The Darcy-Weisbach equation is the standard, general-purpose way to calculate friction head loss in a pipe, applicable to both laminar and turbulent flow once you know the friction factor. This calculator finds head loss, the equivalent pressure drop, or solves for a missing friction factor or velocity from a target head loss.
How the Darcy-Weisbach equation works
The equation hf = f·(L/D)·(v²/2g) says that friction head loss grows linearly with pipe length and with the square of velocity, but shrinks as diameter increases. The friction factor f captures everything about the pipe's internal roughness and the flow regime (laminar vs. turbulent) — it is not a fixed constant, and must be looked up from a Moody chart or computed with the Colebrook equation for a given Reynolds number and relative roughness. Once you have f, the rest of the calculation is straightforward algebra.
Inputs and what they mean
Length (L) and diameter (D) both come from the pipe's physical dimensions — use the internal diameter, not a nominal pipe size, since actual bore diameters vary by schedule and material. Velocity (v) is the mean flow speed; if you only know the volumetric flow rate, divide by the cross-sectional area (πD²/4) first. Because head loss scales with the square of velocity, a small velocity increase (from a smaller pipe or higher flow rate) produces a disproportionately larger head loss — this is the single input most likely to surprise a first-time user.
Limits and edge cases
The Darcy-Weisbach equation only accounts for friction along straight pipe — it does not include minor losses from fittings, valves, elbows, or entrance/exit effects, which need to be added separately (typically as an equivalent length or a K-factor sum). For water distribution systems, the empirical Hazen-Williams equation is sometimes used instead because it avoids looking up a friction factor, at the cost of being water-specific and less accurate outside its calibrated velocity range. If your friction factor estimate is uncertain, treat the head-loss result as an estimate and re-check with a Moody chart before finalizing a pump or system design.