Centrifugal Pump
Power Calculator

One operating point, one SI calculation

P_h = ρgQH   ·   η_p = E_p / 100   ·   P_s = P_h / η_p

Hydraulic power P_h and shaft power P_s are calculated in watts with density ρ in kg/m³, flow Q in m³/s, head H in meters, and standard gravity g = 9.80665 m/s². Divide watts by 1,000 for kW or by 745.69987158227022 for mechanical hp. HHP is hydraulic power in hp; BHP is pump shaft input power in hp.

Conversions use 0.3048 m/ft and 0.003785411784 m³/U.S. gallon. U.S. flow is converted from gallons per minute to m³/s; SI flow from m³/h to m³/s. SG = ρ / 1000 uses a fixed reference density of 1,000 kg/m³, not a temperature-dependent water-property model. Convert an SG on another reference basis, or enter actual operating density in SI mode.

The familiar Q × H × SG / 3960 approximation is not used for calculation. These constants imply a denominator of approximately 3954.27210146, giving about 0.145% higher results for identical U.S. inputs.

Supply total pump head and overall pump efficiency

Total head is the increase across the pump, not simply discharge pressure or elevation lift. For an incompressible liquid, with kinetic-energy correction factors approximated as unity:

H = (p_d − p_s)/(ρg) + (v_d² − v_s²)/(2g) + (z_d − z_s)

Here p is static pressure on a common reference, v is mean velocity, and z is elevation above a common datum; s and d identify suction and discharge. This equation explains the head input; this calculator does not derive head from those measurements. An independently calculated system head includes applicable boundary pressure, elevation, velocity, and system-loss contributions. Do not add system losses again to an already established pump total head.

Use overall pump efficiency for the same flow, head, speed, impeller, and fluid, preferably from applicable manufacturer data. Do not use motor efficiency, wire-to-water efficiency, or internal hydraulic efficiency alone. An assumed efficiency produces an estimate; this model cannot establish whether a particular pump can achieve the duty point.

Model limits

• Steady, single-phase, approximately incompressible liquid at positive flow and positive head. All inputs describe the same operating condition, with density at operating temperature and pressure.
• No automatic fluid properties or viscosity, slurry, entrained-gas, cavitation, or wear corrections. Corrected data require separate engineering work.
• No pump curves, affinity laws, speed prediction, pipe-network analysis, NPSH, allowable operating range, or transient/startup analysis.
• No motor sizing, service factor, drive/transmission loss, electrical input, energy cost, or standard motor rating selection.
• At shutoff, useful hydraulic output is zero but a running centrifugal pump can absorb shaft power. Zero-flow/zero-head shaft power requires other data.

Numerical range failures describe software support limits, not physical pump limits. Efficiency warnings are advisory: below 10%, above 95% but below 100%, and the ideal 100% limiting case.

Engineering references

1. KSB — Head
2. Hydraulic Institute — Why Pump Power is Higher than Expected
3. NIST SP 811 — Conversion factors
4. KSB — Characteristic curves