In short: a 100 ft run of 2 in PVC pipe (C = 150) carrying 50 GPM loses about 4.67 ft of head (2.02 psi) to friction. Head loss grows fast with flow rate and shrinks fast with pipe diameter — cutting the diameter in half multiplies friction loss by roughly 29×. Use the calculator above for your own flow, pipe size, length and material.
These figures are planning aids based on published friction-loss formulas. For system design, code compliance or pump selection, confirm with a licensed engineer.
How to calculate friction head loss
As water moves through a pipe, friction between the water and the pipe wall — and within the water itself — steals energy from the flow. That lost energy shows up as head loss: the pressure at the far end of the pipe is lower than it would be with no friction at all. Two well-established formulas convert a flow rate and a pipe's geometry directly into that head loss.
This calculator converts your inputs to SI units, applies whichever formula you select, and converts the result back to feet, meters, psi and familiar velocity units. For losses through elbows, tees and valves rather than straight pipe, use the fitting pressure drop calculator instead — the two figures add together for the total loss in a system.
Worked example. Take 50 GPM (0.003155 m³/s) through 100 ft (30.48 m) of 2 in (0.0508 m) PVC pipe, C = 150. Q1.852 ≈ 4.62 × 10-5, D4.8704 ≈ 4.90 × 10-6. Working through the formula gives h_f ≈ 1.422 m, which is 4.667 ft — exactly what the calculator shows with its default values. Multiplying by water's unit weight converts that to a pressure drop of about 2.02 psi.
Major loss only. Both formulas model friction along straight pipe. They do not include the extra turbulence at bends, valves, tees or fitting transitions — those are separate "minor losses," typically small by comparison over a long straight run but significant in a pipe with many fittings.
Hazen-Williams vs. Darcy-Weisbach
Hazen–Williams is the workhorse for ordinary water-distribution and plumbing design: it needs only a C-factor for the pipe material and gives head loss directly, with no iteration. It assumes water, turbulent flow and typical ambient temperatures — which describes the overwhelming majority of building and irrigation piping.
Darcy–Weisbach is the more general, physics-based formula. It works for any fluid and any flow regime, because its friction factor is derived from the Reynolds number, which itself accounts for viscosity — and viscosity changes noticeably with water temperature. That is why switching this calculator to Darcy–Weisbach reveals a water-temperature field: colder water is more viscous, giving a lower Reynolds number, a higher friction factor and, all else equal, more head loss than warmer water in the same pipe.
Head loss by flow rate (2 in PVC pipe, 100 ft, C = 150)
Hazen–Williams head loss for a 100 ft run of 2 in PVC pipe as flow rate increases. Notice how much faster head loss grows than flow itself.
| Flow rate | Head loss (ft) | Pressure drop (psi) |
|---|---|---|
| 10 GPM | 0.237 | 0.103 |
| 20 GPM | 0.855 | 0.370 |
| 30 GPM | 1.812 | 0.784 |
| 40 GPM | 3.087 | 1.336 |
| 50 GPM (default) | 4.667 | 2.020 |
| 60 GPM | 6.541 | 2.831 |
| 80 GPM | 11.144 | 4.823 |
| 100 GPM | 16.847 | 7.291 |
Head loss by pipe diameter (50 GPM, 100 ft, C = 150)
The same flow and length, run through different pipe sizes. This is why undersizing a pipe is so costly: head loss falls off steeply as diameter increases.
| Pipe ID | Head loss (ft) |
|---|---|
| 1 in | 136.510 |
| 1.25 in | 46.044 |
| 1.5 in | 18.946 |
| 2 in (default) | 4.667 |
| 2.5 in | 1.574 |
| 3 in | 0.648 |
| 4 in | 0.160 |
Worked examples
Branch line, PVC, Hazen-Williams
4.67 ft
50 GPM through 100 ft of 2 in PVC (C = 150) loses 4.67 ft of head — about 2.02 psi — the calculator's defaults.
Same run in steel, Darcy-Weisbach
5.47 ft
The identical flow, diameter and length in new steel pipe (roughness 0.045 mm, 20 °C water) loses 5.47 ft — about 2.37 psi — using Darcy–Weisbach (Re ≈ 78,800, turbulent).
