A pump horsepower calculator is really three calculators, because a pump has three power figures and they are all different numbers. The water horsepower is the useful hydraulic power actually imparted to the fluid. The shaft or brake horsepower is what the pump absorbs at its coupling, which is larger because no pump is perfectly efficient. The motor input power is larger still, because no motor is perfectly efficient either. This page reports all three and takes every figure from you.
Arb Digital builds free engineering calculators that publish no equipment data and make no product recommendation. There are no pump curves here, no efficiency tables and no suggestion about what to buy. The efficiency you enter has to come from the manufacturer's curve at your specific duty point, and the duty point itself is set by where your system curve crosses that pump curve — a question only the pump manufacturer's data can answer.
What This Pump Horsepower Calculator Does
It converts a flow rate and a total dynamic head into hydraulic power, then divides by the efficiencies you supply to work backwards through the drive train. Flow can be entered in US gallons per minute, cubic metres per hour or litres per second, and head in feet or metres of fluid. Specific gravity scales the whole result, because power is proportional to the weight of fluid lifted rather than its volume.
The headline figure is shaft horsepower, and that choice is deliberate. Water horsepower is what the pump delivers and is useful for judging how much of your energy is doing work. Motor input is what you pay for. But shaft power is what the pump actually demands from whatever turns it, and it is the number against which a motor or engine is normally matched.
What the page cannot do is tell you where on the curve you will operate. Head and flow are not independent for a real pump: they are linked by its characteristic, and the machine settles where that curve meets your system resistance. Enter a flow and head pair that the pump cannot actually produce together and the arithmetic still works while describing nothing real.
How to Use It
- Enter your required flow. This is a process requirement you bring to the problem, not something the calculator can infer.
- Enter total dynamic head, not static lift. Add friction losses through pipe, fittings and valves at the design flow, plus any pressure the discharge has to overcome.
- Set the specific gravity of the actual fluid. Brine, slurry and glycol mixtures are heavier than water and demand proportionally more power for the same head.
- Take the pump efficiency from the curve at your duty point. It falls away sharply either side of the best efficiency point, so a single catalogue peak figure is usually optimistic.
- Add motor efficiency for the electrical figure. Set it to 100 per cent if you only want shaft power.
The Formula: How Pump Horsepower Is Calculated
In US customary units, water horsepower is WHP = Q × H × SG ÷ 3,960, with Q in US gallons per minute, H in feet of fluid and SG the specific gravity. The constant 3,960 comes from 33,000 foot-pounds per minute per horsepower divided by the weight of a US gallon of water in pounds. In SI the same statement is P = ρgQH with Q in cubic metres per second and H in metres, giving watts directly.
The physics underneath is energy conservation in a flowing fluid. OpenStax University Physics, Volume 1, section 14.6 on Bernoulli's equation sets out the relation between pressure, elevation and velocity along a streamline that head is a restatement of: a pump adds energy per unit weight of fluid, and multiplying that by the weight flowing per second gives power.
Shaft horsepower is BHP = WHP ÷ ηpump, and motor input power is BHP ÷ ηmotor. Conversion between horsepower and kilowatts uses 1 hp = 745.699872 W, one of the conversion factors tabulated in NIST Special Publication 811, the NIST Guide to the SI.
Work the defaults by hand. At 500 gpm, 100 feet of head and SG 1.0, water horsepower is 500 × 100 × 1.0 ÷ 3,960 = 12.626 hp. At 75 per cent pump efficiency, shaft power is 12.626 ÷ 0.75 = 16.835 hp, which is 16.835 × 0.7457 = 12.554 kW. At 92 per cent motor efficiency the motor draws 16.835 ÷ 0.92 = 18.299 hp, or 13.646 kW. Note how 12.6 hp of useful work has become 18.3 hp of purchased power: the two efficiencies compound.
Three Powers, Three Different Questions
Water horsepower answers "how much work is being done on the fluid". It is the product of the weight flow and the head, and it is the only one of the three that is pure physics with no machine in it.
Shaft horsepower answers "how hard is the pump working the driver". The gap between it and water horsepower is everything the pump loses internally: hydraulic losses through the impeller and volute, disc friction on the impeller shrouds, recirculation, and leakage back through wear rings. That gap is not constant. It is smallest at the best efficiency point and widens quickly on either side, so a pump run well off its design flow can absorb far more shaft power per unit of useful output than the catalogue peak suggests.
Motor input answers "what does this cost to run". Motor efficiency is comparatively flat over the upper half of its load range but falls away at light load, and a variable-frequency drive adds its own losses on top. If you are estimating running cost, this is the figure that goes into the calculation, and the power converter handles the unit arithmetic.
