Pump Head Loss Calculator
When a pump pushes water through a pipe, friction against the pipe wall consumes energy, and that loss, expressed as a height of water column called head loss, is what the pump must overcome. The Darcy-Weisbach equation is the most general way to compute it: head loss equals the friction factor times the pipe length divided by the diameter, times the velocity squared divided by twice the gravitational constant. This calculator applies that formula in US units of feet and seconds. The friction factor depends on the flow regime and pipe roughness and is usually read from a Moody chart or a correlation; for a quick estimate, typical turbulent values sit around 0.02. Enter the friction factor, the pipe length and inside diameter in feet, and the flow velocity in feet per second, and the tool returns the friction head loss in feet, which you add to elevation change and fitting losses to find the total head a pump must deliver. The velocity-squared term means head loss rises steeply with flow, so oversizing flow is costly. Every figure is computed deterministically from the formula shown below, with a worked example that reconciles exactly to the calculator defaults.
Darcy-Weisbach head loss is f x (L / D) x V^2 / (2g). With f of 0.02, a 100 ft pipe of 0.5 ft diameter at 6 ft/s, the friction head loss is 2.24 feet of water.
Darcy-Weisbach head loss formula
h_f = f x (L / D) x V^2 / (2 x g)
f = Darcy friction factor
L = pipe length (ft), D = inside diameter (ft)
V = flow velocity (ft/s)
g = 32.2 ft/s^2 (gravity)
Head loss is a height of water column in feet. The velocity head, V squared over 2g, is the kinetic energy term; head loss is that velocity head scaled by the friction factor and the length-to-diameter ratio.
Worked example
Suppose the friction factor is 0.02, the pipe is 100 feet long with a 0.5 foot inside diameter, and the velocity is 6 feet per second.
- Length to diameter: 100 / 0.5 = 200
- Velocity head: 6^2 / (2 x 32.2) = 36 / 64.4 = 0.5590 ft
- Head loss: 0.02 x 200 x 0.5590 = 2.24 ft
The friction head loss is 2.24 feet of water column. These are the calculator's default inputs, so the result matches the widget exactly.
Pump Head Loss Calculator: frequently asked questions
What is head loss?
Head loss is the energy a fluid loses to friction and turbulence as it flows through a pipe, expressed as an equivalent height of fluid column in feet. A pump must supply enough head to overcome friction loss plus any rise in elevation plus losses through fittings and valves.
What is the friction factor?
The Darcy friction factor captures how rough the pipe is and how the flow behaves. It depends on the Reynolds number and the pipe's relative roughness, read from a Moody chart or computed from a correlation. For fully turbulent flow in typical pipe, values near 0.02 are common for a quick estimate.
Why does head loss rise so fast with velocity?
The equation includes velocity squared, so doubling the velocity quadruples the friction head loss. This is why pushing more flow through a given pipe quickly becomes energy-intensive, and why engineers size pipes to keep velocities moderate.
How is this different from Hazen-Williams?
Both compute pipe friction loss. Darcy-Weisbach is fundamentally based and works for any fluid and flow regime, but needs a friction factor. Hazen-Williams is a simpler empirical formula limited to water at ordinary temperatures. Darcy-Weisbach is more general; Hazen-Williams is more convenient for water supply.
What else adds to total pump head?
Total dynamic head is friction head loss plus static lift (the elevation the water must rise) plus minor losses through fittings, bends and valves, plus any required pressure at the outlet. This calculator gives the straight-pipe friction component. The Department of Energy publishes pumping-system efficiency guidance.
Official sources
- Pumping systems and energy efficiency guidance: US Department of Energy (DOE). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.