr>1 supercritical
Not Reynolds, not Manning, not Chezy, not Q=Av
Units: SI; v in m/s; L in m; g in m/s²; Fr dimensionless
Boundary conditions: missing v, L, or Fr when required → MISSING_REQUIRED_INPUT
v, L, Fr, or g ≤ 0 → VALUE_MUST_BE_POSITIVE
Re/ρ/μ/ν, n, C/R/S, A/Q → MIXED_INPUT_ENCODING
reynolds, manning, or chezy as mode → INVALID_MODE
Example: v=1 L=1 → Fr=1/√9.80665
Validation cases: 3 published on this page · 17/17 tests · Production surface contract 3/3 · View evidence
v=1 L=1 → Fr=1/√9.80665 subcritical
v=√g L=1 → Fr=1 critical
v=1 L=1 Re=200000 → MIXED_INPUT_ENCODING
Sources: ISO 80000-11 — Characteristic numbers — Froude number Fr
Supports: Fr = v / √(l g); gravity/inertia, not viscous Reynolds
ISO 80000-4 — Mechanics — Velocity, length, acceleration
Supports: v has dimension length/time; L length; g acceleration
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Compute the open-channel Froude number from speed and characteristic length.

Supported and not supported

Supported — Fr from v and L · invert v or L · optional g (default 9.80665) · regime · API physics.fluid.froude

Not supported — Reynolds Re/ρ/μ/ν, Manning n, Chezy C/R/S, Q=Av

Agent / API notes

Capability id: physics.fluid.froude · tool id: froude-number · pin 1.0.0.

{ "v": 1, "L": 1 }

Critical check: { "v": 3.132091952673165, "L": 1 } → Fr=1. Modes: Fr (default), velocity, length. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/froude-number. There is no /calc/fluid.

Other calculators in this family: Reynolds number, Manning formula, Chezy formula, Hydraulic diameter .

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Frequently asked questions

Key distinctions behind the calculation.

Is this Reynolds number?

No. Re = ρ v L / μ is /calc/physics/reynolds. Sending Re, ρ, μ, or ν is MIXED_INPUT_ENCODING.

Is this Manning?

No. Open-channel Q from n is /calc/physics/manning-formula. Sending n is MIXED_INPUT_ENCODING.

Is this Chezy?

No. V = C √(R S) is /calc/physics/chezy-formula. Sending C, R, or S is MIXED_INPUT_ENCODING.

Is this Q = A·v?

No. Volumetric flow from area and velocity is /calc/physics/flow-rate. Sending A or Q is MIXED_INPUT_ENCODING.

Where does this run?

Locally in the browser by default. REST and MCP call the same fluid-engine froudeNumber wrapper.