In short: the Hazen-Williams equation turns a flow rate, pipe diameter, length and roughness (C-factor) into a friction head loss — for 100 US GPM through 1,000 ft of 4-inch PVC pipe (C 150), that's about 5.76 ft of head (2.50 psi) at a velocity of 2.55 ft/s. Smoother pipe, a bigger diameter, or a lower flow rate all reduce the loss.
These figures are planning aids based on the standard Hazen-Williams formula. For potable-water main sizing, fire-protection design or other safety-critical work, confirm with a licensed engineer against local code.
How to calculate friction loss with Hazen-Williams
The Hazen-Williams equation estimates how much pressure a pipe "steals" from water as friction against the pipe wall, for a given flow rate. It needs four things: how much water is moving (flow rate), how big the pipe is inside (diameter), how far it travels (length), and how rough the interior is (the C-factor — higher C means smoother pipe and less friction).
Notice the exponents: flow rate is raised to the power of 1.852, so doubling the flow rate more than triples the friction loss. Diameter is raised to almost the 5th power, so a modest increase in pipe size cuts friction loss dramatically — which is why undersized pipe is such a common source of pressure complaints.
Worked example. Take 100 US GPM through 1,000 ft of 4-inch (inside diameter) PVC pipe, C = 150. Converting: Q = 0.0063090 m³/s, D = 0.1016 m, L = 304.8 m. Plugging into the formula gives hf ≈ 1.756 m, which is 5.76 ft of head — equivalent to a pressure drop of about 2.50 psi (17.2 kPa) over the run. The velocity works out to Q/A ≈ 0.778 m/s, or 2.55 ft/s. That is exactly what the calculator above shows with its default values.
Head loss vs. pressure drop, in one line. "Head loss" is friction expressed as an equivalent height of water (feet or meters); "pressure drop" is the same quantity expressed in force-per-area units (psi, kPa, bar). They describe the identical physical loss — this tool shows both so you can use whichever your drawings or gauges are in.
Why the C-factor changes the answer
The C-factor is the one input in the Hazen-Williams equation that isn't a straightforward physical measurement — it is an empirical roughness rating, and it is the biggest lever on the result. New, smooth-walled pipe like PVC or HDPE carries a C-factor around 150. Older metal pipe that has corroded or built up mineral scale on the inside can drop to 100 or even 80, because that roughness disrupts the smooth flow of water along the pipe wall and converts more of its energy into friction.
Because friction loss scales with C1.852 in the denominator, a pipe that ages from C 150 down to C 100 does not lose a proportional amount of capacity — it loses roughly 80% more head for the same flow, all else equal (see the comparison table below). This is why utilities periodically re-line or replace aging cast-iron mains: the pipe hasn't gotten smaller, but it behaves as if it has. You can read more about how we handle roughness and other flow assumptions on our methodology page.
Friction loss per 100 ft of 4-inch PVC pipe (C 150)
How head loss and velocity climb with flow rate, for a fixed 4-inch pipe at C 150. Loss grows faster than flow because of the 1.852 exponent — doubling the flow rate roughly quadruples the loss.
| Flow rate | Loss per 100 ft (ft) | Loss per 100 ft (psi) | Velocity (ft/s) |
|---|---|---|---|
| 20 GPM | 0.029 | 0.013 | 0.51 |
| 40 GPM | 0.106 | 0.046 | 1.02 |
| 60 GPM | 0.224 | 0.097 | 1.53 |
| 80 GPM | 0.381 | 0.165 | 2.04 |
| 100 GPM (default) | 0.576 | 0.250 | 2.55 |
| 150 GPM | 1.220 | 0.529 | 3.83 |
| 200 GPM | 2.079 | 0.901 | 5.11 |
How C-factor changes friction loss
Same run — 100 GPM through 100 ft of 4-inch pipe — recalculated at different C-factors. Everything else held equal, a rougher pipe costs you noticeably more head.
| C-factor | Typical material | Loss per 100 ft (ft) | Loss per 100 ft (psi) |
|---|---|---|---|
| 150 | New PVC / HDPE | 0.576 | 0.250 |
| 140 | Copper, cement-lined ductile iron | 0.654 | 0.284 |
| 130 | New welded steel, concrete | 0.751 | 0.325 |
| 120 | Older steel or concrete | 0.871 | 0.377 |
| 100 | Old cast iron | 1.220 | 0.529 |
| 80 | Corroded / tuberculated | 1.845 | 0.800 |
Worked examples
Undersized copper branch
9.71 ft loss
8 GPM through 50 ft of ¾-inch copper tube (C 130) loses about 9.71 ft of head — 4.21 psi — at a brisk 5.30 ft/s. That much loss over such a short run is a sign the branch is undersized for the fixture demand.
