Pipe Friction Loss Calculator — Hazen-Williams
Every foot of pipe and every fitting takes a cut of your supply pressure. This calculator runs the Hazen-Williams equation for the loss per 100 feet, then adds the equivalent length of your elbows, tees and valves so you get the loss over the run you are actually installing — not the run you measured.
Work out the loss
Fittings and valves on the run
Each is converted to an equivalent length of straight pipe at this bore.
Loss per 100 ft
Fittings add 20.7 ft of equivalent pipe on top of the 100 ft measured.
Loss over the run
13.37 psi
Developed length
120.7 ft
See the breakdown
Planning estimate. Hazen-Williams assumes water at ordinary temperature in a full pipe; scale, partial blockage and unusual fittings are not modelled. A licensed plumber and your AHJ have final say.
The formula, explained in plain English
One empirical equation, one roughness number, and a trick for turning fittings into pipe.
Why d^4.87 dominates everything
Bore is by far the most powerful term. Going up one nominal size in copper widens the bore about 31% and cuts the loss roughly 73%. No change of material or fitting count comes close to that.
Flow is not linear either
The 1.852 exponent means doubling the flow multiplies the loss by about 3.6, not 2. This is why a pipe that behaves perfectly with one shower running can fall over with two.
Equivalent length in diameters
Computing fittings as a multiple of the bore rather than reading a per-size table means it stays valid at any diameter — and it reproduces the published figures: a 90° ell on 3/4-inch copper comes out at 1.96 ft against a published 2.0.
A tee is not a tee
Straight through, a tee costs about the same as a 90° elbow. Taken through the branch it costs three times as much — 60 diameters against 20. Which port the water takes matters more than the fitting count.
Worked examples
The defaults, one size up, and the case where the fittings cost more than the pipe.
10 gpm, 3/4 inch copper, 100 ft plus fittings
Six 90° elbows, two tees through the branch, two ball valves. The calculator's defaults.
2 × tee branch @ 3.93 ft = 7.85 ft
2 × ball valve @ 0.52 ft = 1.05 ft
developed = 100 + 20.67 = 120.67 ft
loss = 11.08 psi/100 ft × 1.2067 = 13.37 psi
Result: 13.37 psi, of which 2.29 psi is the fittings — 17% of the total from ten components you could easily have ignored. That is 30.9 feet of head.
One size up — 1 inch copper
loss 11.08 → 3.02 psi/100 ft
= 73% less friction for one size
Result: a 31% wider bore cuts the loss by nearly three quarters, because the diameter term is raised to 4.87. Upsizing one step is almost always cheaper than any other way of recovering pressure.
A short, fitting-heavy run — where they dominate
A 15-foot mechanical-room manifold at 10 gpm in 3/4-inch copper: eight 90° elbows, four tees through the branch, one globe valve.
fittings = 53.64 ft against 15 ft of pipe
developed = 68.64 ft — the fittings are 78% of it
loss = 11.08 × 0.6864 = 7.61 psi
Result: the pipe contributes 1.66 psi and the fittings 5.94 psi. A single globe valve is worth 22 feet of 3/4-inch pipe on its own — 340 diameters — which is why ball valves replaced them almost everywhere.
Loss by size at 10 gpm
Type L copper, computed from the same code the calculator runs above.
| Nominal size | Actual bore | Loss per 100 ft |
|---|---|---|
| 1/2" | 0.545 in | 65.52 psi |
| 3/4" | 0.785 in | 11.08 psi |
| 1" | 1.025 in | 3.02 psi |
| 1-1/4" | 1.265 in | 1.08 psi |
| 1-1/2" | 1.505 in | 0.47 psi |
| 2" | 1.985 in | 0.12 psi |
| 2-1/2" | 2.465 in | 0.04 psi |
| 3" | 2.945 in | 0.02 psi |
| 4" | 3.905 in | 0.00 psi |
10 gpm in 3/4 inch — every material
The counter-intuitive result: PEX has the best roughness coefficient and the worst loss, because its bore is the smallest. Schedule 40 wins on both counts at this size.
