Friction Loss Calculator

What this calculator does

Find out how much water pressure you lose along a pipe, so you know what's left at the far end. Water loses pressure as it flows, because it rubs against the pipe walls and against itself. That loss is called friction loss. It's why a top-floor shower at the end of a long run is weaker than the tap by the meter. It's why sprinklers at the far end of a line don't reach as far. It's also why pumps and pipe sizes are chosen together. The loss grows fast with flow. Double the flow in the same pipe, and the loss goes up about 3.6 times.

This calculator gives two standard ways to estimate it. The Hazen–Williams formula is used throughout plumbing, irrigation and fire-protection work. It needs only the flow, the bore (inside width of the pipe), the length and a C factor for the pipe material. The Darcy–Weisbach equation is the general physics method. It works out the Reynolds number, a measure of how smooth or swirling the flow is. Then it finds a friction factor from the pipe's roughness. So it also handles other temperatures, and very small or very large flows. Pick a standard pipe size or type any bore. You'll see the loss as pressure (psi and kPa) and as head (feet and meters of water).

Where it's used

Why this math matters outside the classroom:

• Irrigation design. A landscaper checks that a 10 gpm zone on 100 ft of 1 in PVC loses only about 2.6 psi, leaving enough for the heads.
• Upstairs showers. A plumber adds friction loss and 0.433 psi per foot of rise to see why a third-floor shower runs weak.
• Pump selection. Pump installers add the friction head of the pipe to the lift to find the total head a pump must deliver.
• Fluid mechanics class. Engineering students compute a Reynolds number, read a friction factor and apply Darcy–Weisbach to a pipe.
• Choosing pipe size. Going from 3/4 in to 1 in Type L copper at 10 gpm cuts friction loss by roughly three quarters.

How to use it

1. Choose Hazen–Williams for everyday cold-water problems, or Darcy–Weisbach for the general method.
2. Pick the pipe material and its standard (nominal) size, or enter your own inside diameter.
3. Enter the flow rate and the length of the run. Add any equivalent length for fittings.
4. Choose the C factor (Hazen–Williams), or the roughness and viscosity (Darcy–Weisbach). Then read the pressure drop.

What the inputs mean

Inside diameter

The width of the hole inside the pipe, not its outside or the size it's sold as.

Length of pipe

Fittings, valves and meters add loss too. Their effect is often given as an equivalent length of straight pipe, from the maker's or a handbook's table. Add it to the measured length.

Hazen–Williams C

A higher C means a smoother pipe and less loss. Pipe charts commonly use 150 for PVC, 140 for copper and 100 for steel. The steel figure allows for the way steel pipe gets rougher with use.

Pipe roughness

Absolute roughness is the average height of the bumps on the pipe wall. The listed values are the classic figures used with the Moody diagram, a standard engineering chart.

Kinematic viscosity

Viscosity is how thick or runny a liquid is. It falls as water warms, which lowers friction slightly. The default is water at 20 °C (68 °F).

Formula and method

Hazen–Williams (US units):
  h per 100 ft = 0.2083 × (100 ÷ C)^1.852 × Q^1.852 ÷ d^4.8655   (Q in gpm, d in inches)
Darcy–Weisbach:
  V = Q ÷ (π ÷ 4 × d²),   Re = V × d ÷ ν
  1 ÷ √f = −2 log10(ε ÷ (3.7 d) + 2.51 ÷ (Re √f))   (Colebrook–White; f = 64 ÷ Re if Re < 2300)
  h = f × (L ÷ d) × V² ÷ (2g)
Pressure drop = ρ × g × h   (water at 20 °C, ρ = 998.2 kg/m³)

Hazen–Williams is a formula built from measurements of water in ordinary pipes at ordinary temperatures. In its US form above, h is the head lost and C is the pipe's smoothness factor. Q is the flow in gallons per minute, and d is the bore in inches. It gives feet of head lost per 100 ft of pipe, the form printed on irrigation pipe charts. The result is then scaled to the length.

Darcy–Weisbach comes from basic physics and works for any fluid. In it, V is the water's speed and Re is the Reynolds number. ν (nu) is the viscosity, ε (epsilon) is the roughness and f is the friction factor. L is the pipe length, and g is gravity, 9.80665 m/s². The friction factor depends on the Reynolds number and on the roughness compared with the bore. The calculator finds it from the Colebrook–White equation by trying values until both sides match. Both methods then turn head into pressure using the weight of water. ρ (rho) is water's density.

Worked example

10 gpm of cold water flows through 100 ft of 1 in Schedule 40 PVC (bore 1.029 in), with C = 150.

1. Loss per 100 ft: 0.2083 × (100 ÷ 150)^1.852 × 10^1.852 ÷ 1.029^4.8655 = 0.098303 × 71.1214 ÷ 1.149230 = 6.083608 ft.
2. Over 100 ft that is 6.083608 ft of head, or 1.854284 m.
3. Pressure: 998.2 × 9.80665 × 1.854284 ÷ 6894.757 = 2.632664 psi (18.15 kPa).
4. Darcy–Weisbach for the same pipe (smooth, 20 °C): V = 1.1759 m/s, Re ≈ 30,600, f = 0.02353, giving about 2.75 psi.

Result: The run loses about 2.63 psi to friction by Hazen–Williams, in line with published pipe charts. Darcy–Weisbach gives a similar 2.75 psi.

Understanding the result

Start with the pressure at the source. Subtract the friction loss, and any loss from the pipe climbing (about 0.433 psi per foot of rise). What's left is roughly the pressure at the far end. If too little remains for the fixture, sprinkler or appliance, use a larger pipe, a shorter route or a lower flow.

Loss rises with roughly the square of the flow (the power 1.852 in Hazen–Williams). So a modest increase in flow can use up a lot of pressure. Going up one pipe size usually cuts the loss by half or more.

Assumptions and limitations

• The fluid is water, flowing full and steady through a straight, round pipe of the stated bore.
• Hazen–Williams assumes cold water and turbulent (swirling) flow. Darcy–Weisbach uses the viscosity you enter, and water's density at 20 °C for the pressure.
• Fittings and valves only count through any equivalent length you add.
• Hazen–Williams doesn't work for fluids other than water, for hot water far from room temperature, or for very low flows. Use Darcy–Weisbach for those.
• Between Reynolds numbers of about 2,300 and 4,000, the flow is changing between smooth and swirling. Any friction estimate there is uncertain.
• These are estimates for planning. Pressure, supply sizing and fire-protection systems must follow the codes that apply where you are. They must be designed or approved by a licensed professional.

Frequently asked questions

Sources

• Rain Bird reference: PVC Schedule 40 IPS plastic pipe, Hazen–Williams friction loss chart (C = 150) (checked 2026-10-19)
• Rain Bird reference: Type K copper water tube friction loss chart (C = 140) (checked 2026-10-19)
• Rain Bird reference: Schedule 40 standard steel pipe friction loss chart (C = 100) (checked 2026-10-19)

How this calculator is checked

Method: Hazen–Williams in the US form used on Rain Bird's pipe charts (h/100 ft = 0.2083 (100/C)^1.852 Q^1.852 / d^4.8655) with C 150/140/100 from those charts; Darcy–Weisbach with Colebrook–White friction factor (64/Re for laminar); roughness values from the Moody diagram; Δp = ρgh with water at 20 °C. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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