Rural transmission main
46.5 ft loss
500 GPM through 2 miles of 8-inch cement-lined ductile iron (C 140) loses about 46.5 ft of head — 20.2 psi — at a comfortable 3.19 ft/s. Long transmission mains are sized generously in diameter to keep losses like this manageable.
Aging cast-iron street main
3.06 ft loss
200 GPM through 500 ft of 6-inch old cast iron (C 100) loses about 3.06 ft of head — 1.33 psi — at 2.27 ft/s. The same run in new C 150 pipe would lose noticeably less, which is the case utilities make for pipe replacement.
What else affects the result
Flow regime. Hazen-Williams was fit to turbulent water flow, which covers almost every practical pipe run. At very low velocities in small pipe, flow can become laminar and the equation loses accuracy — the Darcy-Weisbach equation handles that case more rigorously.
Minor losses. This calculator covers straight-pipe friction only. Elbows, valves, tees and fittings add their own losses, which is why a real design also totals up minor losses separately (see our Minor Loss Calculator) rather than folding them into the C-factor.
Temperature and fluid. The formula was developed for water near ordinary temperatures. It is not appropriate for other fluids, and its accuracy drifts for water well outside typical distribution-system temperatures.
C-factor uncertainty. Actual roughness varies with pipe age, water chemistry, and manufacturing tolerance. Treat any C-factor — including the presets here — as a planning estimate, not a guaranteed value.
Frequently asked questions
What does the Hazen-Williams equation calculate?
The Hazen-Williams equation calculates the friction head loss of water flowing through a pipe, from the flow rate, the pipe's inside diameter, its length, and a roughness coefficient called the C-factor. From that head loss you can also get the equivalent pressure drop and the flow velocity.
What is a good C-factor for PVC pipe?
New PVC and HDPE pipe is commonly modeled with a C-factor of about 150, reflecting its very smooth interior. Older or corroded metal pipe can drop to 100 or lower. The C-factor is a modeling input, not a fixed physical constant, so check your pipe manufacturer's data or an AWWA reference for critical designs.
How do I convert head loss to a pressure drop in psi?
Multiply the head loss in feet by about 0.4335 to get pounds per square inch, or multiply meters of head by 1.422. This calculator does the conversion automatically and shows the result in psi, kPa or bar alongside feet and meters of head.
Does the Hazen-Williams equation work for all fluids?
No. It was developed specifically for water at ordinary temperatures in turbulent flow, and its accuracy declines outside that range. For other fluids, laminar flow, or unusual temperatures, the Darcy-Weisbach equation is the more general and physically grounded choice.
What velocity should water move through a pipe?
Many water system design guides aim for roughly 2 to 8 feet per second in distribution piping: fast enough to avoid stagnation and sediment buildup, slow enough to limit friction loss, noise, and water-hammer risk. The right target varies by pipe material, service type and local code, so treat this as a general planning range.
Hazen-Williams or Darcy-Weisbach — which should I use?
Hazen-Williams is simpler to compute and is the long-standing convention for water distribution, plumbing and fire-protection design. Darcy-Weisbach is more rigorous, valid for any fluid and flow regime, but requires solving for a friction factor. For everyday water-pipe sizing, Hazen-Williams is the industry default.
Sources & references
- Williams, G. S., & Hazen, A. (1920). Hydraulic Tables (3rd ed.). John Wiley & Sons.
- American Water Works Association (AWWA). Manual M11: Steel Pipe — A Guide for Design and Installation.
- International Bureau of Weights and Measures (BIPM). The International System of Units (SI).
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)