Centrifugal Pump Power Calculator
Calculate centrifugal pump hydraulic power, shaft power, and motor size from flow rate and head.
Includes specific speed, affinity laws, and unit conversion.
Hydraulic Power The power delivered to the fluid by the pump: P_hydraulic = ρ × g × Q × H Where: ρ = fluid density (kg/m³), water = 1000 kg/m³ g = gravitational acceleration (9.81 m/s²) Q = volumetric flow rate (m³/s) H = total head (m), the sum of static head, friction head, and velocity head
Shaft Power and Efficiency P_shaft = P_hydraulic / η_pump Where η_pump = pump efficiency (typically 0.60–0.85 for centrifugal pumps). Motor P_input = P_shaft / η_motor Overall efficiency η_total = η_pump × η_motor × η_transmission
Total Head Components Static head: elevation difference between source and discharge (m). Friction head: losses in pipes, fittings, valves (use Darcy-Weisbach). Velocity head: (v₂² − v₁²) / (2g), usually small enough to ignore. Pressure head: (P₂ − P₁) / (ρg), for pressurized systems.
Specific Speed (Ns) Ns = N × √Q / H^(3/4) Where N = rotational speed (rpm), Q in m³/s, H in meters. Specific speed is a shape number, not a size: it tells you what kind of impeller suits the duty, and two pumps with the same Ns have geometrically similar impellers no matter how big they are.
| Ns (metric, nq) | Impeller type |
|---|---|
| below 30 | Radial flow. High head, low flow, narrow impeller. |
| 30 to 80 | Francis type, starting to widen. |
| 80 to 160 | Semi-axial / mixed flow. |
| above 160 | Axial (propeller). Low head, high flow. |
Watch the units here, because there are two conventions in circulation and they differ by a factor of about 51.6. The metric nq above uses Q in m³/s and H in metres. American pump curves usually print Ns with Q in US gallons per minute and H in feet, which turns an nq of 30 into an Ns of roughly 1550. If your catalogue number looks about fifty times bigger than the one here, that is why. The calculator reports both.
NPSH (Net Positive Suction Head) NPSH_available = (P_atm − P_vapor) / ρg + z_s − h_f,s Where z_s = suction lift (negative if below pump), h_f,s = suction friction losses. NPSH_available > NPSH_required by at least 0.5–1.0 m to prevent cavitation. Cavitation: vapor bubbles form and collapse — causes noise, vibration, impeller damage.
Affinity Laws When pump speed changes from N₁ to N₂: Q₂/Q₁ = N₂/N₁ | H₂/H₁ = (N₂/N₁)² | P₂/P₁ = (N₂/N₁)³ This is why VFD (variable frequency drive) speed control saves enormous power.
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