Darcy vs. Fanning Friction Factor

Darcy is four times Fanning

Both factors describe the same wall-friction loss. They use different definitions, so the numerical values differ while the predicted pressure drop stays the same when each is paired with its matching equation.

For Frictionless Calc: the pipe pressure-drop calculator uses the Darcy convention. The friction-factor calculator labels Darcy and Fanning outputs separately. The K ↔ equivalent-length calculator requires a Darcy factor.

Equations side by side

Here L is pipe length, D is inside diameter, V is mean pipe velocity, ρ is mass density, τw is wall shear stress, and Re = ρVD/μ. Both friction factors are dimensionless. Use actual pipe ID.

With ρ in kg/m³, V in m/s, and L and D in the same length units, Δp is in Pa. For hL in meters, use V in m/s and g = 9.80665 m/s². US customary equations using lbm and lbf also need the appropriate gc conversion; do not mix mass and force units.

Why the factor of four appears

For steady, fully developed flow in a straight circular pipe, a force balance gives Δp = 4τwL/D. Fanning defines fF = τw/(ρV²/2). Substitution gives Δp = 4fF(L/D)(ρV²/2), which matches the Darcy equation when fD = 4fF.

Convert a friction factor

Enter a known factor and its convention. This converts definitions; it does not calculate a factor from flow conditions. To obtain a factor from Reynolds number and roughness, use the friction factor calculator.

Zero is allowed as a mathematical limit. A real viscous pipe flow has positive wall friction. Displayed digits do not establish accuracy of the input.

Calculate friction factor from Reynolds number and roughness ↗

How to identify an unlabeled factor

1. Read the definition and pressure-loss equation. With dynamic pressure written as ρV²/2 and geometry as L/D, a coefficient f is Darcy; a coefficient 4f is Fanning.
2. Check the laminar branch. For fully developed Newtonian flow in a circular pipe, 64/Re indicates Darcy and 16/Re indicates Fanning.
3. Inspect the chart axis. A conventional Moody chart uses Darcy, also called the Moody friction factor. Verify the actual label because charts are sometimes redrawn using Fanning.
4. Check the entire correlation. Symbols alone are not enough: f, λ, or another symbol can be defined differently by a source. A factor’s magnitude alone cannot reliably identify its convention.

Colebrook form

This form gives the Darcy factor for turbulent pipe flow. Divide the resulting factor by 4 to obtain Fanning. Substituting fD = 4fF throughout gives the equivalent Fanning form:

Changing the factor convention does not change Re or relative roughness ε/D. Follow the chosen correlation’s geometry and flow-regime limits. See the pipe roughness reference.

The conversion is exact; the flow model may be approximate

fD = 4fF holds for matching definitions in laminar, transitional, and turbulent flow. The 64/Re and 16/Re relations have narrower scope: fully developed, Newtonian laminar flow in a circular pipe. Noncircular ducts, developing flow, and non-Newtonian fluids need appropriate correlations. Hydraulic diameter alone does not make 64/Re universally valid.

Worked example: the same pressure loss

Assume ρ = 1,000 kg/m³, V = 2.0 m/s, L = 30 m, D = 0.050 m, and a Darcy factor of 0.020. The corresponding Fanning factor is 0.005. These factors are assumed for demonstration, not calculated from a specified roughness.

Both give hL = 24,000/(1,000 × 9.80665) = 2.447 m. Using 0.005 directly in the Darcy equation gives 6.0 kPa, a 75% underestimate. Using 0.020 in the Fanning equation gives 96.0 kPa, four times the correct loss.

Laminar cross-check

At Re = 1,000 in fully developed Newtonian circular-pipe flow: fD = 64/1,000 = 0.064 and fF = 16/1,000 = 0.016. The ratio is still exactly four.

Fittings: keep K separate from the friction factor

A standard velocity-head loss coefficient K in Δp = KρV²/2 does not change when you switch between Darcy and Fanning conventions. Only the straight-pipe friction expression changes:

These combined expressions assume the terms use the same velocity and density basis. Do not multiply the fitting K sum by 4.

Equivalent-length example

For K = 1.0 and D = 0.050 m, using fD = 0.020 gives Le = KD/fD = 2.5 m. Using fF = 0.005 gives Le = KD/(4fF) = 2.5 m. Omitting the 4 in the Fanning version incorrectly gives 10 m.

For a correlation written K = n fT, identify the convention of fT and keep the coefficient consistent with its source. For example, 30 fT,D equals 120 fT,F, not 30 fT,F. The site’s pipe pressure-drop calculator uses a Darcy-based complete-turbulence reference factor for its n × fT fittings; this is separate from the operating straight-pipe factor.

K-factor guide · K ↔ equivalent length calculator

Common mistakes

• Converting twice: check whether software already converted its output before multiplying or dividing by 4.
• Changing the factor but keeping the wrong equation: use the matching pair shown above.
• Confusing roughness and friction: ε, ε/D, and f are different quantities. No factor-of-four conversion applies to pipe roughness.
• Assuming a smooth pipe has zero friction: a smooth wall removes the roughness contribution, not viscous wall shear.
• Applying liquid equations to large gas density changes: the convention conversion still applies, but a constant-density pressure-loss calculation may not.
• Confusing Darcy friction with Darcy’s law: porous-media permeability and Hazen-Williams C are not Darcy friction factors.

Pipe pressure drop · Friction factor calculator · Reynolds number

Sources and scope

• AFT Fathom: Pressure Drop in Pipes: Darcy-Weisbach convention, factor-of-four relationship, and flow-regime treatment.
• COMSOL Pipe Flow Module: Flow Equations: Darcy friction, roughness, and correlation scope.

The equations above use explicit Darcy and Fanning subscripts; worked examples and the converter follow directly from those definitions. The pressure/head-loss examples assume steady, single-phase, constant-density flow in a straight circular pipe. Add fittings, elevation, acceleration, and equipment terms as required for a complete energy balance.

Sources checked October 1, 2026.