Physics calculator

Hazen–Williams Calculator

Compute SI Hazen–Williams head loss hf = 10.67 L Q^{1.852} / (C^{1.852} D^{4.87}) for a circular water pipe. Runs locally. Not Darcy–Weisbach, not Colebrook, and not Manning.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary Engine tested · Source checked · 17/17 tests · Production surface contract 4/4 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
Model: SI Hazen–Williams circular water-pipe head loss. Invert for Q, D, or C.
Scope: SI Hazen–Williams k=10.67
Verification: Engine tested · 17/17 tests · Production surface contract 4/4 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: ISO 80000-4 — Mechanics — Volume flow rate and hydraulic head
Williams, G.S. and Hazen, A. Hydraulic Tables — Empirical pipe formula
Sources
Evidence: 2 golden · 10 boundary · 5 property · Production surface contract 4/4 · 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) @ 2026-09-17T06:27:56.932Z
Semantic contract: PASS

Formulas

Core equations used by this calculator.

Head losshf = 10.67 L Q^{1.852} / (C^{1.852} D^{4.87})

Friction slopeS = hf / L

iSI only (Q in m³/s, D and L in m). US customary gpm/in is out of scope. This page is not Darcy–Weisbach, not Colebrook, and not Manning.

How to use

Enter C

C is the empirical Hazen–Williams coefficient. Typical water-pipe values are about 80–150. It must be greater than zero.

Enter L, Q, and D

Length, volume flow, and inside diameter. All must be greater than zero. This is not Q=Av: send Q, not v.

Read hf

hf is metres of head. S = hf/L. Invert for Q, D, or C on the other tabs.

Example calculations

Common configurations with formula and result.

Water main

C=120, L=100 m, Q=0.02 m³/s, D=0.2 m

hf = 10.67 L Q^{1.852} / (C^{1.852} D^{4.87})

hf from the SI formula

From slope

Same C, L, D, with S instead of hf

hf = S L

same invert as hf

Hazen–Williams calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 17/17 tests · Production surface contract 4/4
Named expert review Not performed
Calculation version 1.0.0

Review policy · Evidence

Definition: SI Hazen–Williams: hf = 10.67 L Q^{1.852} / (C^{1.852} D^{4.87}). Circular full-flow water pipe. Empirical C. k = 10.67.
What it calculates: SI Hazen–Williams circular water-pipe head loss. Invert for Q, D, or C.
Inputs: mode?
C
L
Q
D
hf|S?
Outputs: hf
Q
v
C
L
D
A
S
k
Formula: hf = 10.67 L Q^{1.852} / (C^{1.852} D^{4.87})
Assumptions: SI Hazen–Williams k=10.67
Circular full-flow water pipe
Empirical C; not Darcy f, not Colebrook, not Manning n
Not Q=Av identities
Not US customary gpm/in
Units: SI; L and D in m; Q in m³/s; hf in m; C dimensionless
Boundary conditions: missing C, L, Q, D, or hf/S when required → MISSING_REQUIRED_INPUT
C, L, Q, D, hf, or S ≤ 0 → VALUE_MUST_BE_POSITIVE
hf and S together → MIXED_INPUT_ENCODING
f, Re, n, v, ρ, R, or C_d → MIXED_INPUT_ENCODING
k given and k ≠ 10.67 → INVALID_MODE
darcy, colebrook, or manning as mode → INVALID_MODE
Example: C=120 L=100 Q=0.02 D=0.2 → hf=10.67 L Q^{1.852}/(C^{1.852} D^{4.87})
Validation cases: 3 published on this page · 17/17 tests · Production surface contract 4/4 · View evidence
C=120 L=100 Q=0.02 D=0.2 → hf = 10.67 L Q^{1.852}/(C^{1.852} D^{4.87})
mode=flow C=120 L=100 D=0.2 hf from golden → Q recovers 0.02
C=120 L=100 Q=0.02 D=0.2 f=0.02 → MIXED_INPUT_ENCODING
Sources: ISO 80000-4 — Mechanics — Volume flow rate and hydraulic head
Supports: Q is volume flow; hf is a length of hydraulic head
Williams, G.S. and Hazen, A. Hydraulic Tables — Empirical pipe formula
Supports: Hazen–Williams C correlation for water pipes; SI form uses k=10.67 with Q in m³/s and D in m
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Compute pipe head loss from the SI Hazen–Williams formula.

Supported and not supported

Supported — hf, Q, D, or C from the SI circular-pipe formula · API physics.fluid.hazen_williams

Not supported — Darcy–Weisbach f, Colebrook, Manning, Q=Av identities, US customary gpm/in, non-circular sections, compressible flow

Agent / API notes

Capability id: physics.fluid.hazen_williams · tool id: hazen-williams · pin 1.0.0.

{ "mode": "head_loss", "C": 120, "L": 100, "Q": 0.02, "D": 0.2 }

Invert flow: { "mode": "flow", "C": 120, "L": 100, "D": 0.2, "hf": 0.272 }. Slope encoding: S instead of hf (hf = S L). Modes: head_loss (default), flow, diameter, C. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/hazen-williams. There is no /calc/fluid.

Other calculators in this family: Darcy–Weisbach, Colebrook, Manning formula, Hydraulic diameter, Minor loss .

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Frequently asked questions

Key distinctions behind the calculation.

Is this Darcy–Weisbach?

No. Pipe head loss from a given Darcy f is /calc/physics/darcy-weisbach. Sending f or ρ is MIXED_INPUT_ENCODING.

Is this Colebrook?

No. Turbulent-pipe f from Re and ε/D is /calc/physics/colebrook. Sending Re or ε/D is MIXED_INPUT_ENCODING.

Is this Manning?

No. Open-channel Q=(1/n) A R^{2/3} S^{1/2} is /calc/physics/manning-formula. This page is a circular water pipe with empirical C. Sending n or R is MIXED_INPUT_ENCODING.

Is this Q = A·v?

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

Can I use US customary gpm and inches?

No. This page is SI only (k=10.67). Sending k other than 10.67 is rejected.

Where does this run?

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