Formula
Shaft power (kW) = Hydraulic power / ηpump
Motor power (kW) = Shaft power / ηmotor
Where ρ is fluid density (kg/m³), g is 9.81 m/s², Q is flow rate (m³/s), H is total head (m), and ηpump / ηmotor are the pump and motor efficiencies as fractions.
Quick version for flow in m³/h: Hydraulic power (kW) = Q (m³/h) × H (m) × SG / 367.
How to Use
Enter the flow rate, total developed head, fluid density, and the pump and motor efficiencies from the datasheet or field test. The calculator returns hydraulic, shaft, and motor power together so you can size a motor with adequate margin.
Worked Example
Water (1,000 kg/m³) at 50 m³/hr against 30 m total head, pump efficiency 65%, motor efficiency 92%:
Shaft power = 4.09 / 0.65 ≈ 6.29 kW
Motor power = 6.29 / 0.92 ≈ 6.84 kW → 7.5 kW motor
If the receiving vessel is under pressure, add it to the head first: head (m) = ΔP (Pa) / (ρ × 9.81). The full article has a second example with a pressurised receiver.
Engineering Notes & Assumptions
This is a steady-state power estimate. It doesn't account for startup transients, NPSH-limited operation, or a pump running away from its best-efficiency point. Always cross-check against the pump curve and motor nameplate rating, and apply your site's standard safety margin (commonly 10–20%) on top of the calculated motor power.
Frequently Asked Questions
How do you calculate pump power?
Hydraulic power (kW) = ρ × 9.81 × Q (m³/s) × H (m) / 1,000. Shaft power = hydraulic power / pump efficiency. Motor power = shaft power / motor efficiency.
What motor size do I need for my pump?
Work out the motor input power, then pick the next standard motor rating above it. In the example above, 6.84 kW becomes a 7.5 kW motor.