HomeCalculatorsPhysicsFluid MechanicsColebrook Friction Factor Calculator
Physics calculator

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.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Colebrook–White turbulent f from Re and ε/D; + O3 tabulated f.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Colebrook–White turbulent f from Re and ε/D; + O3 tabulated f.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (friction, smooth, awkward, boundary, invalid-domain) · Matrix
Deferred
Not Darcy hf from given f, not laminar 64/Re, and not Swamee–Jain as the product.
Numerical scope
O2: Colebrook–White 1/√f = −2 log10(ε/D/3.7 + 2.51/(Re√f)) via Haaland start + Newton on √f (≤2 ULP). Not Darcy hf, not laminar 64/Re, and not Swamee–Jain as the product. ≤2 ULP vs O3 applies only to the published tabulated Colebrook vectors. Not Darcy hf and not laminar 64/Re.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Darcy friction factor f from the Colebrook–White equation.
Scope
Turbulent circular full-flow pipe, Re ≥ 4000
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Colebrook–White turbulent f from Re and ε/D; + O3 tabulated f.· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-26.o2-o3.cov.iut
Verification revision
2026-09-26.o2-o3.cov.iut · 1/1 property · digest c54ce22c5aa4
Legacy regression
9/9 tests · Production surface contract 6/6
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
5/5 golden · 6/6 CVP boundary · 5/5 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract · Manifest
Sources
  • Colebrook, C.F. (1939). Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws — Journal of the Institution of Civil Engineers, 11, 133–156
  • White, F.M. Fluid Mechanics — pipe flow friction — Colebrook–White equation
Sources
Evidence
1 legacy golden · 5 legacy boundary · legacy regression suite · 5/5 oracle-backed golden · 5/5 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.

Colebrook–White1/√f = −2 log₁₀(ε/D / 3.7 + 2.51/(Re √f))
iHaaland is used only as the Newton initial guess. This page does not return laminar 64/Re and does not look up a Moody chart.

How to use

1

Enter Reynolds number

Re must be at least 4000. Transitional and laminar pipes are out of range for this correlation.

2

Enter relative roughness

ε/D (dimensionless). REST also accepts absolute roughness ε and diameter D.

3

Read Darcy friction factor f

f is the Darcy–Weisbach factor. Use it on a head-loss page; this page does not compose Δp.

Example calculations

Common configurations with formula and result.

ϟ

Smooth-ish commercial pipe

Re=1e5, ε/D=0.0002

Colebrook–White
f≈0.019005

Colebrook Friction Factor calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Colebrook–White: 1/√f = −2 log10(ε/D/3.7 + 2.51/(Re √f)). Turbulent pipes Re≥4000. Not laminar f=64/Re.
What it calculates
Darcy friction factor f from the Colebrook–White equation.
Inputs
  • Re
  • rel_roughness | eps_m+D_m
Outputs
  • f
  • Re
  • rel_roughness
  • inv_sqrt_f
Formula
1/√f = −2 log10(ε/D/3.7 + 2.51/(Re √f))
Assumptions
  • Turbulent circular full-flow pipe, Re ≥ 4000
  • Incompressible; constant properties
  • Not laminar 64/Re
  • Not a Moody-chart lookup
  • Does not compose Darcy head loss or Reynolds
Units
  • SI; ε/D dimensionless
Boundary conditions
  • Re < 4000 → VALUE_OUT_OF_RANGE
  • rel_roughness > 0.05 → VALUE_OUT_OF_RANGE
  • missing rel_roughness and missing eps_m+D_m → MISSING_REQUIRED_INPUT
  • rel_roughness together with eps_m+D_m → MIXED_INPUT_ENCODING
Example
Re=1e5 rel_roughness=0.0002 → f≈0.019005
Validation cases

2 published on this page · 9/9 tests · Production surface contract 6/6 · View evidence

  • Re=1e5 rel_roughness=0.0002 → f≈0.019005; residual of Colebrook ≈ 0
  • Re=2300 rel_roughness=0 → VALUE_OUT_OF_RANGE
Sources
  • Colebrook, C.F. (1939). Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws — Journal of the Institution of Civil Engineers, 11, 133–156
    Supports: 1/√f = −2 log10(ε/D/3.7 + 2.51/(Re √f))
  • White, F.M. Fluid Mechanics — pipe flow friction — Colebrook–White equation
    Supports: Implicit turbulent-pipe friction factor; not laminar 64/Re
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute the Darcy friction factor from Colebrook–White.

Supported and not supported

Supported — turbulent-pipe f from Re and ε/D · REST also accepts ε and D · API physics.fluid.colebrook

Not supported — laminar f=64/Re, Moody-chart lookup, Darcy head-loss composition, compressible pipe flow

Agent / API notes

Capability id: physics.fluid.colebrook · tool id: colebrook · pin 1.0.0.

{ "Re": 100000, "rel_roughness": 0.0002 }

Alternate encoding: { "Re": 100000, "eps_m": 2e-5, "D_m": 0.1 }. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING.

Calculator URL stays /calc/physics/colebrook. There is no /calc/fluid.

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Frequently asked questions

Key distinctions behind the calculation.

Is this the same as laminar f=64/Re?

No. Colebrook–White is a turbulent-pipe correlation. This page rejects Re below 4000 instead of switching formulas.

Does this look up a Moody chart?

No. It solves the implicit Colebrook–White equation. Moody’s chart is a graphical presentation of the same family, not this solver.

Can I enter ε and D instead of ε/D?

Yes on REST and MCP: eps_m and D_m. The web form uses ε/D. Do not send both encodings together.

Does this compute head loss?

No. It returns f. Head loss is /calc/physics/darcy-weisbach from a given f.