Colebrook Equation Calculator

The Colebrook equation calculator solves the implicit Colebrook-White relation to find the Darcy friction factor for turbulent pipe flow. This friction factor is essential for estimating head loss and pressure drop in piping systems using the Darcy-Weisbach equation.

The Colebrook-White Equation

The Colebrook equation combines the effects of Reynolds number and relative pipe roughness into a single implicit formula:

1/√f = -2 log&sub1;&sub0;( ε/(3.7D) + 2.51/(Re√f) )

Where f is the Darcy friction factor, ε is absolute roughness, D is pipe diameter, and Re is the Reynolds number. Because f appears on both sides of the equation, the calculator solves it iteratively using fixed-point iteration.

How to Use

Enter the pipe's absolute roughness, internal diameter, and Reynolds number. Select the appropriate units for roughness and diameter. The calculator converts all inputs to meters, computes the relative roughness, and iteratively solves the Colebrook equation. The result updates in real time as you modify any input.

If the Reynolds number is below 2,000 (laminar flow), the calculator automatically uses f = 64/Re instead, since the Colebrook equation applies only to turbulent flow.

Applications

The Colebrook equation is widely used in pipe system design, HVAC engineering, process piping, and hydraulics education. It replaces visual Moody chart lookup with a precise numerical value that can be carried into downstream head-loss and pressure-drop calculations.

Common Mistakes

• Using the Colebrook equation for laminar flow — use f = 64/Re instead.
• Confusing absolute roughness with relative roughness.
• Mixing Darcy and Fanning friction factors — the Darcy value is four times the Fanning value.