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 CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Fr = v / √(g L), default g=9.80665, plus velocity and length solves, + O3 mpmath tabulated Fr.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: Fr = v / √(g L), default g=9.80665, plus velocity and length solves, + O3 mpmath tabulated Fr.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (Fr, solve, alias, awkward, invalid-domain) · Matrix
Deferred: Not Reynolds, not Manning, not Chezy, and not Q=Av.
Numerical scope: O2: Froude vs a separate-module identity (≤2 ULP). Not Reynolds, not Manning, not Chezy, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated Froude vectors. Not Reynolds, not Manning, not Chezy, and not Q=Av.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
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 · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Fr = v / √(g L), default g=9.80665, plus velocity and length solves, + O3 mpmath tabulated Fr.· View Manifest · CVP overview · Specification
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-26.o2-o3
Verification revision: 2026-09-26.o2-o3 · 1/1 property · digest 9bc7c7e150bc
Legacy regression: 17/17 tests · Production surface contract 5/5
Trust layers: Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review: Not performed
Named expert review: Not performed
CVP suite: 4/4 golden · 9/9 CVP boundary · 10/10 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 5/5 CVP contract · Manifest
Sources: ISO 80000-11 — Characteristic numbers — Froude number Fr
ISO 80000-4 — Mechanics — Velocity, length, acceleration
Sources
Evidence: 2 legacy golden · 10 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 10/10 invalid · Artifact integrity PASS
Semantic contract: PASS

Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

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 5/5
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 5/5 · 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: Alternate Depth Calculator, Bernoulli Equation Calculator, Broad-Crested Weir Calculator, Cavitation Number Calculator, Chezy Formula Calculator, Colebrook Friction Factor Calculator, Concentric Reducer Calculator, Critical Depth Calculator . Explore all Fluid Mechanics.

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.