Pump Power and Sizing Calculator

Hydraulic, shaft and electrical power of a pump from flow and head, the standard motor size, the yearly energy cost and the NPSH available.

How it works

A pump adds energy to a liquid: the useful (hydraulic) power is the weight of liquid lifted per second times the head. The motor must supply more than this because the pump and the motor are not perfectly efficient.

Phyd = ρ g Q H, Pshaft = Phyd ÷ ηpump, Pinput = Pshaft ÷ ηmotor

The total head is the height the liquid is lifted plus the pressure to be delivered plus the pipe and fitting losses (see the Pipe Flow and Pressure Drop Calculator). NPSH available is the pressure margin at the pump inlet above the liquid’s vapor pressure: NPSHa = (Pa − Pv) ÷ (ρ g) + hs − hf. The pump will cavitate unless it is greater than the pump’s NPSH required.

Worked example

Water at 20 °C is pumped at 20 L/s against a total head of 30 m. The pump is 70 % efficient, the motor 92 %, with a 10 % margin; it runs 6 000 hours a year at 0.12 per kWh. The pump takes water from a tank 2 m above it with 0.5 m of suction losses.

  • Phyd = 998.2 × 9.80665 × 0.020 × 30 = 5 873 W (5.87 kW).
  • Pshaft = 5 873 ÷ 0.70 = 8 391 W. Pinput = 8 391 ÷ 0.92 = 9 120 W.
  • Motor: 8 391 × 1.10 = 9 230 W, so the next standard size is 11.0 kW.
  • Energy: 9.12 kW × 6 000 h = 54 721 kWh a year, costing 6 567.
  • NPSHa = (101 325 − 2 339) ÷ (998.2 × 9.80665) + 2 − 0.5 = 11.61 m.

Things to know

The efficiency of a real pump depends on where it works on its curve: it is highest at the best efficiency point. A pump run far from it is both less efficient and more likely to wear and cavitate.

Pump curves, not formulae, decide the final choice: check that the duty point (flow and head) lies on the pump curve near its best efficiency point, and that the motor is not overloaded at the end of the curve.

For fluids denser or thicker than water the power rises with the density, and a viscous liquid also lowers the pump efficiency and head: ask the maker for corrected curves.

A variable-speed drive saves energy when the flow varies: power falls roughly with the cube of speed (the affinity laws).

Use the vapor pressure of the liquid at its working temperature: hot liquids lose NPSH quickly, and liquids near their boiling point need a large positive suction head.

The motor sizes are IEC kilowatt ratings; US motors are sold in horsepower steps (1, 1.5, 2, 3, 5, 7.5, 10, 15, 20, 25, 30, 40, 50 hp).

Common questions

How do I calculate the head for a pump?

Add the static lift (the height difference between the liquid levels), the pressure difference converted to head (Δp ÷ ρ g) and the pipe friction and fitting losses at the design flow.

What is NPSH?

Net positive suction head: the energy at the pump inlet above the point where the liquid would boil. The pump needs NPSH available to exceed its NPSH required, or vapor bubbles form and collapse (cavitation), damaging the pump.

Why is the motor larger than the shaft power?

To allow for the margin: the real duty point can lie beyond the design point, the motor must start the pump, and a motor runs most efficiently at 60 to 100 percent load.

What is a typical pump efficiency?

Small centrifugal pumps 40 to 60 percent, medium 60 to 80 percent, large over 85 percent, at the best efficiency point.

Sources

  • Hydraulic Institute, ANSI/HI 9.6.1, Rotodynamic Pumps: Guideline for NPSH Margin; ISO 9906 (pump performance tests).
  • Karassik, I. J. et al., Pump Handbook, McGraw-Hill; IEC 60034-30-1 (motor efficiency classes).

Last reviewed: November 2, 2026