Pipe Head Loss Calculator (Darcy-Weisbach)
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/8/2026
Head loss in a pipe is calculated with the Darcy-Weisbach equation: ΔP = f × (L ÷ D) × (ρ × v² ÷ 2), where f is the friction factor, L the pipe length, D its diameter, ρ the fluid density, and v its flow velocity. For a 100 m water pipe, 10 cm in diameter, a friction factor of 0.02, and a velocity of 2 m/s, the head loss is 40,000 Pa.
Explanation
The Darcy-Weisbach equation is the reference formula for estimating head loss — the pressure drop due to friction — of a fluid flowing through a pipe. It combines the pipe's geometry (the length-to-diameter ratio, L/D: the longer and narrower a pipe, the greater the head loss) with the fluid's kinetic energy per unit volume (ρv²/2), scaled by the friction factor f, which depends both on the pipe's inner roughness and the flow regime, laminar or turbulent — determined by the Reynolds number. This friction factor is not calculated directly by this calculator: it must be estimated beforehand, generally from a Moody chart or an empirical correlation such as the Colebrook equation, based on the Reynolds number and the pipe's relative roughness — a typical value of 0.02 to 0.03 is common for turbulent flow in a standard metal pipe. This head loss adds directly to the pressure a pump must supply to maintain a given flow rate, and factors into the sizing of any piping network — see also our volumetric flow rate calculator and our pipe diameter from flow rate calculator.
Example: a 100 m water pipe, 10 cm in diameter, velocity 2 m/s
Inputs
Friction factor: 0.02. Length: 100 m. Diameter: 0.1 m. Density: 1,000 kg/m³ (water). Velocity: 2 m/s.
Calculation
ΔP = 0.02 × (100 ÷ 0.1) × (1,000 × 2² ÷ 2) = 0.02 × 1,000 × 2,000 = 40,000 Pa.
Result
The head loss in this pipe is 40,000 Pa, or 40 kPa.
Frequently asked questions
Where does the friction factor f come from?
It's generally determined from the flow's Reynolds number and the pipe's relative roughness (its inner roughness divided by its diameter), using a Moody chart or an empirical correlation such as the Colebrook equation. This calculator does not compute it: it must be entered as an input, from a measured, tabulated, or pre-estimated value.
Why does head loss increase with the square of velocity?
Because the term ρv² ÷ 2 represents the fluid's kinetic energy per unit volume, which grows with the square of velocity. In practice, doubling the flow velocity in the same pipe quadruples the head loss, all else being equal — a direct consequence of this quadratic dependence, not to be underestimated when sizing a pump.
Does this formula apply to all fluids?
It applies to both liquids and gases, provided the flow can be considered incompressible — the usual assumption for liquids, and valid for gases as long as the relative pressure drop stays small. For a gas undergoing a large pressure drop relative to its absolute pressure, more advanced compressible flow equations are needed.