Enter the volumetric flow, density, pump head, and efficiency into the calculator to determine the pump shaft power.

Pump Shaft Power Calculator

Enter any 4 values to calculate the missing variable

Pump Shaft Power Formula

Pump shaft power is the mechanical power that must be supplied at the pump shaft so the pump can deliver a required flow rate against a given head. In practical terms, hydraulic power is the useful power transferred to the fluid, while shaft power is the larger input required after internal pump losses are considered.

P_s = \frac{P_h}{\eta}

The hydraulic power of the fluid is:

P_h = \rho g Q H

When flow is entered in cubic meters per hour, the calculator-friendly form is:

P_s = \frac{q \rho g h}{3.6 \times 10^6 \eta}
  • Ps = pump shaft power
  • Ph = hydraulic power
  • q = flow rate in m3/hr
  • Q = flow rate in m3/s
  • ρ = fluid density
  • g = gravitational acceleration
  • h or H = pump head
  • η = pump efficiency as a decimal

How this calculator is used

This calculator links five variables: flow, density, pump head, efficiency, and shaft power. If four are known, the remaining value can be determined. That makes it useful for pump sizing, motor selection, system checks, and troubleshooting when operating conditions change.

Rearranged forms

If you are solving manually, these equivalent forms are often useful:

\eta = \frac{P_h}{P_s}
h = \frac{3.6 \times 10^6 P_s \eta}{q \rho g}
q = \frac{3.6 \times 10^6 P_s \eta}{\rho g h}
\rho = \frac{3.6 \times 10^6 P_s \eta}{q g h}

How to calculate pump shaft power

  1. Determine the required flow rate.
  2. Use the correct fluid density for the liquid being pumped.
  3. Determine the total pump head, not just the vertical lift.
  4. Enter the pump efficiency. If calculating by hand, convert a percent to a decimal first.
  5. Compute hydraulic power, then divide by efficiency to obtain shaft power.

Example

Suppose a pump moves a fluid at 400 m3/hr with a density of 1,225 kg/m3, develops 3 m of head, and operates at 70% efficiency.

P_h = \frac{400 \times 1225 \times 9.81 \times 3}{3.6 \times 10^6}
P_h \approx 4.01 \text{ kW}
P_s = \frac{4.01}{0.70} \approx 5.72 \text{ kW}

The required shaft power is approximately 5.72 kW.

What affects pump shaft power?

  • Flow rate: Higher flow increases shaft power in direct proportion.
  • Density: Heavier fluids require more power than lighter fluids at the same flow and head.
  • Head: More developed head means more energy must be added to the fluid.
  • Efficiency: Lower efficiency increases required shaft power because more input is lost internally.

Pump shaft power vs. hydraulic power

Hydraulic power is the useful energy delivered to the fluid. Shaft power is the mechanical input required at the pump shaft. Because no real pump is perfectly efficient, shaft power is greater than hydraulic power except in the idealized case of 100% efficiency.

Important application notes

  • Use total dynamic head when possible, since friction losses and elevation changes both affect the required power.
  • For water at ordinary conditions, density is often approximated near 1000 kg/m3, but the actual fluid value should be used for better accuracy.
  • Shaft power is the demand at the pump shaft, not necessarily the electrical power drawn from the supply.
  • If you are sizing a motor, also consider motor efficiency, drive losses, startup conditions, and a reasonable service margin.
  • For highly viscous or non-standard fluids, real-world pump performance may deviate from simple theoretical estimates.

Common input and unit considerations

  • Flow: m3/hr, L/s, or ft3/min
  • Density: kg/m3 or lb/ft3
  • Head: m or ft
  • Power output: kW or horsepower

Frequent mistakes to avoid

  • Using efficiency as 70 instead of 0.70 in hand calculations.
  • Using static lift only and ignoring friction losses in the piping system.
  • Mixing unit systems without converting flow, head, density, or power consistently.
  • Confusing shaft power with motor input power or with hydraulic power.
  • Using an estimated density that does not match the actual process fluid.

Why shaft power matters

Knowing shaft power helps verify whether a pump can meet process requirements, whether an installed motor is adequate, and how changes in fluid properties or head conditions will affect operation. It is one of the most important calculations for pump selection, energy planning, and equipment protection.