Darcy-Weisbach Calculator

The Darcy-Weisbach equation computes friction head loss in a pipe: hf = f · (L/D) · (v² / 2g), where f is the Darcy friction factor, L is pipe length, D is inner diameter, v is mean flow velocity and g is gravity. It is the most physically grounded head-loss formula in fluid mechanics because the friction factor comes from the flow physics (Reynolds number and pipe roughness) instead of empirical constants. This darcy weisbach calculator implements the equation directly in your browser.

Measure the pipe length L and inner diameter D, find the mean velocity v (or compute it from the flow rate as v = 4Q / πD²), look up the fluid's kinematic viscosity and the pipe roughness, solve the Colebrook equation for the friction factor f, and plug into hf = f·(L/D)·(v²/2g). Add minor losses ΣK·(v²/2g) for fittings and valves. This calculator does every step automatically.

For laminar flow (Re < 2300) use f = 64/Re exactly. For turbulent flow, solve the implicit Colebrook–White equation 1/√f = −2·log₁₀(ε/3.7D + 2.51/Re√f) by iteration — this page iterates it to better than 1e−12 starting from the explicit Haaland approximation. You can also read f off a Moody chart, or enter a measured value in the manual mode.

The Colebrook equation — also called the colebrook-white equation — is 1/√f = −2·log₁₀(ε/(3.7D) + 2.51/(Re·√f)). It relates the Darcy friction factor f to the Reynolds number Re and the relative roughness ε/D in fully turbulent pipe flow. Because f appears on both sides, it must be solved iteratively; the explicit Haaland equation 1/√f = −1.8·log₁₀((ε/3.7D)^1.11 + 6.9/Re) is an excellent starting guess (within about 2%).

The Reynolds number Re = v·D/ν is the ratio of inertial to viscous forces, with ν the kinematic viscosity of the fluid. Below about 2300 the flow is laminar (smooth layers, f = 64/Re); above about 4000 it is turbulent (f from Colebrook); between 2300 and 4000 lies the transitional zone. Re decides which friction-factor formula applies, so the calculator computes it first.

Absolute roughness ε is the average height of the wall's surface irregularities — for example 0.045 mm for commercial steel or 0.0015 mm for drawn tubing. What matters in the Colebrook equation is the relative roughness ε/D. Smoother pipe (smaller ε/D) gives a smaller friction factor and less head loss. The calculator ships with roughness presets for common pipe materials plus a custom entry.

Darcy-Weisbach is physics-based and works for any fluid, any Reynolds number and any pipe roughness because the friction factor adapts to the flow. Hazen-Williams is an empirical shortcut that only applies to water near room temperature in the turbulent range, using a roughness coefficient C. Use Darcy-Weisbach whenever you need generality or accuracy outside normal water conditions.

For laminar flow (Re < 2300 in a circular pipe) the laminar flow friction factor is exact: f = 64/Re, so head loss becomes hf = (64/Re)·(L/D)·(v²/2g). Since Re = vD/ν, head loss in the laminar regime scales linearly with velocity rather than with velocity squared. This calculator applies f = 64/Re automatically whenever the Reynolds number is laminar.

Minor losses are the extra head loss from fittings, valves and pipe entrances/exits, computed as hLm = ΣK·(v²/2g) where each K is a minor loss coefficient — for example 0.5 for a sharp entrance, 1.0 for a pipe exit, 0.3 for a flanged 90° elbow or 10 for a fully open globe valve. Add them to the friction head loss for the total. The calculator includes a fittings table so you can tally K automatically.

Multiply head loss (in meters of fluid) by ρ·g: Δp = ρ·g·hf. For water at 20 °C (ρ ≈ 998 kg/m³), 1 m of head equals about 9.79 kPa or 1.42 psi. The calculator shows the equivalent pressure drop in kPa and psi automatically, using the density of the fluid you selected. In other words, this page also works as a pressure drop calculator for water pipes and ducts.

Yes. The Darcy-Weisbach equation applies to any Newtonian fluid — the result hf is simply "meters of flowing fluid". Select air at 20 °C (or water at other temperatures) from the fluid menu, or enter custom kinematic viscosity and density. For gases the pressure drop Δp = ρghf is only exact for short ducts where density barely changes; long compressible gas lines need integrated methods.

Length in m, km, ft or miles; diameter in mm, cm, m, inches or ft; velocity in m/s or ft/s; flow rate in m³/s, L/s, L/min, gpm or ft³/s. Everything is converted to SI internally. Results are reported as head in meters and feet, and pressure drop in kPa and psi.

The iteration converges to a relative tolerance of 1e−12, far beyond engineering need — the result matches the Moody chart to the thickness of the printed line. The dominant real-world uncertainty is your input data (especially pipe roughness and actual inner diameter), not the solver.

Almost always one of three things: reading error on the logarithmic Moody axes, a different roughness assumption (chart curves step in coarse ε/D increments), or the flow being in the transitional zone where the chart is approximate. The Colebrook solution here is the same curve the chart is drawn from, so a careful re-read usually closes the gap.

The total head a pump must deliver is H = hf (friction) + hLm (minor losses) + elevation difference + any required pressure head at the outlet. Pick a trial diameter, compute the head loss, and iterate: larger pipe costs more upfront but cuts hf roughly as 1/D⁵ for a fixed flow rate, since v²/D ~ Q²/D⁵. Pump catalogs list curves of head versus flow for exactly this match-up.

No. Every calculation — the Reynolds number, the Colebrook iteration, the unit conversions — runs entirely in your browser with JavaScript. Nothing you enter leaves your device; there are no accounts, no analytics beacons from this tool, and no external requests of any kind.