| Material | Bore | C | Loss per 100 ft |
|---|---|---|---|
| Copper, Type L | 0.785 in | 140 | 11.08 psi |
| Copper, Type M | 0.811 in | 140 | 9.45 psi |
| PEX (SDR-9) | 0.681 in | 150 | 19.55 psi |
| CPVC, Schedule 40 | 0.824 in | 150 | 7.70 psi |
| PVC, Schedule 40 | 0.824 in | 150 | 7.70 psi |
| Galvanized steel, Schedule 40 | 0.824 in | 120 | 11.64 psi |
Fitting equivalent lengths
Expressed in pipe diameters, so they hold at any size, with the value for 3/4-inch Type L copper worked out alongside.
| Fitting | Equivalent diameters (L/D) | Feet at 3/4" copper |
|---|---|---|
| 90 degree elbow | 30 | 1.96 ft |
| 45 degree elbow | 16 | 1.05 ft |
| Tee, straight through | 20 | 1.31 ft |
| Tee, through the branch | 60 | 3.93 ft |
| Ball valve, full open | 8 | 0.52 ft |
| Gate valve, full open | 8 | 0.52 ft |
| Globe valve | 340 | 22.24 ft |
| Swing check valve | 100 | 6.54 ft |
Sources & standards: the Hazen-Williams equation as applied in IPC Appendix E and ASPE design guidance, cross-checked here against the independent head-loss form (the two agree within 1.3%). Pipe dimensions from ASTM B88, F876 and D1785, with every bore computed from outside diameter and wall thickness. Fitting equivalents are the classic L/D ratios, validated against published per-size tables. Local amendments override the model code.
Frequently asked questions
Common questions about friction loss, Hazen-Williams, and fitting equivalent lengths.
How much pressure do I lose over 100 feet of pipe?
It depends far more on bore than on length. At 10 gpm, 100 feet of 3/4-inch Type L copper costs 11.08 psi; the same flow in 1-inch copper costs 3.02 psi — a 73% cut for one size up. There is no single answer to quote, which is why a calculator beats a rule of thumb here.
What is Hazen-Williams and why this formula?
It is the standard empirical equation for water in full pipes at ordinary temperatures, and it is what plumbing design has used for a century because it needs only one roughness number, C. Darcy-Weisbach is more physically complete and handles other fluids and temperatures, but it needs an iterative friction factor. For cold water in a building, the two agree closely enough that Hazen-Williams is the sensible choice.
What is developed length?
The measured pipe plus the equivalent length of every fitting and valve, because an elbow costs pressure exactly the way a length of pipe does. On 3/4-inch copper a 90° elbow is worth about 1.96 feet of pipe, a tee taken through the branch about 3.93 feet, and a ball valve about 0.52 feet. Add them up and the defaults here turn a 100-foot run into a 120.7-foot one.
Does PEX lose less pressure than copper?
No — usually more, at the same nominal size, and this surprises people. PEX has the better roughness coefficient (150 against copper's 140) but a much smaller bore: 0.681 in against 0.785 in at 3/4 inch. At 10 gpm that is 19.55 psi per 100 ft in PEX against 11.08 in copper — nearly double. Bore beats smoothness, because the friction term goes as diameter to the power of 4.87.
What C value should I use for old galvanized pipe?
New galvanized steel is taken at C = 120, and it degrades toward C = 100 or lower as it scales internally. That is roughly a 40% increase in friction loss for the same pipe, and it is why an old galvanized house loses pressure long before anything visibly fails. The calculator uses 120 for galvanized; assume worse on anything more than a few decades old.
How do I convert psi of loss into feet of head?
Multiply by 2.309, since one psi is 2.309 feet of water column. The default 13.37 psi of total loss here is 30.9 feet of head. Pumps are specified in feet, supply pressure in psi, so you will convert constantly — the breakdown panel above shows both.
Should I add a safety factor?
Rather than pad the number, size against a real pressure budget. The Water Pipe Size Calculator subtracts elevation, fixture requirement and meter loss from the supply pressure and spends what is genuinely left, which is more honest than a blanket margin. If you want conservatism, put it in the C value or the fitting count.
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