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Pump Efficiency from Hydraulic and Shaft Power

η=PhydPshaft\eta = \frac{P_{hyd}}{P_{shaft}}
sig figs

Worked example: 15 kW delivered from 20 kW at the shaft → eta = 0.75. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Where Pump Efficiency from Hydraulic and Shaft Power fits

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Pump Brake Horsepower
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See also

Pump Brake Horsepower: Both use pump efficiency and shaft power.Pump Water Horsepower: Both use hydraulic power.Hydraulic Power (P = ρgQh): Both use hydraulic power.Fan Affinity Law: Power vs Speed: Both use shaft power.Fan Brake Horsepower: Both use shaft power.Pump Affinity Law: Power vs Speed: Both use shaft power.
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Pump Efficiency from Hydraulic and Shaft Power explained

PshaftPhydη

Everything a pump fails to put into the water it puts into heat, noise and vibration. A unit delivering 15 kW of hydraulic power while absorbing 20 kW at the shaft is 75% efficient, and the missing 5 kW is warming the casing and the liquid. Large water-supply pumps reach 85–90%; small close-coupled circulators struggle to pass 40%; and any positive-displacement chemical metering pump is efficient in a different sense entirely.

The trap is comparing efficiencies measured at different boundaries. Pump efficiency is hydraulic over shaft; wire-to-water efficiency multiplies that by the motor and drive efficiencies and is the number that matters on the electricity bill. A 75% pump on a 92% motor behind a 97% VFD is 67% wire-to-water, so if you are calculating operating cost from a "75% efficient" pump, you will underestimate the annual energy by about 12%.

Pump Efficiency from Hydraulic and Shaft Power formula

η=PhydPshaft\eta = \frac{P_{hyd}}{P_{shaft}}
Where
  • η\eta= Pump efficiency
  • PhydP_{hyd}= Hydraulic power (W)
  • PshaftP_{shaft}= Shaft power (W)
In this toolkit

Pump power and efficiency

7 formulasWater horsepower, brake horsepower, pump efficiency, NPSH available and specific speed — sizing the motor and keeping the impeller wet.

Revised 30 October 2026
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formula.expert. (2026, October 30). Pump Efficiency from Hydraulic and Shaft Power Calculator. https://formula.expert/solvers/pump-efficiency-power

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