Pump hydraulic power calculator
Work out the hydraulic power a pump must deliver from flow, head and efficiency — the first figure for sizing the motor and VFD.
Pump hydraulic power
Formula: P_h (W) = ρ × g × Q × H with g = 9.81, flow in m³/s and head in m. Shaft power: P_shaft = P_h / η_pump, motor input: P_motor = P_shaft / η_drive. The recommended size picks the smallest standard motor rating at least 1.15× the input power (service factor). Water is 1000 kg/m³; use ~998 kg/m³ for cold water and ~1200–1250 kg/m³ for typical slurries.
About — affinity laws
For a centrifugal pump driven by a variable-speed motor, flow scales linearly with speed and head scales with the square of speed, while the power absorbed scales with the cube of speed. Halving the speed of a constant-speed motor cuts its power draw to roughly one eighth — which is why a VFD saves real energy at part load instead of throttling a valve against a full-speed impeller.
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Frequently asked questions
How do I calculate the hydraulic power of a pump?
Hydraulic power is P_h (W) = ρ × g × Q × H, with g = 9.81, flow in m³/s and head in m, divided by 1000 for kW. With the defaults — 20 m³/h, 30 m head, water at 1000 kg/m³ — that is 1000 × 9.81 × (20/3600) × 30 / 1000 ≈ 1.64 kW. Flow in L/min or GPM and head in feet are converted to m³/s and metres automatically.
What is the difference between hydraulic power, shaft power and motor power?
Hydraulic power is the useful energy transferred to the fluid; shaft power divides it by pump efficiency (P_shaft = P_h / η_pump); and motor input power divides again by drive or VFD efficiency (P_motor = P_shaft / η_drive). With the default 70% pump efficiency and 95% drive efficiency, the 1.64 kW hydraulic figure becomes about 2.34 kW at the shaft and about 2.46 kW at the motor input.
How do I choose the motor size for a pump?
The recommended size is the smallest standard motor rating at least 1.15× the required input power (service factor). Starting from the defaults, about 2.46 kW × 1.15 ≈ 2.83 kW, which rounds up to the next standard frame at 3.7 kW. Water is 1000 kg/m³; use about 998 kg/m³ for cold water and roughly 1200–1250 kg/m³ for typical slurries.
AO Ctrl provides this tool for reference only.