HomeCalculatorsPhysicsFluid MechanicsChezy Formula Calculator
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 CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · V = C √(R S), plus C, R, and S solves, + O3 mpmath tabulated velocity.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
V = C √(R S), plus C, R, and S solves, + O3 mpmath tabulated velocity.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (velocity, solve, alias, awkward, invalid-domain) · Matrix
Deferred
Not Manning n, not Hazen–Williams, and not Q=Av.
Numerical scope
O2: Chezy vs a separate-module identity (≤2 ULP). Not Manning n, not Hazen–Williams, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated venturi vectors. Not Q=Av, not Manning, and not Darcy.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
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 · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · V = C √(R S), plus C, R, and S solves, + O3 mpmath tabulated velocity.· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-25.o2-o3
Verification revision
2026-09-25.o2-o3 · 1/1 property · digest 5f307067821a
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
Sources
Evidence
2 legacy golden · 10 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 10/10 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

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

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

1

Enter Chezy C

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

2

Enter hydraulic radius R

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

3

Enter slope S

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

4

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.

ϟ

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

Uniform open-channel mean velocity

V = 50 √(1 × 0.001)
v ≈ 1.581 m/s
ϟ

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

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

→ Alternate Depth Calculator Compute both rectangular depths at the same specific energy from E, Q, and width b. Runs locally. Not specific energy from y+v; not specific force M; not hydraulic jump y2; not critical depth yc as the product. › → Bernoulli Equation Calculator Incompressible Bernoulli along a streamline: solve P2, v2, or h2. Runs locally in your browser. › → Broad-Crested Weir Calculator Compute rectangular broad-crested weir discharge Q = C_d (2/3)^{3/2} b √g H^{3/2}. Default C_d=0.85. Runs locally. Not a thin-plate weir, not Manning, not Q=Av, and not an orifice. › → Cavitation Number Calculator Compute the cavitation number σ = (p − p_v) / (½ ρ v²). Runs locally. Not NPSH, not Thoma NPSH/H, not Weber, and not Euler Eu=Δp/(ρ v²). › → Colebrook Friction Factor Calculator Solve the Colebrook–White equation for Darcy friction factor f from Re and ε/D. Turbulent pipes Re≥4000. Runs locally. Not laminar 64/Re and not a Moody-chart lookup. › → Concentric Reducer Calculator Compute concentric-reducer loss h = K v₂² / (2g) with K = 0.5 (1 − A₂/A₁) referenced to the downstream speed. Runs locally. Not sudden expansion, not gradual contraction α, not vena-contracta C_c, not catalog K, and not Q=Av. › → Critical Depth Calculator Compute rectangular critical depth yc = (q²/g)^{1/3}. Runs locally. Not a Froude wrap, not specific energy, not a hydraulic jump, and not Q=Av. › → Critical Slope Calculator Compute rectangular critical bed slope Sc such that yn=yc using SI Manning at y=yc. Runs locally. Not Manning A,R; not normal-depth yn; not critical-depth yc as the product; not Chezy; not Q=Av. ›

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.