Pump Power Calculator

Calculate hydraulic and shaft power required by a pump to deliver a specified flow rate and head.

Fluid Mechanics II

Common fluids — click to auto-fill density

Inputs

Flow rate Q (L/s)

Total head H (m)

Fluid density ρ (kg/m³)

Pump efficiency η (%)

Centrifugal: 60–92 % · Axial: 80–90 % · PD: 70–90 %. Enter 100 for ideal.

Theory

Hydraulic (water) power — ideal, no losses:

P_h = ρ × g × Q × H [W]

Shaft power — accounting for pump efficiency:

P = P_h / η = (ρ × g × Q × H) / η [W]

Full efficiency chain:

P_motor = P_h / (η_pump × η_motor)

This calculator covers pump shaft power only. Multiply by a motor efficiency η_motor (typically 0.90–0.97) for total electrical input.

Where:

P_h = hydraulic power [W] — energy transferred to the fluid
P = shaft (brake) power [W] — power input to the pump shaft
ρ = fluid density [kg/m³]
g = gravitational acceleration = 9.81 m/s²
Q = volumetric flow rate [m³/s]
H = total pump head [m] — includes pressure, velocity, and elevation terms
η = pump efficiency (0–1) — ratio of hydraulic to shaft power

Typical pump efficiencies:

Pump type	η range
Large centrifugal pump	80–92 %
Small centrifugal pump	60–80 %
Axial-flow pump	80–90 %
Positive displacement	70–90 %
Gear / vane pump	60–80 %

Pump power scales linearly with flow rate, head, and density. Doubling the flow rate doubles the power; doubling the head also doubles the power — but in centrifugal pumps operating on a system curve both Q and H change together (affinity laws apply).