Friction Factor: the Darcy friction factor sets how much pressure a pipe flow loses to wall friction. For laminar flow it is simply 64/Re; for turbulent flow it comes from the Colebrook equation using the relative roughness. This free calculator returns the Darcy factor (and the Fanning factor) with every step shown.
To find the friction factor, first find the Reynolds number Re for the flow. If Re is below about 2300 the flow is laminar and the Darcy friction factor is simply f = 64/Re, independent of the wall roughness. Above that value the flow is turbulent, and the Darcy factor comes from the implicit Colebrook equation, 1/sqrt(f) = -2 log10(relative roughness / 3.7 + 2.51/(Re sqrt(f))), which this calculator solves by iteration.
Enter the Reynolds number and the relative roughness — the wall roughness height divided by the pipe diameter (ε/D). Use 0 for a perfectly smooth pipe. The calculator picks the laminar or turbulent branch automatically and shows the full working: the governing formula, your numbers substituted in, and the resulting Darcy factor together with the Fanning factor.
The friction factor is the missing piece in the Darcy-Weisbach head-loss equation, so it is often the first thing you compute in a pipe-flow problem. To find the flow speeds and pressures that set the Reynolds number in the first place, see the Bernoulli equation calculator; to convert the resulting head loss into a pressure drop, use the pressure calculator. For the underlying terms, see the physics glossary.
Water flowing at Re = 100 000 in a pipe with a relative roughness of 0.0001 gives a Darcy friction factor of about 0.0185 (Fanning about 0.0046) from the Colebrook equation — the calculator reaches this by iterating the implicit formula until it converges. In the laminar range the roughness drops out entirely: at Re = 2000 the flow is laminar, so f = 64/2000 = 0.032 regardless of how rough the pipe wall is.
The friction factor feeds the Darcy-Weisbach head-loss equation, so it drives pump sizing, pipe diameter selection and pressure-drop estimates in water, oil and gas networks and HVAC ducts. Get it wrong and a pump is either undersized or wastes energy. The Fanning factor (one quarter of the Darcy value) is common in chemical engineering, so this tool reports both. Fluid properties such as viscosity set the Reynolds number that decides the flow regime — see the viscosity converter to work in the units your problem uses.
A dimensionless number in the Darcy-Weisbach equation that quantifies frictional pressure loss in a pipe; it depends on the Reynolds number and the pipe roughness.
The Darcy factor is four times the Fanning factor (Darcy = 4 x Fanning); make sure you use the one matching your head-loss equation.
Roughly, laminar below Re 2300 and turbulent above 4000, with a transition region between; laminar uses f = 64/Re.
An implicit formula for the turbulent Darcy factor from Reynolds number and relative roughness; it must be solved iteratively, as this calculator does.
The pipe's absolute roughness height divided by its inside diameter; smooth drawn tubing is near zero, while old cast iron can be a few thousandths.