Pipe Friction Factor Calculator: Colebrook-White (Moody Chart), Reynolds Number and Head Loss

Darcy friction factor and head loss for a full pipe.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the pipe diameter and the roughness of the pipe wall.

Enter the velocity, the kinematic viscosity, the density and the length of the pipe.

The calculator gives the Reynolds number, the friction factor, the head loss and the pressure drop.

Formulas used

  • Re = \frac{vD}{\nu}
  • \frac{1}{\sqrt f} = -2\log_{10}\left(\frac{\varepsilon/D}{3.7} + \frac{2.51}{Re\sqrt f}\right)
  • h_f = f\,\frac{L}{D}\,\frac{v^2}{2g}

Worked example

With the default numbers in the calculator above:

  1. Reynolds number: 199203
  2. Relative roughness: 0.00045
  3. Darcy friction factor (Colebrook-White, solved by repeating): 0.018567
  4. Swamee-Jain shortcut for comparison: 0.018672
  5. Head loss along the pipe: 3.7867 m of fluid
  6. Pressure drop along the pipe: 37.06 kPa

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: Mean velocity of the fluid 0.01 m/s.

  1. Reynolds number: 996.016
  2. Relative roughness: 0.00045
  3. Darcy friction factor (laminar: 64 / Re): 0.064256
  4. Head loss along the pipe: 0.00032761 m of fluid
  5. Pressure drop along the pipe: 0.0032064 kPa

Common questions

What is the Colebrook equation used for?

It gives the Darcy friction factor for turbulent flow in a rough pipe. The same equation is behind the Moody chart.

Why does the calculator repeat the calculation?

The friction factor appears on both sides of the Colebrook equation, so it is solved by repeating until the answer stops changing.

What friction factor is used for laminar flow?

For a Reynolds number under about 2300 the friction factor is 64 divided by the Reynolds number, and the roughness does not matter.

What is the Swamee-Jain equation?

A direct formula that gives nearly the same friction factor as Colebrook-White without repeating, good to about 1 percent over the usual range.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any fluid mechanics text (the Moody chart and the Colebrook-White equation).

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