SizingKitDarcy-Weisbach
Pipe pressure loss calculator
Enter a flow, a pipe and a length and this returns the pressure drop over the run in psi and bar, and the same loss as feet and meters of head. It is free, needs no account, and solves the Colebrook-White friction factor by iteration instead of assuming one, so the answer holds for oil, glycol and hot water as well as for cold water — enter a density and a kinematic viscosity and it uses those. Fittings are costed from Crane TP-410 as equivalent pipe diameters, not as a percentage guess.
- 100% free
- No signup
- Colebrook solved, not assumed
- 16 valves and fittings
- Any fluid by ρ and ν
The run
Feet unless you write a unit. Measure along the pipe, not across the building.
ASME B36.10M. The name is 2 in; the hole is 2.0670 in.
Clean and new is 0.0457 mm (1.50e-4 ft); the service range runs 0.0457–0.1219 mm. Moody's commercial-steel value, 0.045 mm, for clean new pipe. Mild corrosion and scale take it toward the top of the range within a decade or two of service on untreated water.
Default 60 °F — The customary US reference temperature for water in waterworks and plumbing practice (AWWA, ASPE). Water at 60 °F weighs 62.37 lb/ft³ and 8.337 lb/gal; the familiar 62.4, 8.33, 0.433 psi/ft and 2.31 ft/psi are that density rounded. At 60 °F the table gives 62.366 lb/ft³ and 1.123 cSt.
Fitting schedule
Count what is on the run. Each fitting is stored as L/D — a resistance in pipe diameters — so one figure serves every size, and the feet it becomes depend on the bore you picked above.
| Fitting | L/D | Count | Equivalent ft |
|---|---|---|---|
| Gate valve, fully open | 8 | — | |
| Ball valve, full bore, fully open | 3 | — | |
| Globe valve, fully open | 340 | — | |
| Angle valve, fully open | 150 | — | |
| Butterfly valve, 2–8 in, fully open | 45 | — | |
| Swing check valve, fully open | 100 | — | |
| 90° elbow, standard radius | 30 | — | |
| 90° elbow, long radius | 20 | — | |
| 45° elbow, standard radius | 16 | — | |
| 180° return bend | 50 | — | |
| Tee, flow through the run | 20 | — | |
| Tee, flow through the branch | 60 | — | |
| Pipe entrance, sharp-edged (inward flow) | K 0.5 → 26 | — | |
| Pipe entrance, projecting inward | K 0.78 → 41 | — | |
| Pipe entrance, well rounded | K 0.04 → 2 | — | |
| Pipe exit into a tank or the air | K 1 → 53 | — |
Crane Technical Paper No. 410, Flow of Fluids Through Valves, Fittings and Pipe — resistance of valves and fittings expressed as equivalent length in pipe diameters (L/D), with K = f_T × L/D. Entrance and exit coefficients are Crane's fixed K values.
PRESSURE DROP OVER THE RUN
5.14 psi · 0.354 bar
AS HEAD OF THE FLUID
11.9 ft · 3.62 m
| Bore used | 2.0670 in · 52.5 mm (Steel, Schedule 40, 2 in) |
|---|---|
| Velocity | 5.74 ft/s · 1.75 m/s |
| Velocity head v²/2g | 0.51 ft · 0.16 m |
| Reynolds number | 81,765 — turbulent |
| Relative roughness ε/D | 8.704e-4 |
| Friction factor f | 0.02221 |
| Straight pipe | 180 ft · 54.86 m |
| Fittings as equivalent length | none entered |
| Effective length L | 180 ft · 54.86 m |
| Loss per 100 ft of effective length | 2.86 psi · 0.197 bar · 6.59 ft · 2.01 m |
How f was found. Colebrook-White, solved by iteration to f = 0.02221. Swamee-Jain's explicit form gives 0.02236 on the same inputs, a difference of 0.67%.
What the drop is made of. No fittings entered, so this is straight pipe only. Add the elbows, tees and valves below — on a short run they are usually the larger half.
