Home › Calculators › Pipe Friction Loss Calculator
How much pressure does it cost to push this much water through this much pipe? Enter the flow and the pipe, or work backward and let it pick the smallest size that works. Darcy-Weisbach with an iterative Colebrook friction factor, real published inside diameters, and fitting losses included.
Pressure is not a fixed thing your house has. It is a budget that gets spent on the way to the fixture. The street or the pump supplies a certain pressure. Elevation takes a cut. The meter and the backflow preventer take a cut. And then friction takes a cut for every foot of pipe and every fitting between the source and the tap. Whatever survives all of that is what comes out of the shower head.
This calculator quantifies the friction portion. That is usually the part people can do something about, because it is the part that depends on choices — pipe size, material, routing, and how many turns the water has to make.
This is the most common real complaint, and the answer is almost always in the branch, not the main. Pressure is spent along a path, so the fixture at the end of the longest, smallest, most convoluted run pays the most.
Consider a second-floor bathroom fed by 70 feet of half-inch PEX with eight elbows, when the rest of the house runs three-quarter inch. At 4 gpm that half-inch branch is doing real damage — run it through the calculator above and you will typically see something in the range of 20 to 30 psi consumed by that branch alone, before elevation. Meanwhile the three-quarter inch main that fed it may have spent 3 psi covering twice the distance.
Nothing is broken. The pipe is doing exactly what physics says it should. The branch was simply sized for a fixture, not for a fixture at the end of a long run.
You can have acceptable pressure loss and still have a pipe that is a problem, because velocity carries its own two limits.
Water moving fast through pipe is audible, and it is audible inside walls where nobody can get at it. Above roughly 8 feet per second most people notice a hiss or rush when a fixture opens elsewhere in the house. In bedrooms and quiet spaces the practical threshold is lower — call it 5 to 6 feet per second for pipe running through or near occupied rooms.
This one is not about comfort. Copper tube protects itself with a thin oxide film that forms on the inside wall. Move water across it fast enough and the film is stripped away mechanically, exposing fresh copper, which oxidizes, which gets stripped again. The wall thins from the inside until it pinholes. The failures show up on the outside of elbows and just downstream of fittings, where the water is turning and the local velocity is highest.
The conventional design ceilings are 8 ft/s for cold water and 5 ft/s for hot. Hot is lower because the reaction runs faster at temperature — a recirculating hot water loop that runs continuously at 6 or 7 ft/s is a well-documented way to destroy copper in a decade or less.
Plastic pipe — PEX, CPVC, PVC — does not have an oxide film and does not suffer erosion corrosion. Its ceiling is set by noise and by fitting stress, usually taken as about 10 ft/s. This is a real advantage of plastic that rarely gets mentioned, because the conversation is always about cost and labor instead.
People assume plastic is rougher. It is the opposite — PEX is hydraulically smoother than drawn copper. The reason PEX loses more pressure is entirely about how it is dimensioned.
PEX is manufactured to copper tube size on the outside, with a thick wall to handle pressure. That wall eats into the opening:
| Nominal size | Copper Type L ID | PEX SDR-9 ID | Area lost |
|---|---|---|---|
| 1/2" | 0.545" | 0.485" | 21% |
| 3/4" | 0.785" | 0.677" | 26% |
| 1" | 1.025" | 0.863" | 29% |
A 29 percent reduction in area at one inch is not a rounding error, and because loss scales so hard with diameter, it translates into substantially more pressure spent per foot. Run both through the calculator at the same flow and compare.
None of this makes PEX a bad choice. It means you cannot substitute PEX for copper size-for-size on a long run and expect the same result. On a short branch the difference is invisible. On a seventy foot run to a far bathroom it is the whole problem. The fix is simply to go up a size where the run is long — which is often still cheaper and faster than copper.
