SizingKitPipe & pumps
Pump head calculator
Total dynamic head is static lift plus friction plus the pressure the outlet has to hold plus velocity head, and this page returns the four separately, in feet and meters, so the term worth attacking is visible instead of buried in a total. Friction is solved by Darcy-Weisbach on the real bore of the pipe you pick — 2 in Schedule 40 steel is 2.067 in, not 2 in — with Crane equivalent lengths for every valve and elbow you count. It is free, takes no signup, and it draws the system curve at seven flows and crosses it with three points off a manufacturer's curve.
- 100% free
- No signup
- Four head terms, kept apart
- 9 pipe families
- 12 Crane fittings
- System curve at 7 flows
The system the pump has to push against
Everything from the water surface at the source to the point the water leaves. The suction side belongs to a different question and is worked out on the NPSH calculator.
Friction is the only term that moves with this. The other three are the same at any flow.
Measured surface to surface, not pump to discharge. Where the pump sits between them makes no difference to this term.
What the outlet still has to hold with the flow moving. This site cannot source a default for it — the 20 prefilled is an illustration. A 40/60 pressure switch makes it 60; a pipe emptying into an open tank makes it 0.
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. It sets the viscosity in the friction term and the density in the pressure term.
Bore 2.067 in · OD 2.375 in · wall 0.154 in
Run along the pipe, up and along, not the straight-line distance.
Valves and fittings on the run
Counted, not guessed at 10%. Crane rates each one in pipe diameters — 3 for a full-bore ball valve, 340 for a globe valve, fully open — so in 2 in pipe that one valve is worth 58.6 ft of extra straight pipe on its own.
Adds 51 ft of equivalent pipe to the 260 ft of straight run.
Default 0.0457 mm for Commercial steel, wrought iron. 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. That is clean new pipe; the band covering age and scale runs 0.0457 to 0.1219 mm.
Total dynamic head
TOTAL DYNAMIC HEAD
146.7 ft
44.7 m
At 100 gpm this column stands at 63.6 psi (4.38 bar) on a gauge at the pump. Read the curve in feet, size the piping in psi.
| Term | Feet | Meters | Share |
|---|---|---|---|
| Static lift | 45 | 13.72 | 31% |
| Friction, pipe and fittings | 54.15 | 16.5 | 37% |
| Discharge pressure | 46.18 | 14.08 | 31% |
| Velocity head | 1.42 | 0.43 | 1% |
Friction is the largest of the four at 54.1 ft. Friction is the one term a larger pipe reduces, and it falls with roughly the fourth to fifth power of the bore.
Going up one size to Steel, Schedule 40 2-1/2 in — bore 2.469 in against 2.067 in — takes friction from 54.1 ft to 22.8 ft and the total from 146.7 ft to 114.6 ft.
VELOCITY IN THE DISCHARGE PIPE
9.56 ft/s · 2.91 m/s
| Steel, general water service · noise | 10 ft/s | under |
|---|---|---|
| Quiet occupancy — bedrooms, hospitals, studios · noise | 4 ft/s | over |
| General building water distribution · noise | 8 ft/s | over |
| Pump suction line · suction | 5 ft/s | over |
| Pump discharge line · noise | 10 ft/s | under |
The tightest of these is 4 ft/s on noise grounds — quiet occupancy — bedrooms, hospitals, studios. Flow noise is roughly proportional to the fifth power of velocity, so halving the velocity is not a small improvement. Where a riser passes a bedroom wall, size it for 4 ft/s and take the extra pipe.