What this rests on. Darcy-Weisbach, h = f (L/D) v²/2g, with g taken as 32.174 ft/s² by the 1901 definition of standard gravity. Bore, flow area and every dimension come from the schedule, never from the nominal size — the gap between the two is worked through on the pipe size calculator. Reference tables and arithmetic only: the local code and a licensed engineer decide what gets installed.
How to price the drop across a run of pipe
Three inputs decide the answer and the fourth decides how badly the usual shortcuts miss it.
Give it the flow and the actual bore
Type the design flow in gpm, L/s or m³/h, then pick the pipe from the schedule list or type a measured bore. Picking the pipe matters more than it looks: a 2 in Schedule 40 steel pipe has a 2.067 in hole and a 2 in PEX tube has a 1.653 in hole, and the velocity term is squared, so the same flow costs the PEX run roughly two and a half times the drop.
Count the fittings instead of guessing a percentage
Fill in the schedule: elbows, tees through the branch, the gate valve at the isolation point, the swing check on the discharge. Each carries a resistance in pipe diameters, so a 90° standard elbow is 30 diameters whether it is a half inch or twelve — 2.1 ft of equivalent pipe in a 3/4 in line and 29.9 ft in a 12 in one. A globe valve alone is 340 diameters.
Set the wall condition and the fluid, then read what the answer rests on
The roughness field starts at Moody's clean-and-new figure for the material and is meant to be moved: forty-year-old galvanized runs at four times its new roughness with a smaller bore as well. Under the answer the page prints the velocity, the Reynolds number, the relative roughness and the friction factor it used, which is what somebody checking your submittal against a handbook will ask for.
Technical specifications
| Method | Darcy-Weisbach, h = f (L/D) v²/2g, with g = 32.17404855 ft/s² from the 1901 definition of standard gravity |
|---|---|
| Friction factor | Colebrook-White solved by fixed-point iteration on 1/√f, seeded with Swamee-Jain, converging to 1e-12 in four or five passes. Both values are printed so the 1% gap between them is visible |
| Laminar branch | f = 64/Re below Re 2000, with no roughness term at all. Between Re 2000 and 4000 the two ends are blended and the page says the result is an estimate |
| Pipe dimensions | ASME B36.10M Schedules 40 and 80, ASTM B88 copper types K, L and M, ASTM F876 PEX, ASTM D2846 CTS CPVC, ASTM D1785 PVC — 9 families, NPS 1/8 through 24 |
| Fitting resistances | 16 rows from Crane Technical Paper 410 as L/D: gate valve 8, ball valve 3, standard 90° elbow 30, long-radius elbow 20, tee through the branch 60, swing check 100, globe valve 340 |
| Roughness range | 13 materials from Moody 1944: 0.0015 mm drawn tubing, 0.045 mm commercial steel, 0.15 mm galvanized, 0.26 mm cast iron, 3.05 mm riveted steel, 45.7 mm corrugated metal — editable, with each material's own service range beside the field |
| Fluid properties | Water 32–212 °F interpolated from 21 anchor points every 5 °C — density, dynamic and kinematic viscosity — or your own density and kinematic viscosity in cSt for anything else |
| Privacy | No account, no upload; the iteration runs in your browser and nothing is stored |
Frequently asked questions
Why does this ask for viscosity when other pressure loss calculators do not?
Because the friction factor is a function of the Reynolds number, and the Reynolds number is velocity times diameter divided by kinematic viscosity — remove the viscosity and there is no way to know which part of the Moody chart you are on. Calculators that skip it have quietly assumed cold water. That assumption is harmless on a chilled-water loop and badly wrong on a 40 cSt hydraulic line, where the same flow in the same pipe can be laminar rather than turbulent and the friction factor is a different equation entirely.
Should I use Colebrook or Swamee-Jain?
Use Colebrook for a number you are going to defend and Swamee-Jain when you need a formula you can write on a page. Swamee-Jain is an explicit fit to Colebrook and stays within about 1% of it over 5000 ≤ Re ≤ 10⁸ and 10⁻⁶ ≤ ε/D ≤ 10⁻²; this page prints both so you can see the gap on your own numbers. Outside that window Swamee-Jain degrades without saying so, which is the argument for iterating.