Every direction change costs pressure. The standard way to account for it is equivalent length: each fitting is treated as a certain number of extra feet of straight pipe, expressed as a multiple of the pipe diameter so it scales correctly across sizes.
| Fitting | Equivalent length (L/D) | As feet of 3/4" copper |
|---|---|---|
| 90° elbow, standard | 30 | 2.0 ft |
| 90° elbow, long radius | 20 | 1.3 ft |
| 45° elbow | 16 | 1.0 ft |
| Tee, flow straight through | 20 | 1.3 ft |
| Tee, flow turning into branch | 60 | 3.9 ft |
| Ball valve, full port, open | 3 | 0.2 ft |
| Gate valve, open | 8 | 0.5 ft |
| Globe valve, open | 340 | 22.2 ft |
| Swing check valve | 100 | 6.5 ft |
Two things in that table deserve attention.
A tee taken on the branch costs three times a tee taken straight through, and it costs twice what an elbow costs. A manifold layout that sends every fixture its own home run avoids a great many branch tees, and that is a genuine hydraulic advantage of home-run plumbing, separate from the convenience of having a shutoff for every fixture in one place.
A globe valve is a catastrophe. At 340 diameters it is worth about 22 feet of three-quarter inch pipe — a single valve costing more than most of the run it sits in. Globe valves are for throttling, and if one is installed where a ball valve would do, replacing it is one of the cheapest pressure recoveries available.
Rough reference for Type L copper at 60°F, showing what a reasonable design flow produces:
| Size | Flow | Velocity | Loss per 100 ft |
|---|---|---|---|
| 1/2" | 2 gpm | 2.8 ft/s | 3.5 psi |
| 3/4" | 5 gpm | 3.3 ft/s | 3.0 psi |
| 1" | 10 gpm | 3.9 ft/s | 2.9 psi |
| 1-1/4" | 16 gpm | 4.1 ft/s | 2.4 psi |
| 1-1/2" | 25 gpm | 4.5 ft/s | 2.3 psi |
| 2" | 45 gpm | 4.7 ft/s | 1.8 psi |
If your run is landing well outside this territory, the size is probably wrong for the flow you are asking of it.
Darcy-Weisbach, which is the general form valid for any fluid and any flow regime:
h_f = f × (L/D) × V² / (2g)
Total equivalent length is straight pipe plus the sum of fitting equivalent lengths, so L/D becomes L_straight/D + Σ(L/D)_fittings. Elevation change is added separately as static head and is not affected by pipe size.
Laminar flow (Re < 2000) uses f = 64/Re. Turbulent flow (Re > 4000) uses the Colebrook-White equation, solved by fixed-point iteration to a tolerance of 1×10-12:
1/√f = -2 log₁₀( ε/(3.7D) + 2.51/(Re√f) )
The transition band between Re 2000 and 4000 is linearly interpolated and flagged in the output, because flow there is genuinely unpredictable and no correlation is trustworthy in that range.
Colebrook is used rather than an explicit approximation such as Swamee-Jain because the iteration converges in well under twenty passes and costs nothing in a browser, so there is no reason to accept the approximation error.
Density from the Kell/Thiesen formulation. Dynamic viscosity from the Vogel-type correlation referenced to 1.002 cP at 20°C, valid 0 to 100°C. Both are temperature-dependent rather than fixed, which matters for hot water and recirculation loops — viscosity at 140°F is 42 percent of its value at 60°F.
Inside diameters are published values — ASTM B88 for copper, ASME B36.10 for Schedule 40 steel, ASTM F876 for PEX, ASTM F441/D2846 for CPVC, ASTM D1785 for Schedule 40 PVC. Nominal size is never used as a diameter.
L/D values from Crane Technical Paper No. 410. Expressed in diameters rather than fixed feet so they scale correctly with pipe size.
The friction factor routine was checked against published Moody diagram values at three points and agrees to four decimal places:
Water properties were checked against reference tables: 1.122 cP at 60°F and 0.467 cP at 140°F. Resulting head loss values were compared against published copper tube friction loss tables across six sizes.
Liquid water only, single phase, full pipe, steady state. Isothermal along the run. Does not account for aging, scale, or internal corrosion — use a rougher material selection or a reduced diameter if you are modeling old pipe.