What is the difference between water horsepower, brake horsepower and motor horsepower?

They are the same power seen at three places. Water horsepower is what actually goes into the fluid: its weight flow times the head. Brake horsepower is what the pump's shaft must be turned with, which is more, because the pump loses some to friction, leakage and turbulence; divide water power by the pump efficiency to get it. Motor input is what the electrical supply provides, more again, because the motor has losses of its own; divide brake power by the motor efficiency. A pump with 70% efficiency driven by a 90% motor draws about 1.6 times its water power from the supply.

Where does the 3,960 in the US formula come from, and why is this page slightly different?

One horsepower is 33,000 foot-pounds of work a minute, and a US gallon of water, 3.785 litres, weighs about 8.33 lb (3.78 kg), so 33,000 divided by 8.33 is about 3,960: a gallon a minute lifted one foot is 1/3,960 of a horsepower. That 8.33 lb gallon is water slightly lighter than 1,000 kg per cubic metre (62.4 lb per cubic foot), the density this page multiplies the specific gravity by. The two answers therefore differ by about 0.15%, which three significant figures usually hide; the DOE sourcebook's example of 15,000 gallons a minute (946 L/s) at 150 ft (45.72 m) comes to 568.2 water horsepower by its divisor and 569.0 here.

How do I turn a pressure gauge reading into head?

Divide the pressure by the fluid's weight per unit volume. For water that is about 2.31 ft of head for every psi, or about 0.102 m for every kPa; a fluid heavier than water gives less head for the same pressure, so divide by its specific gravity. The total head across a running pump is the discharge gauge's head minus the suction gauge's, allowing for any difference in their heights and pipe sizes.

Which efficiency should I enter if I only know the pump's best efficiency?

Use the efficiency at the flow and head the pump will actually run at, read from its curve. The best efficiency point is the top of the curve, and a pump running well to either side of it is less efficient, sometimes by a wide margin; entering the peak figure for an off-peak duty understates the power. Where the duty is not known yet, the honest answer is a range: work the page at the efficiency either side of the expected point.

Does a pump at zero head use no power?

The formula's water power is zero, because nothing is lifted, but the pump still turns and still draws power. A centrifugal pump running with its discharge shut moves no water yet churns it, and one running into no resistance at all moves a lot of water and usually draws its greatest power. Both points are on the maker's curve; this page only prices the work done on the fluid at a point you choose.

Plumbing & HVAC

Pump Power Calculator (Horsepower and kW)

Water, brake and motor-input power, in horsepower and kilowatts, for a pump lifting a flow through a head, from specific gravity and the two efficiencies.

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Flow Rate

The flow the pump delivers at the operating point you are costing, not the largest flow on its label.

Take it from the duty the system needs, or from a flow meter on a running system. A pump's catalogue flow is one point on its curve; the same pump delivers more against a lower head and less against a higher one, and its power changes with it. Litres per second and US gallons per minute are both offered: 1 L/s (15.85 gal/min) is a small booster's territory, and a building's chilled water main can be fifty times that.

Tools needed: Flow meter, or the system's design schedule

Total Head

The total dynamic head at that flow: the lift from the water surface to the outlet, plus every friction and pressure loss on the way.

Head is the energy per unit weight the pump adds, written as a height of the fluid being pumped. Add the static lift (suction water level to the highest delivery point), the pipe, fitting and valve losses at this flow, and any pressure the outlet must hold, converted to head. A gauge reading converts at about 2.31 ft per psi (0.102 m per kPa) for water; for another fluid divide by its specific gravity. The page's related head-loss and pressure pages work those parts out.

Tools needed: Pressure gauges on suction and discharge, Levels or drawings for the static lift

Specific Gravity of the Fluid (water = 1)

How heavy the fluid is compared with water; 1 for clean cold water.

The power to lift a column of fluid is proportional to its weight, so a fluid twice as heavy as water needs twice the power for the same flow and head. Take the figure from the fluid's data sheet at its pumping temperature; the limitations below say which water the page calls 1. Specific gravity does not capture viscosity: a thick fluid also lowers the pump's efficiency, which is a separate correction from the pump maker.

Pump Efficiency at This Point (%)

The pump's hydraulic efficiency at this flow and head, read off its performance curve.

