Friction Factor Calculator

How to use this calculator

Enter the average flow velocity, the pipe's inner diameter, its absolute roughness, and the fluid's kinematic viscosity, then click Calculate. The tool computes the Reynolds number, classifies the flow regime, and solves for the Darcy-Weisbach friction factor. Click Clear to reset all fields to the defaults and start a new calculation.

The formula

The Reynolds number is computed first, since it determines which friction-factor formula applies:

Re = V·D / ν

where V is flow velocity (m/s), D is the pipe's inner diameter (m), and ν is the fluid's kinematic viscosity (m²/s). Below Re ≈ 2300 the flow is laminar and the Darcy friction factor has a closed-form solution:

f = 64 / Re

Above Re ≈ 4000 the flow is turbulent, and the friction factor is found from the implicit Colebrook-White equation, which this calculator solves numerically by iteration:

1/√f = −2·log₁₀( (ε/D)/3.7 + 2.51/(Re·√f) )

Here ε/D is the relative roughness — the pipe's absolute roughness ε divided by its inner diameter D. Between Re ≈ 2300 and 4000 the flow is transitional; there is no universally accepted formula for this zone, so the calculator applies the Colebrook-White solution as a reasonable estimate and flags the result as transitional.

Head loss

Once f is known, the Darcy-Weisbach equation gives the friction head loss over a length L of straight pipe:

h_f = f · (L/D) · V² / (2g)

The calculator reports this loss for a reference length of 100 m, using standard gravity g = 9.80665 m/s². Scale it linearly for any other pipe length (for example, double the value for 200 m).

Interpreting the results

The friction factor (f) is the highlighted primary result — larger values mean more energy is lost to friction per unit length. The Reynolds number and flow regime explain which formula produced that value. The head-loss figure translates the dimensionless friction factor into a physical pressure drop, expressed as meters of fluid over 100 m of pipe.

Frequently Asked Questions

What is the difference between the Darcy and Fanning friction factor?

This calculator reports the Darcy (Darcy-Weisbach) friction factor, the version used in the Darcy-Weisbach head-loss equation hf = f(L/D)(V²/2g). The Fanning friction factor, common in chemical engineering, is exactly one-quarter of the Darcy value (f_Darcy = 4 × f_Fanning). Always check which convention a source is using before comparing numbers.

Why does the calculator use iteration to solve the Colebrook-White equation?

The Colebrook-White equation has the friction factor f on both sides (inside a logarithm and outside it), so it cannot be solved directly with algebra. The calculator starts from the Swamee-Jain explicit approximation as an initial guess, then refines it with a few iterations until the result converges to within a very small tolerance — effectively the same answer an engineer would get reading a Moody chart, but exact.

What roughness value should I use for my pipe?

Typical absolute roughness values are about 0.0015mm for drawn copper or plastic tubing, 0.045mm for commercial (new) steel pipe, 0.15-0.3mm for galvanized steel, and 0.15-0.5mm for cast iron. Older or corroded pipes can have effective roughness several times higher than the new-pipe value, so measured or manufacturer data is always preferable to a table lookup when precision matters.

Why does flow regime matter for the friction factor?

In laminar flow (Re below about 2300), friction is dominated by viscous shear between fluid layers and the pipe wall roughness has essentially no effect, so f = 64/Re. In turbulent flow (Re above about 4000), chaotic mixing means wall roughness matters a great deal, and f depends on both Re and the relative roughness ε/D through the Colebrook-White equation. The transitional zone between them is unstable and not reliably predicted by any single formula.