Why the Duty Point, Not the Formula, Governs
The calculation above treats flow and head as independent inputs. A real pump does not. Its characteristic curve fixes a relationship between the two, and it will operate at the single point where that curve intersects the resistance curve of your piping. Move the throttle valve, foul the pipe, or change the static lift and the duty point moves along the curve, taking flow, head and efficiency with it.
That is why the efficiency box on this page is a user input rather than a stored value. Efficiency is a property of the operating point, not of the pump. Reading the peak figure off a catalogue and applying it at a duty well away from that peak understates shaft power, sometimes substantially.
It is also why nothing on this page should be treated as a selection. The manufacturer's published curve, the affinity laws for any speed change, and the manufacturer's own application limits govern what a specific machine will do. Suction conditions are a separate constraint entirely: the NPSH calculator covers the available net positive suction head, which must exceed the pump's required NPSH from its curve or the machine cavitates regardless of how much power you give it.
Specific Gravity, Viscosity and the Limits of This Model
Specific gravity scales power linearly, and this page handles that. Pumping a fluid at SG 1.2 to the same head at the same flow needs 20 per cent more power, because head expressed in feet of fluid is a length and the weight behind it has gone up.
Viscosity is a different matter, and this calculator does not model it. A viscous fluid degrades a centrifugal pump's head, flow and efficiency simultaneously, and the standard approach is to apply published viscosity correction factors to the water-based curve before doing any power arithmetic. If your fluid is appreciably more viscous than water, the numbers here need that correction first.
Solids in suspension, entrained gas, and non-Newtonian behaviour all fall outside this model too. So does positive-displacement pumping, where flow is nearly independent of head and the power relationship works differently. For the incompressible-hydraulics side of a fluid power system, the hydraulic cylinder force calculator converts pressure and geometry into actuator force and flow into rod speed, which is the actuator counterpart to what this page does for a pump.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using static lift instead of total dynamic head — friction losses at the design flow are often a large fraction of the total, and leaving them out understates every power figure.
- Applying the peak catalogue efficiency at an off-design duty — efficiency is a property of the operating point and falls away on both sides of it.
- Quoting water horsepower as the motor size — the motor has to supply shaft power, which is larger, and then draws more still from the supply.
- Ignoring specific gravity — head in feet of fluid is a length, so a denser fluid needs proportionally more power for the same head and flow.
- Treating a viscous fluid like water — viscosity degrades head, flow and efficiency together, and needs published correction factors applied to the curve first.
Related Free Tools From Arb Digital
Check suction conditions with the NPSH calculator before worrying about power at all. Get the flow figure from the flow rate calculator and the friction component of head from the pipe flow calculator, with the static component from the hydrostatic pressure calculator. Convert between head and pressure units with the pressure converter, and between power units with the power converter or the horsepower calculator. For fluid power actuators rather than pumps, use the hydraulic cylinder force calculator. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
Water horsepower is the useful hydraulic power delivered to the fluid. Brake or shaft horsepower is what the pump absorbs at its coupling, and it is larger by the pump's inefficiency. Dividing water horsepower by pump efficiency gives shaft horsepower.
Shaft horsepower, the mechanical power the pump absorbs at the coupling. Water horsepower and motor input power in both horsepower and kilowatts are shown alongside it, because all three are different numbers and each answers a different question.
From the manufacturer's performance curve, read at your actual duty point. Efficiency varies across the curve and peaks at the best efficiency point, so a single catalogue headline figure is usually optimistic for a duty away from that point.
Because head expressed in feet or metres of fluid is a length, and power depends on the weight of fluid raised through that height. A fluid 20 per cent denser than water needs 20 per cent more power for the same head and flow.
No. It tells you the power a duty requires given the efficiencies you supply. Which machine meets that duty is decided by the manufacturer's curve, where your system curve crosses it, and the suction conditions at site. That work belongs to the manufacturer and a qualified engineer.
Not directly. Viscosity reduces a centrifugal pump's head, flow and efficiency at the same time, and published viscosity correction factors have to be applied to the water-based curve before any power calculation. Specific gravity alone does not capture it.
It is the total energy per unit weight the pump has to add: static lift, plus friction losses through pipe, fittings and valves at the design flow, plus any pressure difference the discharge works against. It is usually considerably larger than the vertical distance alone.
This tool is provided for educational and study use. It evaluates published power relations from figures you supply and contains no pump data, no efficiency tables and no product recommendation. The pump curve and the manufacturer's data govern the real duty point, suction requirement and application limits. Pump and motor selection and installation should be carried out by a qualified engineer.
