Find the head loss due to friction in a pipe from the friction factor, length, diameter, and velocity, see the equivalent pressure drop, or solve for a missing variable — hf = f·(L/D)·(v²/2g).
Pipe & fluid properties
Typical turbulent-flow range: 0.008–0.09 (from the Moody chart or Colebrook equation).
Use the internal diameter. 100 mm = 0.1 m.
Standard gravity: 9.81 m/s².
Water ≈ 1000 kg/m³ at room temperature.
Head loss
—
Enter the friction factor, length, diameter, and velocity to compute.
Pressure drop (kPa)—
Pressure drop (psi)—
Compare scenarios
Scenario
Head loss
This pipe (L)
—
Double the length (2L)
—
Head loss is directly proportional to length — twice the length means twice the head loss, all else equal.
Pipe & fluid properties
Water ≈ 1000 kg/m³ at room temperature.
Pressure drop
—
Enter the friction factor, length, diameter, velocity, and density to compute.
Head loss (m)—
Pressure drop (psi)—
Solve for a missing variable
Solved value
—
Choose a variable, set the target head loss, and enter the other known values.
3 min read5 steps7 terms3 examples6 FAQshf = f · (L/D) · (v²/2g)
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.
📋
Walk-through
How to Use This Calculator
5 steps▸
1
Enter the friction factor
Type the Darcy friction factor f for the pipe. Typical turbulent-flow values run 0.008–0.09; look it up on a Moody chart or the Colebrook equation for your pipe's roughness and Reynolds number.
2
Enter pipe length and diameter
Fill in the pipe length L and internal diameter D in meters. Use the actual internal diameter, not the nominal or outer pipe size.
3
Enter the flow velocity
Enter the mean flow velocity v in m/s. If you only know the flow rate, divide it by the pipe's cross-sectional area (πD²/4) first.
4
Read the head loss and pressure drop
The Head Loss tab shows friction head loss in meters with the equivalent pressure drop in kPa and psi. Switch to the Pressure Drop tab for the same result framed around ΔP.
5
Solve for a missing variable
On the Solve tab, pick friction factor or velocity, enter a target head loss and the other known values, and the calculator inverts the equation for you.
⚡
Reference
Formula & Methodology
1 formula▸
Darcy-Weisbach equation
hf = f · (L/D) · (v²/2g)
hf is the head loss due to friction in meters, f is the dimensionless Darcy friction factor, L is pipe length in meters, D is internal pipe diameter in meters, v is mean flow velocity in m/s, and g is gravitational acceleration (9.81 m/s²). The equivalent pressure drop follows from ΔP = ρ·g·hf, where ρ is the fluid density in kg/m³.
📖
Glossary
Key Terms Explained
7 terms▸
Darcy-Weisbach equation ↗The standard equation relating friction head loss in a pipe to the friction factor, length, diameter, and velocity: hf = f(L/D)(v²/2g). It applies to both laminar and turbulent flow.
Head loss ↗The energy lost to friction as fluid flows through a pipe, expressed as an equivalent height of fluid column in meters (or feet). Larger head loss means more energy the system must supply.
Friction factor ↗The dimensionless Darcy friction factor f, which depends on the pipe's relative roughness and the Reynolds number. Found from a Moody chart or computed with the Colebrook equation.
Pipe diameter ↗The internal (bore) diameter of the pipe, in meters. Head loss is extremely sensitive to diameter since it appears to roughly the fifth power in the flow-rate form of the equation.
Velocity ↗The mean flow velocity of the fluid through the pipe cross-section, in meters per second, equal to the volumetric flow rate divided by the cross-sectional area.
Pressure drop ↗The pressure lost along the pipe run due to friction, ΔP = ρ·g·hf, expressed in pascals, kilopascals, or psi. A pump or upstream pressure source must overcome this loss.
Moody chart ↗A chart (or the equivalent Colebrook equation) that gives the Darcy friction factor as a function of Reynolds number and the pipe's relative roughness (ε/D).
👥
Scenarios
Real-World Examples
3 worked examples▸
🚰
Facilities engineer
100 m water supply run
Friction factor f 0.02Length L 100 mDiameter D 0.1 mVelocity v 2 m/s
hf = 0.02 × (100/0.1) × (2²/(2×9.81)) ≈ 4.08 m of head loss. At water's density (1000 kg/m³) that equals a 40.0 kPa (5.8 psi) pressure drop — the pump feeding this run must supply at least that much extra pressure.
🏭
Process engineer
Same pipe, framed as pressure drop
Friction factor f 0.02Density ρ 1000 kg/m³
With the same head loss (4.08 m) and water's density, the Pressure Drop tab reports ΔP = 1000 × 9.81 × 4.08 ≈ 40.0 kPa directly — useful when sizing a pump against a manufacturer's pressure spec rather than a head spec.
📏
Piping designer
Doubling the pipe length
Length L 200 m (was 100 m)All other inputs unchanged
Head loss is directly proportional to length, so doubling L to 200 m doubles the head loss to about 8.15 m — exactly what the Head Loss tab's scenario-compare card shows. Everything else in the equation stays fixed.
🔗
Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
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.
❓
Questions
Frequently Asked Questions
6 questions▸
What is the Darcy-Weisbach formula?+
hf = f · (L/D) · (v²/2g), where hf is head loss in meters, f is the dimensionless friction factor, L is pipe length, D is internal diameter, v is mean velocity, and g is gravitational acceleration (9.81 m/s²).
How do I find the friction factor?+
Look it up on a Moody chart using the Reynolds number and the pipe's relative roughness (ε/D), or compute it directly with the Colebrook equation. Typical turbulent-flow values for common pipe materials range from about 0.008 to 0.09.
How is pressure drop related to head loss?+
Pressure drop equals ΔP = ρ·g·hf, where ρ is the fluid's density. For water (ρ ≈ 1000 kg/m³), 1 meter of head loss equals about 9.81 kPa (1.42 psi) of pressure drop.
What units does this calculator use?+
Length, diameter, and head loss are in meters; velocity is in meters per second; gravity is in m/s²; density is in kg/m³. Pressure drop is shown in both kilopascals (kPa) and pounds per square inch (psi) for convenience.
What happens if the pipe is longer?+
Head loss is directly proportional to length — doubling the pipe length doubles the head loss, with everything else held constant. The Head Loss tab's scenario-compare card shows this side by side.
How is this different from the Hazen-Williams equation?+
Darcy-Weisbach is a general, physically-derived equation that works for any fluid and flow regime once you know the friction factor. Hazen-Williams is an empirical shortcut calibrated specifically for water flow, using a roughness coefficient (C-factor) instead of a friction factor.
📄
Save & share
Get a branded PDF of your results
Download a one-page PDF of your numbers instantly. Add your email to also get our occasional calculator tips — no spam, unsubscribe anytime. Privacy.