Friction solved by Darcy-Weisbach with the Colebrook-White factor at f = 0.0211 and Re = 136,276, over 311 ft of equivalent pipe. Dimensions from ASME B36.10M; fitting resistances from Crane Technical Paper 410. Pressure converted to head at 62.37 lb/ft³, the density of water at 60 °F, and velocity head at g = 32.17405 ft/s². Nominal pipe size (NPS) is a name, not a measurement. It matched the approximate inside diameter of wrought-iron pipe in the 1890s and has been a label ever since. A 3/4 in steel pipe measures 1.050 in outside and 0.824 in inside; 3/4 in is neither. From NPS 14 up the name finally equals the outside diameter, and below it the outside diameter is a fixed legacy value that every schedule of that size shares — the schedule changes the wall, which changes the inside diameter, never the outside. Copper, PEX and CPVC tube each run on a different naming convention again, so a 1/2 in copper tube, a 1/2 in PEX tube and a 1/2 in steel pipe have three different bores.
The system curve
Total head at seven flows, with the friction term solved again at each one rather than scaled by an assumed exponent. This is the curve a pump curve has to cross.
| Flowgpm · L/min | Velocityft/s · m/s | Frictionft · m | Total headft · m | At the dischargepsi · bar |
|---|---|---|---|---|
| 0 · 0 | 0 · 0 | 0 · 0 | 91.2 · 27.8 | 39.5 · 2.72 |
| 25 · 95 | 2.39 · 0.73 | 4 · 1.2 | 95.3 · 29 | 41.3 · 2.85 |
| 50 · 189 | 4.78 · 1.46 | 14.6 · 4.4 | 106.1 · 32.3 | 45.9 · 3.17 |
| 75 · 284 | 7.17 · 2.19 | 31.3 · 9.5 | 123.3 · 37.6 | 53.4 · 3.68 |
| 100 · 379 | 9.56 · 2.91 | 54.1 · 16.5 | 146.7 · 44.7 | 63.6 · 4.38 |
| 125 · 473 | 11.95 · 3.64 | 83.1 · 25.3 | 176.5 · 53.8 | 76.5 · 5.27 |
| 150 · 568 | 14.34 · 4.37 | 118.2 · 36 | 212.6 · 64.8 | 92.1 · 6.35 |
Cross it with a pump curve
Read three points off the catalog sheet — shutoff, somewhere in the middle, and the far right end. A pump does not run where you want it to; it runs where its curve meets the one above.
OPERATING POINT
95.4 gpm at 141.9 ft
361 L/min at 43.3 m. That lands within 5% of the design flow, which is as close as a fixed-speed pump and a fitted curve are worth reading.
To land the crossing on 100 gpm exactly, the curve has to be run at 102.1% of the speed it was published at — which by the cube law is 106% of the shaft power.
Exact for a speed change on a fixed impeller and approximate for an impeller trim. Both forms assume the efficiency is unchanged, which holds over a moderate speed change and degrades with a trim, since trimming the impeller does not shrink the casing with it. Neither form moves the system curve: a pump slowed to 50% speed does not deliver 50% of the flow into a real system unless that system's resistance is pure friction with no static head. Where there is static head — and a well or a lift station is nearly all static head — the flow falls off far faster than the speed does, and below some speed the pump delivers nothing at all.
The head this page returns is head, not pressure, so it is the same number for any liquid of any density — but the pressure the gauge reads and the horsepower the motor draws are not. Both of those are worked out on the well pump size calculator, and the friction term on its own, per 100 ft, is on the pipe pressure loss calculator.
How to work out total dynamic head
Three passes: the two ends of the system, then the pipe between them, then the pump that has to bridge the gap.
Measure surface to surface, then say what the outlet needs
Static lift is the vertical distance from the water surface at the source to the point the water leaves, and it is measured surface to surface — where the pump sits between the two changes nothing. Then enter the pressure the discharge must still hold with flow moving: a pressure switch's cut-out, a sprinkler head's design pressure, or zero for an open discharge.
Pick the pipe by family and size, then count the fittings
Choose the dimensional family before the size, because a 1 in bore is 0.957 in in Schedule 80 steel and 1.055 in in type M copper — a fifth more flow area under the same name. Then count the elbows, tees and valves rather than adding a flat percentage — a globe valve is 340 pipe diameters and a full-bore ball valve is three, so two runs with the same fitting count can differ by a factor of ten.