Downsizing one pipe size
18.95 ft
Drop from 2 in to 1.5 in at the same 50 GPM and length, and head loss jumps to 18.95 ft — about 4× higher from a single pipe-size reduction.
What else affects the result
Pipe age and condition. C-factors and roughness values assume a clean, new pipe. Scale, corrosion and tuberculation raise roughness (or lower C) over time, sometimes dramatically in old cast iron or galvanized steel — a pipe that started at C = 130 can drop toward C = 90–100 after decades in service.
Flow regime. Both formulas assume turbulent flow, typical for pressurized water pipes at ordinary velocities. In Darcy–Weisbach mode, if the calculated Reynolds number falls below about 2,300 — very low flow or very viscous fluid — the calculator switches to the laminar friction factor (f = 64/Re) automatically.
Minor losses. Fittings, valves, entrances and exits add losses this calculator does not include. On a long, straight run they are usually small next to friction loss; in a pipe with many bends and valves over a short distance, they can dominate — check them separately with the fitting pressure drop calculator.
Frequently asked questions
What is the formula for pipe friction head loss?
For water pipes, the Hazen–Williams formula gives head loss directly as h_f = 10.67 × L × Q1.852 / (C1.852 × D4.8704), using a pipe roughness coefficient C. The Darcy–Weisbach formula, h_f = f × (L/D) × V²/(2g), is more general — it works for any fluid, temperature and flow regime, using a friction factor f found from the Reynolds number and pipe roughness. Both give head loss in the same units (feet or meters of water), and this calculator supports both.
Hazen-Williams or Darcy-Weisbach — which should I use?
Hazen–Williams is simpler and is the industry default for ordinary water distribution and plumbing design at typical velocities and temperatures — you just need a C-factor for the pipe material. Darcy–Weisbach is more rigorous and the better choice outside those conditions: very cold or hot water, non-water fluids, low-velocity or laminar flow, or whenever you have a reliable roughness value and want the most accurate answer.
What C-factor or roughness value should I use for my pipe?
Use the material presets as a starting point — PVC and plastic pipe run high (C ≈ 150, roughness ≈ 0.0015 mm), new steel and ductile iron are lower (C ≈ 130, roughness ≈ 0.045 mm), and old, tuberculated cast iron can drop to C ≈ 100. These values decline with age, scale and corrosion, so a pipe's actual C-factor can be measured in the field and entered as a custom value if you need precision.
Does friction head loss include losses from fittings and valves?
No. This calculator covers major loss — friction along the straight length of pipe only. Elbows, tees, valves and other fittings add separate minor losses, which you can estimate with the fitting pressure drop calculator and add to this result.
How does pipe diameter affect friction loss?
Enormously. In the Hazen–Williams formula, head loss is proportional to 1/D4.8704, so cutting the pipe diameter in half increases head loss by roughly 29 times at the same flow rate. Undersizing a pipe by even one standard size can multiply the friction loss several times over — always check head loss before finalizing a pipe size.
Is this calculator valid for laminar flow?
The Hazen–Williams formula assumes turbulent flow and is not accurate for laminar or slow-moving flow. If you switch to Darcy–Weisbach and your calculated Reynolds number comes out below about 2,300, the calculator automatically uses the laminar friction factor (f = 64/Re) instead of the turbulent correlation.
Sources & references
- Williams, G. S., & Hazen, A. (1905). Hydraulic Tables — basis of the Hazen–Williams formula.
- Swamee, P. K., & Jain, A. K. (1976). Explicit equations for pipe-flow problems. Journal of the Hydraulics Division, ASCE, 102(5), 657–664.
- American Water Works Association (AWWA) M11 — Steel Pipe: A Guide for Design and Installation — C-factor and roughness reference values.
John Mac, PE
Water Systems Specialist · Austin, Texas
Texas-licensed Professional Engineer with 13+ years in residential water systems and 180+ completed projects. Writes and reviews the calculators on watercalculator.us. Read full bio
Texas PE (2016) · BS Civil Engineering, Hydraulics (2013)