Pump power calculator

This free pump power calculator finds the hydraulic power a pump duty adds to the fluid, the shaft power the pump draws (also called brake power, bkW or absorbed power), and the electrical power the motor takes. Results read in kW or hp with a metric or imperial toggle, and a fluid preset or a custom density sets the fluid. Useful for early sizing and for sanity-checking a pump selection against its duty point.

Method

The hydraulic (useful) power added to the fluid is

P_hyd = rho g Q H

where rho is density (kg/m^3), g is the standard gravity 9.80665 m/s^2, Q is volumetric flow (m^3/s) and H is the pump head (m of the fluid pumped). Dividing by efficiencies steps out to the shaft and then the electrical input:

P_shaft = P_hyd / eta_pump
P_elec  = P_shaft / eta_motor

Head is expressed in metres of the pumped fluid. If you have a pressure rise instead, convert with H = dp / (rho g). This is standard pump fundamentals rather than anything of ours, and the sources are listed in the references at the foot of this page.

Limits. This is a duty-point power calculation. It does not select a pump, find the operating point against a system curve, or account for viscosity corrections on the pump curve. The Studio plots pump duty, the best efficiency point and the system curve for that.

Inputs

• Fluid preset (density) or a custom density (kg/m^3).
• Flow Q (L/s, or gpm on the imperial toggle).
• Head H (m of fluid).
• Pump efficiency eta_pump (per cent).
• Optional motor efficiency eta_motor (per cent), to add the electrical power.

Outputs

• Hydraulic power.
• Shaft power.
• Electrical power, if a motor efficiency is given.

Worked example

Water (density 998.2 kg/m^3) at 20 L/s against 30 m of head, with a pump efficiency of 70 per cent and a motor efficiency of 90 per cent:

P_hyd   = 998.2 x 9.80665 x 0.020 x 30 = 5.87 kW
P_shaft = 5.87 / 0.70 = 8.39 kW
P_elec  = 8.39 / 0.90 = 9.32 kW

Typical pump efficiencies

Efficiency depends strongly on size and specific speed, so read the real value off the manufacturer's curve at your duty point and enter that. As a starting estimate:

Indicative ranges compiled from standard pump handbook guidance (for example the Grundfos and KSB pump handbooks and Hydraulic Institute material).

Typical motor efficiencies

Rounded from the IE3 (premium efficiency) minimums in IEC 60034-30-1 for 4-pole, 50 Hz motors. Older IE1 or IE2 motors sit a few points lower, and part-load efficiency falls off below about half load, so use the nameplate or datasheet figure where you have one. The standard has been revised since the values here were tabulated, so check the current edition if you are working to it.

Quick reference: pump shaft power for water

Shaft power for water at 20 degrees C (998.2 kg/m^3) at a pump efficiency of 70 per cent, computed with the calculator's own formula (g = 9.80665 m/s^2). Power scales linearly with flow and head, so interpolate freely, or rerun the calculator with your own efficiency.

Frequently asked questions

What is the difference between hydraulic, shaft and electrical power?

Hydraulic power is rho g Q H, the useful power added to the fluid. Shaft power (also called brake power, bkW or absorbed power) is hydraulic power divided by the pump efficiency, and electrical power divides again by the motor efficiency. The calculator reports all three when a motor efficiency is entered.

What is the pump power formula in kW?

P(kW) = rho g Q H / (1000 eta) with Q in m3/s and H in metres. For water this reduces to the quick rule P(kW) is approximately Q(L/s) x H(m) / (102 x eta), which is the same expression the calculator evaluates.

Is the pump head in metres or pressure?

Metres of the pumped fluid. Convert a pressure rise with H = dp / (rho g), and for water 10 m of head is about 98 kPa.

Where do I get the pump efficiency?

From the manufacturer's curve at your duty point, ideally near the best efficiency point. The typical pump efficiency table on this page is a starting estimate only, and the Studio plots the duty point against the curve.

Can I get the result in horsepower?

Yes. Switch the unit toggle to Imperial (US) and power reads in hp, flow in gpm and head in ft, with the values you have already entered converted in place.

Does it work for fluids other than water?

Yes. Pick a preset (water and seawater, glycols and brines, fuels and oils, chemicals, and ammonia) or choose Custom and enter a density. Density is all the power formula needs, but note a viscous fluid also lowers the pump's own efficiency, which comes from the corrected pump curve, not this calculator.

References

• IEC 60034-30-1, Rotating electrical machines - Part 30-1: Efficiency classes of line operated AC motors (IE code), International Electrotechnical Commission, for the motor efficiency table. webstore.iec.ch
• White, F. M., Fluid Mechanics, McGraw-Hill, for the hydraulic-power derivation.
• Grundfos and KSB pump handbooks, and Hydraulic Institute material, for the indicative pump efficiency ranges. These are vendor and association publications rather than a single standard, which is why the table is given as a range.

Related

• Pipe flow and pressure drop calculator to find the friction head the pump must overcome.
• Hazen-Williams calculator for water-main head loss as the head input.
• Pump and system curve worked example for the duty point against a real system curve.
• Pump system design guide for the wider workflow.
• Sizing a pump against a real system? Open the Studio to solve the pump against the network and read its true duty point.