Read the largest term, then cross the curve
The four terms come back with their percentages and the largest is named. Friction is the only one a bigger pipe reduces, and the page prices the next size up for you. Then type three points off the pump's published curve — shutoff, middle, run-out — and the page reports the flow and head where that curve meets the system curve, which is where the pump will actually run.
Technical specifications
| Friction method | Darcy-Weisbach, h = f (L/D) v²/2g, with the Colebrook-White friction factor solved by fixed-point iteration seeded from Swamee-Jain. Below Re 2000 it switches to the exact laminar f = 64/Re; between 2000 and 4000 the two ends are blended and the answer is an estimate. |
|---|---|
| Pipe dimensions | Nine families: ASME B36.10M steel Schedule 40 and 80, ASTM D1785/F441 PVC and CPVC schedule pipe, ASTM B88 copper types K, L and M, ASTM F876 PEX and ASTM D2846 CTS CPVC. Bores are computed as OD − 2 × wall, never tabulated. |
| Fitting resistance | Crane Technical Paper 410 equivalent lengths in pipe diameters, twelve fittings from a 3 D full-bore ball valve to a 340 D globe valve. K = f_T × L/D, with f_T computed from the fully-rough Colebrook limit rather than read off Crane's printed column. |
| Velocity head | v²/2g at the discharge bore, with g = 32.17405 ft/s² — the CGPM 1901 standard gravity of exactly 9.80665 m/s² expressed in feet. |
| Pressure converted to head | psi × 144 ÷ the density of water at the temperature you enter, interpolated from a 0–100 °C anchor table. The shop constant 2.31 ft per psi is that arithmetic at 60 °F only, and it is 4% wrong on a 200 °F system. |
| System curve | Seven flows from zero to 1.5 × design, with the friction term solved again at each point rather than scaled by an assumed square law. Zero flow is handled explicitly, because 64/Re at Re = 0 is not a number. |
| Pump curve | Three points fitted to H = a + bQ + cQ² by Lagrange interpolation, then intersected with the system curve by 60 rounds of bisection. The search stops at the largest flow you entered — past the end of the published curve the parabola is this page's invention, so it refuses instead. |
| Where the arithmetic runs | In the browser tab. Flows, lengths, fitting counts and the curve points you read off a catalog sheet are never uploaded, so the page keeps working in a plant room with no signal. |
Frequently asked questions
Does total dynamic head include the suction lift?
Yes — static head is measured from the water surface at the source, not from the pump, so a suction lift is already inside the static term. Where the pump sits between the source surface and the discharge changes nothing about the total: a pump lifting 10 ft from a wet well and pushing 40 ft up has the same 50 ft of static head as one flooded by the wet well and pushing 50 ft. What the pump's position does change is whether the liquid arrives at the impeller without flashing, and that is a separate calculation on the NPSH page.
My friction head came out bigger than the static lift. Is that wrong?
It is common and it is the signal that the pipe is undersized rather than that the arithmetic is. Friction rises with about the square of flow and falls with roughly the fourth to fifth power of the bore, so a long run in small pipe can easily produce more head than the height being climbed. The page prices the next size up beside the answer for exactly this case: it is usually far cheaper to change the pipe once than to buy the extra impeller diameter and then pay for it in kilowatt-hours for twenty years.
Should I count both the discharge velocity head and the exit loss?
No — they are the same foot of water counted twice. The velocity head v²/2g is the kinetic energy the water leaves with, and the exit loss coefficient of K = 1.0 for a pipe discharging into a tank or the air is that same kinetic energy being thrown away. Include one of them. This page includes the velocity head term and leaves the exit out of the fitting list, which is why only the twelve fittings with a Crane L/D appear there and the entrance and exit coefficients do not.
Does the head change if I pump something other than water?
