Physics calculator

Chezy Formula Calculator

Compute open-channel mean velocity V = C √(R S). Runs locally. Not Manning n, not Q=Av, not Hazen–Williams, and not Darcy.

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 Chezy mean velocity V=C √(R S). Invert C, R, or S.
Scope: Uniform open-channel flow; V = C √(R S)
Verification: Engine tested · 17/17 tests · Production surface contract 3/3 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: ISO 80000-4 — Mechanics — Volume flow rate and hydraulic radius
Chow, V.T. Open-Channel Hydraulics — Chezy formula
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.

Mean velocityV = C √(R S)

Chezy CC = V / √(R S)

Hydraulic radiusR = V² / (C² S)

iSI. C is Chezy C, not Manning n and not Hazen–Williams pipe C. This page is not Q=Av, not Darcy–Weisbach, and not Manning.

How to use

Enter Chezy C

C is the Chezy coefficient. It is not Manning n. Invert for C on the C tab.

Enter hydraulic radius R

R is in metres. Invert for R on the R tab. Do not send area A or discharge Q.

Enter slope S

S is the friction slope (rise/run). Invert for S on the S tab.

Read v

v = C √(R S). Invert velocity uses the v field (v_m_s in the URL).

Example calculations

Common configurations with formula and result.

C=50, R=1 m, S=0.001

Uniform open-channel mean velocity

V = 50 √(1 × 0.001)

v ≈ 1.581 m/s

Invert C

v≈1.581 m/s, R=1 m, S=0.001

C = v / √(R S)

C=50

Chezy Formula 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: Open-channel Chezy: V = C √(R S). C is Chezy C. R is hydraulic radius. S is friction slope.
What it calculates: Open-channel Chezy mean velocity V=C √(R S). Invert C, R, or S.
Inputs: mode?
C
R
S
v?
Outputs: v
C
R
S
mode
model
Formula: V = C √(R S)
Assumptions: Uniform open-channel flow; V = C √(R S)
C is Chezy C, not Manning n, not Hazen–Williams pipe C
Not Q=Av, not Darcy, not a weir, not Manning
Units: SI; R in m; S dimensionless; v in m/s; C in m^{1/2}/s
Boundary conditions: missing C, R, S, or v when required → MISSING_REQUIRED_INPUT
C, R, S, or v ≤ 0 → VALUE_MUST_BE_POSITIVE
n, k, A, Q, D, L, hf, f, Re, ε, K, Kv, Cv, D1/D2, C_d → MIXED_INPUT_ENCODING
manning, darcy, or hw as mode → INVALID_MODE
Example: C=50 R=1 S=0.001 → V=50 √0.001
Validation cases: 3 published on this page · 17/17 tests · Production surface contract 3/3 · View evidence
C=50 R=1 S=0.001 → v=50√0.001
mode=C v=1.5811388300841898 R=1 S=0.001 → C=50
C=50 R=1 S=0.001 n=0.013 → MIXED_INPUT_ENCODING
Sources: ISO 80000-4 — Mechanics — Volume flow rate and hydraulic radius
Supports: Hydraulic radius R is a length; mean velocity is length per time
Chow, V.T. Open-Channel Hydraulics — Chezy formula
Supports: Uniform-flow Chezy V = C √(R S); Manning is a later roughness encoding of C
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Compute open-channel mean velocity from the Chezy formula.

Supported and not supported

Supported — v, C, R, or S from V = C √(R S) · API physics.fluid.chezy

Not supported — Manning n, Q=Av identities, Hazen–Williams pipe C, Darcy–Weisbach, weirs, compound channels

Agent / API notes

Capability id: physics.fluid.chezy · tool id: chezy-formula · pin 1.0.0.

{ "C": 50, "R": 1, "S": 0.001 }

Invert C: { "mode": "C", "v": 1.5811388300841898, "R": 1, "S": 0.001 }. Modes: velocity (default), C, R, S. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/chezy-formula. There is no /calc/fluid.

Other calculators in this family: Manning formula, Hydraulic diameter, Flow rate, Weir discharge .

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Frequently asked questions

Key distinctions behind the calculation.

Is this Manning?

No. SI Manning Q=(1/n) A R^{2/3} S^{1/2} is /calc/physics/manning-formula. Sending n is MIXED_INPUT_ENCODING. Manning C = R^{1/6}/n is not this page.

Is this Q = A·v?

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

Is this Hazen–Williams?

No. Empirical water-pipe hf from C, D, L, and Q is /calc/physics/hazen-williams. Chezy C is not HW C. Sending D or L is MIXED_INPUT_ENCODING.

Is this Darcy–Weisbach?

No. Pipe head loss from a given f is /calc/physics/darcy-weisbach. Sending f, Re, or ε is MIXED_INPUT_ENCODING.

Where does this run?

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