Every pump curve carries efficiency contours or an efficiency line; read it where the flow and head entered meet the curve. The DOE pumping sourcebook puts real pumps anywhere from 35% to more than 90%, highest at the best efficiency point and falling either side of it. The 70% the page opens on is a worked example, not a typical value for any particular pump.

Motor Efficiency (%)

The drive motor's efficiency at the load it runs at, from its nameplate or data sheet.

Nameplate efficiency is stated at full load; a motor running well below its rating is usually a little less efficient. The DOE sourcebook's own cost example uses 95% for a large motor, while small single-phase motors are well below that. If a variable speed drive sits in front of the motor, its losses come on top and are not included here.

Brake power at the pump shaft

3.791 horsepower

High confidence

Water power is the weight of fluid moved each second times the head it is lifted through; the shaft has to deliver that divided by the pump's efficiency, and the supply that again divided by the motor's. All three belong to the one flow and head entered: move along the pump's curve and the efficiency, and so every figure here, moves with it.

Water power, the energy the fluid gains: 2.65 horsepower
Brake power at the pump shaft: 3.79 horsepower
Motor input from the supply: 4.21 horsepower
Brake power in kilowatts (kW): 2.83 kW
Brake power in horsepower (hp): 3.79 hp
The head as a pressure, in this fluid: 28.61 psi

Then change the inputs to see how far the answer moves.

Show calculation logic

How this was calculated

Formula source(s)

US Department of Energy Industrial Technologies Program and the Hydraulic Institute, Improving Pumping System Performance: A Sourcebook for Industry, second edition (May 2006), section 1: fluid power = H x Q x s.g. / 3,960 (head in feet, flow in gpm, power in horsepower); pump efficiency = fluid power / shaft power, the motor's brake horsepower for a directly coupled pump; pump efficiencies from 35% to more than 90%; motor input = brake horsepower x 0.746 kW/hp / motor efficiency; a radial centrifugal pump's brake horsepower rises with flow, an axial pump's falls
The same sourcebook, Appendix C, Pumping Systems Tip Sheet 3 (DOE/GO-102005-2157, October 2005): 15,000 gpm at a total head of 150 ft, specific gravity 1.0, pumps at 81% and 78% efficiency, a reduction of (150 x 15,000 x 1.0 / 3,960) x (1/0.78 - 1/0.81) = 27 bhp (the tip sheet prints the two terms the other way round, which as written is negative)
NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B.8: horsepower (550 ft·lbf/s) = 745.6999 W, horsepower (electric) = 746 W, horsepower (metric) = 735.4988 W; standard acceleration of free fall gn = 9.80665 m/s², exact

Inputs used

Flow Rate: 159 gal/min
Total Head: 66 ft
Specific Gravity of the Fluid (water = 1): 1
Pump Efficiency at This Point (%): 70
Motor Efficiency (%): 90

Intermediate steps

Water power, the energy the fluid gains: 2.65 horsepower
Brake power at the pump shaft: 3.79 horsepower
Motor input from the supply: 4.21 horsepower
Brake power in kilowatts (kW): 2.83 kW
Brake power in horsepower (hp): 3.79 hp
The head as a pressure, in this fluid: 28.61 psi

Final result3.79 horsepower

Confidence note: Water power is the weight of fluid moved each second times the head it is lifted through; the shaft has to deliver that divided by the pump's efficiency, and the supply that again divided by the motor's. All three belong to the one flow and head entered: move along the pump's curve and the efficiency, and so every figure here, moves with it.

What this calculation does not cover

One operating point. A radial centrifugal pump's shaft power rises as its flow rises, and an axial pump's falls, so the most power a pump ever asks of its motor is found by reading the maker's curve across the whole range it will run over, not at the duty point alone.
No motor size is chosen. Matching a motor to a pump also weighs the curve's maximum power, the motor's service factor, starting duty and any drive, which belong to the pump maker's selection and the designer; the motor input here is an estimate of what the supply provides at this one point.
The head must already be the total dynamic head at this flow. Static lift alone leaves out the friction that grows with flow, and the page does not add pipe or fitting losses of its own.
Viscous fluids, slurries and hot liquids near boiling are outside it. Specific gravity scales the power for a fluid's weight, but viscosity lowers a centrifugal pump's head, flow and efficiency together, a correction the pump maker publishes, and a liquid close to its vapour pressure raises suction questions (net positive suction head) this arithmetic cannot see.
The 3,960 in the US formula stands for water a little lighter than the 1,000 kg per cubic metre (62.4 lb per cubic foot) the page uses, so a hand calculation with 3,960 comes out about 0.15% lower than the page.

