Pump Power Formula
How to calculate hydraulic power, shaft power and motor size for any pump.
The Formula
Hydraulic Power (kW) = ρ × g × Q × H ÷ 1000
where:
ρ = fluid density (kg/m³) — water = 1000
g = 9.81 m/s²
Q = flow rate (m³/s)
H = total head (metres)
Shaft Power (kW) = Hydraulic Power ÷ Pump Efficiency
Motor Size (kW) = Shaft Power × 1.15 (service factor)
Example
500 LPM flow, 30 m head, 75% pump efficiency, water (ρ=1000):
Q = 500 ÷ 60,000 = 0.00833 m³/s
Hydraulic Power = 1000 × 9.81 × 0.00833 × 30 ÷ 1000 = 2.45 kW
Shaft Power = 2.45 ÷ 0.75 = 3.27 kW
Motor Size = 3.27 × 1.15 = 3.76 kW → Select 3.7 kW (5 HP) motor
What is Total Head?
Total Head = Static Head + Friction Head + Velocity Head + Pressure Head
Static Head = elevation from pump inlet to discharge point
Friction Head = losses in pipes, valves, elbows
Pressure Head = any back pressure at discharge