How to calculate friction loss in a pipe

1. What friction loss actually is

When water moves through a pipe it drags against the pipe wall, and that drag steadily eats away at the pressure pushing it along. That lost pressure is friction loss (also called head loss or pressure drop). It is the reason a tap at the far end of a long run dribbles while the one next to the tank gushes, and the reason a pump has to be sized for more than just the height it lifts water. Friction loss is separate from static head — the pressure needed to raise water to a height — and separate again from the losses at fittings and valves. This guide is about the friction in the straight pipe itself, which for most runs is the biggest single piece.

Three things drive it: how fast the water is moving (more flow through a given pipe means more friction), how narrow the bore is (the single biggest factor), and how rough the pipe wall is. The Hazen-Williams equation rolls all three into one tidy formula, which is why it has been the plumber's and civil engineer's go-to for water systems for over a century.

2. The Hazen-Williams equation

In SI units the head loss in metres of water is h = 10.67 × L × Q^1.852 ÷ (C^1.852 × d^4.87), with L in metres, Q in cubic metres per second and d — the inside diameter — in metres. The equation is empirical, fitted to real water-flow measurements, which is why the exponents are those odd non-round numbers. The two that matter most are the exponent on flow (1.852, a little less than linear) and the exponent on diameter (4.87, close to a fifth power). That diameter exponent is the headline: because loss depends on roughly the fifth power of the bore, a small change in pipe size swings the answer enormously.

Head loss in metres or feet of water converts directly to pressure: one metre of water column is about 0.0981 bar, and one foot of water is about 0.433 psi. So a run that loses 7.9 feet of head is losing about 3.4 psi. The calculator does the whole thing in SI internally and shows you both the head and the pressure drop, so you never have to juggle the units by hand.

3. The roughness coefficient C

C is the one input that is not a measurement of your own system — it is a standard published property of the pipe material. A higher C means a smoother wall and less friction. Typical values are 150 for plastic (PVC, PEX, ABS, HDPE), 140 for copper and brass, 130 for new cast iron, 120 for new steel or galvanised iron, around 110 for concrete, and dropping toward 100 for old, rough or corroded iron. These are engineering constants from Hazen-Williams reference tables, not code minimums — they describe the physics of the pipe, not a legal requirement.

Age matters. A galvanised or cast-iron line that started near C 120–130 loses smoothness as scale and corrosion build up, and after a couple of decades it can behave like C 100 or worse. That is why an old house on original steel pipe often has weak flow that new plastic or copper would fix at the same size: the material change alone cuts the friction. Running the same flow and bore in the calculator at C 150 versus C 100 shows the gap plainly — the rough pipe loses more than double the head.

4. A worked example

Say you are running a 100-foot copper line at 10 GPM and choosing between 3/4-inch and 1-inch. Through the 1-inch bore the friction loss is about 6.3 feet of head — roughly 2.7 psi over the run. Through the 3/4-inch bore it jumps to about 25.8 feet of head, or over 11 psi. Same flow, same water, same length — the only change is one pipe size, and the loss quadruples. On a house with 50–60 psi to start, giving up 11 psi to a single run is a lot; giving up under 3 is barely noticeable. That is the fifth-power diameter rule doing the work.

The same in metric: 40 litres per minute through a 25 mm copper line over 30 metres loses about 2.8 metres of head, or roughly 0.28 bar — about 9.4 metres of head for every 100 metres of pipe. Comfortable for that bore. Halve the diameter and, just as in the imperial case, the loss climbs out of all proportion. The lesson is the same in both systems: when a long run comes up short on pressure, sizing up the pipe is almost always the fix.

5. Friction loss by flow and pipe size (chart)

Friction loss in feet of head per 100 feet of copper pipe (C 140), for common flows and inside diameters, from the Hazen-Williams equation. Cells in bold are impractically high — the pipe is far too small for that flow and would be noisy and starved.

Read down a column and the flow effect shows; read across a row and the diameter effect dwarfs it. A 1/2-inch line is only sensible for a few gallons a minute, while a 1-inch bore carries 10–15 GPM at a modest loss. These use nominal type-L copper inside diameters for illustration; your real pipe has its own inside bore, which is what you should feed the calculator.

6. Getting the inputs right

The answer is only as good as its inputs, and two of them trip people up. First, inside diameter: never use the nominal size or the outside diameter. A “3/4-inch” pipe rarely has a 3/4-inch bore, and the wall thickness varies by material and schedule. Look up the true inside diameter for your pipe — the same figure the pipe volume calculator uses — because the equation is so sensitive to it. Second, flow rate: use a real number where you can. If you are checking an existing line, the GPM calculator measures it from a timed fill; if you are designing, add up the demand the run has to serve.

Two things this straight-pipe figure does not include. Fittings — every elbow, tee and valve adds loss — are usually handled by the equivalent-length method: look up the equivalent straight length for each fitting, add them to the pipe length, and use that total in the length box. And static lift, the pressure to raise water to a height, is added on top of friction loss when sizing a pump. Friction loss also travels with velocity, so it is worth checking your run against the pipe velocity calculator as well — a fast line is both a noisy line and a lossy one. The rest of the estimating tools on the plumbing hub follow the same measure-first, then-calculate approach.

Common questions

How do you calculate friction loss in a pipe?

Use the Hazen-Williams equation, the standard method for water. In SI: head loss h (metres) = 10.67 × L × Q^1.852 ÷ (C^1.852 × d^4.87), where L is length (m), Q is flow (m³/s), d is the inside diameter (m) and C is the roughness coefficient. It gives the head loss in metres or feet of water, which you can turn into a pressure drop in psi or bar.

What is a Hazen-Williams C value?

C is the Hazen-Williams roughness coefficient — a standard published number for each pipe material describing how smooth it is. Higher C means less friction: plastic (PVC, PEX) about 150, copper about 140, new steel or cast iron about 120–130, dropping toward 100 as iron corrodes with age. It is a physical property of the pipe, not a code value.

How much pressure do you lose per 100 feet of pipe?

It depends on the flow, bore and material. As a feel for it, 10 GPM through a 1-inch copper line loses roughly 3 psi (about 6–8 feet of head) per 100 feet, while the same flow through a 3/4-inch line loses over 11 psi. Friction loss climbs steeply as the pipe gets smaller.

Does a smaller pipe cause more friction loss?

Yes, dramatically. Friction loss rises with roughly the inverse fifth power of the diameter (d^4.87 in the equation), so a small drop in bore causes a large jump in loss. Going up one pipe size is the most effective way to cut friction loss and recover pressure on a long run.

How do you account for fittings and valves?

Elbows, tees and valves each add loss, usually handled with the equivalent-length method: look up the equivalent straight-pipe length for each fitting, add them to the real pipe length, and use that total. The calculator computes the straight-run loss, so add the fittings' equivalent length to the length input.