How much should I add for fittings if I do not know the count yet?
Nothing — get the count, because the usual allowances fail in exactly the case where the number matters. On a long straight main the fittings are a rounding error and any allowance works; on a short packed run inside a mechanical room they are most of the loss, and a 10% allowance can be out by a factor of ten. A single globe valve is 340 pipe diameters, which in a 4 in line is 114 ft of equivalent pipe: more than most mechanical rooms contain in actual pipe.
The equivalent length of my entrance and exit came out in feet — where did the K go?
It was converted through Crane's own identity, K = f_T × L/D. Entrances and exits are tabulated as a fixed K because their loss depends on the shape of the opening rather than on the pipe wall, so to add them to a length-based schedule the page divides that K by the fully rough friction factor of your pipe and bore. That f_T is computed from the Colebrook limit with the Reynolds term removed rather than read out of TP-410's printed table, which is why it works at sizes the table does not print.
Why is the drop higher than my pipe supplier's chart says for the same size?
Check which bore the chart used. Most published friction charts are drawn for Schedule 40 steel and reused for everything, and a 3/4 in PEX tube has a 0.681 in bore against Schedule 40's 0.824 in — 32% less flow area, which lands at 31.6 ft of head per 100 ft against 15.1 ft at 8 gpm, a little over double. The second usual cause is roughness: a chart printed for clean new pipe is optimistic for anything that has been in service, and this page lets you move the roughness up its own range instead of pretending it did not.
Can I use this on compressed air or steam?
No, and the reason is not the equation but the assumption under it. Darcy-Weisbach as used here treats the fluid as incompressible — one density for the whole run — and a gas expands as it loses pressure, so its velocity rises down the pipe and the loss is not linear in length. It is a reasonable approximation only while the total drop is under roughly 10% of the absolute inlet pressure. Steam adds condensate and a phase change on top of that and is a different calculation altogether.
What does the critical zone warning mean for my answer?
It means the number in front of you is an interpolation across a gap rather than a prediction. Between Re 2000 and 4000 two identical pipes carrying identical flow can show friction factors a factor of two apart, depending on upstream disturbance the equation cannot see. Nothing is wrong with your inputs; the physics is genuinely undetermined there. If the result matters, change the design so the operating point sits clear of the band — usually by dropping a pipe size, which raises the velocity and pushes Re up.
About Darcy-Weisbach and the friction factor
Darcy-Weisbach is derived from the momentum equation rather than fitted to a data set, which is the whole reason it survives outside the conditions anybody tested. Head loss is the friction factor times the length-to-diameter ratio times the velocity head, and the only thing in it that is not geometry is f. Everything hard about the method is therefore packed into finding f, and for seventy years that meant reading a Moody chart by eye. The Colebrook-White equation the chart is drawn from is implicit — f appears on both sides — so it has to be iterated, which is why the explicit approximations exist and why a calculator that will not tell you which one it used is hiding the only interesting decision it made.
The input that decides the most and gets the least attention is the bore. Nominal pipe size is a name, and the sizes sold as “half inch” across four materials have four different holes; velocity goes as the inverse square of the bore and head loss goes as velocity squared, so a 10% error in diameter is roughly a 60% error in the answer. That is a bigger effect than every other assumption on this page combined, and it is the reason the size list here prints the bore next to the name. If you are choosing the size rather than checking one, the pipe size calculator works the problem the other way around, against a velocity ceiling and a drop budget at once.
Where this method is not the right one: when a code names another. Fire sprinkler hydraulic calculations are performed under NFPA 13 with Hazen-Williams and that standard’s own C values, and a submittal worked any other way is not a submittal — the pipe friction loss calculator carries that method and the C table with it. The band this page interpolates across, and what the flow regime does to the friction factor either side of it, is worked through on the Reynolds number calculator. For a gravity drain nothing here applies at all, because a partly full pipe is an open channel: that is Manning’s equation and the drain pipe slope calculator.
Where this calculation happens
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.