Add the equipment this sizes

This result is a specification — 3.791 horsepower — not a quantity. Put the thing it sizes into your project: how many, what you call it, and your supplier’s price.

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Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.

Sources checked 2026-10-05 · v1.0.0

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Sizing a Water Feature's Pump

How to calculate pump power (horsepower and kW) in 6 steps

Flow RateThe flow the pump delivers at the operating point you are costing, not the largest flow on its label.
Total HeadThe total dynamic head at that flow: the lift from the water surface to the outlet, plus every friction and pressure loss on the way.
Specific Gravity of the Fluid (water = 1)How heavy the fluid is compared with water; 1 for clean cold water.
Pump Efficiency at This Point (%)The pump's hydraulic efficiency at this flow and head, read off its performance curve.
Motor Efficiency (%)The drive motor's efficiency at the load it runs at, from its nameplate or data sheet.
Brake power at the pump shaftThe tool computes the brake power at the pump shaft from those figures and shows the formula, its sources, and a confidence rating alongside it.

Brake power at the pump shaft by flow rate

Page defaults, not your figures above.

Flow Rate	Brake power at the pump shaft (horsepower)
100 gal/min	2.37
150 gal/min	3.56
200 gal/min	4.74
250 gal/min	5.93
300 gal/min	7.11

Frequently asked questions

What is the difference between water horsepower, brake horsepower and motor horsepower?: They are the same power seen at three places. Water horsepower is what actually goes into the fluid: its weight flow times the head. Brake horsepower is what the pump's shaft must be turned with, which is more, because the pump loses some to friction, leakage and turbulence; divide water power by the pump efficiency to get it. Motor input is what the electrical supply provides, more again, because the motor has losses of its own; divide brake power by the motor efficiency. A pump with 70% efficiency driven by a 90% motor draws about 1.6 times its water power from the supply.
Where does the 3,960 in the US formula come from, and why is this page slightly different?: One horsepower is 33,000 foot-pounds of work a minute, and a US gallon of water, 3.785 litres, weighs about 8.33 lb (3.78 kg), so 33,000 divided by 8.33 is about 3,960: a gallon a minute lifted one foot is 1/3,960 of a horsepower. That 8.33 lb gallon is water slightly lighter than 1,000 kg per cubic metre (62.4 lb per cubic foot), the density this page multiplies the specific gravity by. The two answers therefore differ by about 0.15%, which three significant figures usually hide; the DOE sourcebook's example of 15,000 gallons a minute (946 L/s) at 150 ft (45.72 m) comes to 568.2 water horsepower by its divisor and 569.0 here.
How do I turn a pressure gauge reading into head?: Divide the pressure by the fluid's weight per unit volume. For water that is about 2.31 ft of head for every psi, or about 0.102 m for every kPa; a fluid heavier than water gives less head for the same pressure, so divide by its specific gravity. The total head across a running pump is the discharge gauge's head minus the suction gauge's, allowing for any difference in their heights and pipe sizes.
Which efficiency should I enter if I only know the pump's best efficiency?: Use the efficiency at the flow and head the pump will actually run at, read from its curve. The best efficiency point is the top of the curve, and a pump running well to either side of it is less efficient, sometimes by a wide margin; entering the peak figure for an off-peak duty understates the power. Where the duty is not known yet, the honest answer is a range: work the page at the efficiency either side of the expected point.
Does a pump at zero head use no power?: The formula's water power is zero, because nothing is lifted, but the pump still turns and still draws power. A centrifugal pump running with its discharge shut moves no water yet churns it, and one running into no resistance at all moves a lot of water and usually draws its greatest power. Both points are on the maker's curve; this page only prices the work done on the fluid at a point you choose.

Preliminary estimate, not certified engineering. This tool produces an indicative quantity calculation for planning purposes only — it is not a certified structural analysis, a guaranteed material takeoff, or a substitute for building department approval. Always verify measurements on-site and have a licensed contractor or structural engineer review any load-bearing, code-sensitive, or safety-critical work before purchasing materials or starting construction. Spotted an arithmetic or standards error? Report it to contact@craftquantities.com with your inputs — a confirmed fix gets a permanent check of its own, so the same mistake cannot come back.