Inputs
Liquid-water properties reference ↗ · Pure water, 0–99°C at 100 kPa absolute.
Results
Equations
Pshaft = Pₕ / η
Hydraulic power is the rate of energy added to the liquid. Required shaft power is higher by the inverse of pump efficiency. This calculator does not include motor or drive efficiency unless you include those losses in the efficiency value yourself.
What pump power means
Hydraulic power is the rate at which useful mechanical energy is transferred to the liquid. It can be calculated from flow and differential head, Pₕ = ρgQH, or from flow and pressure rise, Pₕ = QΔP. The required pump shaft power is higher because real pumps are not 100% efficient.
This calculator reports shaft power using the pump efficiency you enter. It does not automatically include motor, variable-frequency-drive, gearbox, or coupling losses. If you need electrical input power, apply the appropriate motor and drive efficiencies after the pump shaft-power calculation.
When to use it
- Estimating pump shaft power from a known duty point.
- Converting between pressure rise and head for a liquid of known density.
- Screening motor size before reviewing the pump and motor curves.
- Comparing the energy effect of alternative flows, heads, or efficiencies.
Assumptions
- The entered flow, head or pressure rise, density, and efficiency describe the same operating point.
- The liquid is treated as incompressible over the pump.
- The efficiency entered is pump hydraulic efficiency if the desired output is pump shaft power.
- The calculation is steady-state and does not include startup torque or transient loads.
Common mistakes
- Using only pipe friction as the required pump head. Total system head can also include elevation change, vessel pressure difference, equipment losses, and required terminal pressure.
- Using motor efficiency as pump efficiency. Pump efficiency converts hydraulic power to shaft power. Motor efficiency converts electrical input power to shaft power.
- Assuming one efficiency at every flow. Centrifugal-pump efficiency varies across the pump curve and is normally best near its best efficiency point.
- Confusing pressure with head. Head is energy per unit weight and is independent of liquid density for a given pump operating point, while the equivalent pressure rise changes with density.
- Sizing the motor exactly at calculated shaft power. Final motor selection should follow the pump curve, service factor, operating range, startup conditions, and applicable design standards.
Building the pump duty
A useful workflow is to calculate frictional line loss with the Pipe Friction Loss Calculator, add static elevation and pressure-boundary requirements, then evaluate the resulting pump duty here. Separately check suction conditions with the NPSH Available Calculator.
Reference background: the U.S. Department of Energy pump-system resources cover pump selection, system requirements, efficiency, and energy use. DOE Pump Systems.
Equation values and input guide
Enter operating flow, density, pump efficiency and either total differential head or pressure rise. Use a pump efficiency from a curve at the intended duty point. Read shaft power as the mechanical input required at the pump.
- Q
- Operating liquid volume flow, converted to m³/s.
- ρ, g
- Liquid density (kg/m³) and gravitational acceleration (9.80665 m/s²).
- H
- Total differential head added by the pump, in m after conversion, including the system’s pressure, elevation, velocity and loss requirements.
- ΔP
- Equivalent total pressure rise ρgH, in Pa after conversion. A static gauge difference alone may need elevation and velocity corrections.
- η
- Pump efficiency as a fraction in the equation. Enter a percentage in the efficiency field; 70% means η = 0.70.
- Pₕ, Pshaft
- Hydraulic power delivered to the liquid and mechanical shaft power required. Both are W in the SI equations, then converted for display.
Use the unit selectors beside the inputs. Units shown in the equations must be consistent when checking the math by hand.