Quick answer
The Hazen–Williams equation gives head loss h_f = 10.67 L Q^1.852 ÷ (C^1.852 d^4.87) in SI units. For 300 L/min through a 50 mm pipe 100 m long with C = 140, head loss is 13.43 m (131.7 kPa) at a velocity of 2.546 m/s.
Enter the flow, inside diameter, pipe length and Hazen–Williams C. The calculator returns head loss, pressure drop and velocity. Use this friction loss calculator to check your own figures.
Related tools: Gallons per Minute Calculator: Flow in gallons per minute from pipe size and velocity, or volume and time. Pipe Pressure Drop Calculator: Pressure drop in a straight pipe from the Darcy–Weisbach equation.
How to use the Friction Loss Calculator
- Enter flow (L/min) (above 0).
- Enter inside diameter (mm) (above 0).
- Enter pipe length (m) (above 0).
- Enter hazen–Williams C (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Flow | A number, in L/min | > 0 |
| Inside diameter | A number, in mm | > 0 |
| Pipe length | A number, in m | > 0 |
| Hazen–Williams C | A number. Roughness coefficient for your pipe material | > 0 |
Formula and method
Formula
h_f = 10.67 L Q^1.852 ÷ (C^1.852 d^4.87) (SI: m, m³/s, m)
IEEE-754 double precision; shown to the decimals indicated.
Valid for water at ordinary temperatures in turbulent flow; C depends on pipe material and age.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Flow = 300; Inside diameter = 50; Pipe length = 100; Hazen–Williams C = 140.
| Result | Value |
|---|---|
| Head loss | 13.429 m |
| Pressure drop | 131.6935 kPa |
| Velocity | 2.546 m/s |
Example 2
Inputs: Flow = 120; Inside diameter = 25; Pipe length = 40; Hazen–Williams C = 120.
| Result | Value |
|---|---|
| Head loss | 38.2931 m |
| Pressure drop | 375.527 kPa |
| Velocity | 4.074 m/s |
Example 3
Inputs: Flow = 900; Inside diameter = 100; Pipe length = 250; Hazen–Williams C = 130.
| Result | Value |
|---|---|
| Head loss | 10.074 m |
| Pressure drop | 98.7923 kPa |
| Velocity | 1.91 m/s |
The first line is the headline result (head loss). Below it the friction Loss Calculator lists pressure drop and velocity, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
C values
C describes the pipe's roughness: about 150 for new plastic, 140 for new steel or copper, 100 for old cast iron. A smaller C means more friction.
Scope
The equation suits water at ordinary temperatures in full pipes, not viscous fluids or very high velocities. For other fluids use the Pipe Pressure Drop (Darcy–Weisbach) calculator. Add fittings and elevation changes separately.
How the result changes with flow
Holding every other input at the first worked example, this table changes only flow. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Flow | Head loss | Pressure drop | Velocity |
|---|---|---|---|
| 150 | 3.7199 m | 36.4802 kPa | 1.273 m/s |
| 300 | 13.429 m | 131.6935 kPa | 2.546 m/s |
| 600 | 48.4787 m | 475.4141 kPa | 5.093 m/s |
| 1200 | 175.0084 m | 1,716.2463 kPa | 10.186 m/s |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Flow: entering "0" shows "Flow must be greater than 0." beside that field and no result.
- Hazen–Williams C: entering "0" shows "Hazen–Williams C must be greater than 0." beside that field and no result.
Choosing between the Friction Loss Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Gallons per Minute Calculator](/engineering/gallons-per-minute/) | use | Flow |
| [Hydraulic Cylinder Force Calculator](/engineering/hydraulic-cylinder-force-calculator/) | units, pressure and bore diameter | Extend force |
| [Pipe Pressure Drop Calculator](/engineering/pipe-pressure-drop-calculator/) | flow, inside diameter and length | Pressure drop |
| [Pump Flow Calculator](/engineering/pump-flow-calculator/) | displacement, speed and volumetric efficiency | Flow |
| [Weight Loss Calculator](/health/weight-loss-calculator/) | units, current weight and goal weight | Days to reach goal |
Background: fluid flow
Volumetric flow rate is Q = A × v (cross-sectional area times average velocity). Bernoulli's equation, P + ½ρv² + ρgh = constant, holds along a streamline for steady, incompressible, frictionless flow, so real pipes need friction corrections. The Reynolds number Re = ρvL/μ compares inertia with viscosity.
Laminar flow in a pipe is usually quoted below Re of about 2,100 to 2,300 and fully turbulent above about 4,000, with an uncertain transition between; treat the thresholds as approximate.
Assumptions and limitations
- Not valid for viscous fluids
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for flow and hazen–Williams C to confirm this.
Frequently asked questions
What is head loss?
Energy lost to friction, expressed as a height of fluid.
Does smaller pipe increase loss?
Yes, very sharply: loss varies with d to the 4.87 power.
Can I use it for oil?
No, it is for water.
What does the Friction Loss Calculator calculate?
Pipe friction head loss with the Hazen–Williams equation. It returns Head loss, Pressure drop and Velocity.
What formula does the Friction Loss Calculator use?
h_f = 10.67 L Q^1.852 ÷ (C^1.852 d^4.87) (SI: m, m³/s, m). Valid for water at ordinary temperatures in turbulent flow; C depends on pipe material and age.
What do I need to enter in the friction Loss Calculator?
You enter Flow (L/min), Inside diameter (mm), Pipe length (m) and Hazen–Williams C.
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Not valid for viscous fluids.
What is an example of a friction Loss result?
With flow 300, inside diameter 50, pipe length 100 and hazen–Williams C 140, the head loss is 13.429 m.
Where does the method come from?
The method follows: Hazen–Williams equation, SI form (e.g. Crane Technical Paper 410; Engineering Toolbox references).
Can I rely on this calculator for a decision?
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them. For this calculator in particular: Not valid for viscous fluids.
Related calculators
- Gallons per Minute Calculator — Flow in gallons per minute from pipe size and velocity, or volume and time.
- Pipe Pressure Drop Calculator — Pressure drop in a straight pipe from the Darcy–Weisbach equation.
- Pump Flow Calculator — Pump output from displacement, speed and volumetric efficiency.
- Friction Force Calculator — Friction force from the coefficient of friction and the normal force.
Sources
- Hazen–Williams equation, SI form (e.g. Crane Technical Paper 410; Engineering Toolbox references)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.