Head does not change; pressure and power do. A centrifugal impeller gives a fluid a fixed amount of energy per unit weight, so a pump that makes 100 ft of head on water makes 100 ft on diesel and 100 ft on 50% glycol at the same flow and speed. The gauge reading changes with density — 100 ft of diesel at a specific gravity of 0.85 reads 37 psi against water's 43 — and so does the shaft horsepower, which scales directly with specific gravity. The friction term also moves, because viscosity feeds the Reynolds number, and this page's water property table does not cover other fluids.
Why does the pump run at a different flow from the one I designed for?
Because a fixed-speed pump has no way to know your design flow — it settles where its own curve crosses the system curve, and nowhere else. If the system turns out less restrictive than assumed, the pump runs out to the right at more flow, more power and possibly past the end of its curve; if it is more restrictive, the pump rides back up the curve toward shutoff, where efficiency collapses and recirculation heats the casing. Entering three curve points here reports that crossing, and the speed ratio the affinity laws would need to move it onto the design flow.
Is a flat 10% allowance for fittings good enough instead of counting them?
It is fine on a long run and badly wrong on a short one. The fittings' contribution is a fixed number of pipe diameters, so it scales with the bore rather than with the length: on 500 ft of 4 in pipe a dozen elbows are a few percent, but on 30 ft of 1 in pipe with a globe valve and a check valve the fittings are worth more than the pipe. Short suction lines and pump-room manifolds are exactly where the percentage rule fails, and they are also where the head matters most.
How do I get from head to the horsepower and the motor?
Multiply flow in gpm by head in feet by specific gravity and divide by 3960 for water horsepower, then divide by the pump's efficiency at that point on its curve for shaft horsepower. The efficiency is the input that moves the answer most and the one most often guessed — a small residential submersible can be at 40% where a well-matched end-suction unit is at 70%. The well pump page does that arithmetic with the efficiency exposed as an editable field.
About total dynamic head, and the four terms it is made of
Total dynamic head is the whole energy a pump must add to a unit weight of liquid, expressed as a height of that liquid, and it exists as a single number only so that it can be read against a curve drawn on the same axis. The reason to keep the four terms apart is that they behave nothing like each other. Static lift is pure geometry: it is the same at 10 gpm and at 200 gpm, and no impeller, valve or pipe size touches it. Friction is the term that rises with roughly the square of flow and falls with the fourth to fifth power of the bore, which makes it the only term a larger pipe fixes and the reason an undersized run is a permanent bill rather than a one-off mistake. The pressure term is not a loss at all — it is a requirement, whatever the outlet has to still hold once the water is moving. Velocity head is usually under a foot and is here because a term that is quietly dropped is a term nobody can check.
What separates a defensible head figure from a plausible one is almost always the friction term, and that comes down to two things most calculators get wrong. The first is the bore: nominal pipe size is a name, and a page that squares the nominal instead of the actual inside diameter is 10 to 30% out on area before it starts. The second is the fittings. Crane's Technical Paper 410 rates each fitting as a number of pipe diameters, which is why a 90° elbow is 30 diameters whether it is half an inch or twelve, and why a globe valve at 340 diameters is worth more than a hundred feet of straight 4 in pipe. Both are why this page asks which family of pipe you have before it asks the size, and asks for a count rather than a percentage. If you want the friction term alone, per 100 ft and in psi, the pipe pressure loss calculator reports it with the intermediate steps, and the Reynolds number calculator shows which regime the friction factor came from.
One head figure is not a pump selection. The discharge side answered here tells you what the pump must make; the suction side decides whether it can make it without the liquid flashing to vapor at the impeller eye, and hot water will cavitate a pump that handled the same duty cold — that is the NPSH calculator. For a domestic well the head is assembled from measurements taken at the well itself — static water level, drawdown, the drop pipe and the pressure switch — and turned into horsepower and a tank size on the well pump size calculator. None of these pages is a stamped design: they are reference tables and arithmetic, and the pump manufacturer's own curve at the duty point, plus whoever signs the installation off, remain the authority.
Where the head calculation runs
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.