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Darcy-Weisbach Head Loss Calculator

Calculate the friction head loss and pressure drop along a pipe with the Darcy-Weisbach equation — the physically-based standard for pipe flow. Enter the friction factor, pipe length, internal diameter and flow velocity and get head loss in metres, pressure loss in kPa and the gradient per 100 m.

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How to use this calculator

Enter Values

Enter your values and press Calculate to see results.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Enter the Darcy friction factor f (from the Moody chart or the Friction Factor calculator) and the pipe length L in metres.
  2. Enter the internal diameter D in millimetres (it is converted to metres internally) and the mean flow velocity v in m/s.
  3. Read the friction head loss hf, the equivalent pressure loss in kPa (for water) and the head loss per 100 m of pipe.

How it works

The Darcy-Weisbach equation is hf = f · (L/D) · v²/(2g). The diameter is converted from mm to m, the velocity is squared and divided by 2g (g = 9.81 m/s²), then multiplied by the friction factor and the length-to-diameter ratio. Pressure loss is hf·ρ·g with water density ρ = 1000 kg/m³, and the per-100 m gradient is hf/L × 100.

Worked example

Worked example. For f = 0.02, L = 100 m, D = 100 mm (0.1 m) and v = 1.5 m/s: hf = 0.02 × (100/0.1) × 1.5²/(2×9.81) = 0.02 × 1000 × 0.11468 = 2.2936 m, which for water is 22.5 kPa.

Common mistakes

  • Confusing the Darcy friction factor with the Fanning friction factor — the Fanning value is exactly four times smaller, so mixing them gives a 4× error.
  • Entering the diameter in metres when the field expects millimetres (or vice versa), which shifts the result by a factor of 1000.
  • Forgetting to add minor (fitting) losses from bends, tees and valves, which this equation does not include.

Frequently asked questions

Where do I get the friction factor f?

The Darcy friction factor depends on the Reynolds number and the pipe's relative roughness. Read it from the Moody chart or compute it with the Colebrook or Swamee-Jain equation — the Friction Factor (Moody) calculator does exactly this.

How is this different from Hazen-Williams?

Hazen-Williams is an empirical water-only formula with a roughness coefficient C, valid near room temperature. Darcy-Weisbach is physically based, works for any fluid and temperature, and is generally preferred where accuracy matters.

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