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# Pumps - Power Calculator

## Calculate pumps hydraulic and shaft power.

### Hydraulic Pump Power

The ideal hydraulic power to drive a pump depends on

• the mass flow rate the
• liquid density
• the differential height - either it is the static lift from one height to an other or the total head loss component of the system - and can be calculated like

Ph(kW) = q ρ g h / (3.6 106)

= q p / (3.6 106)                  (1)

where

Ph(kW) = hydraulic power (kW)

q = flow (m3/h)

ρ = density of fluid (kg/m3)

g = acceleration of gravity (9.81 m/s2)

p = differential pressure (N/m2, Pa)

The hydraulic Horse Power can be calculated as:

Ph(hp)Ph(kW) / 0.746                                  (2)

where

Ph(hp) = hydraulic horsepower (hp)

Or - alternatively

Ph(hp) = qgpm hft SG / (3960 η)                              (2b)

where

qgpm = flow (gpm)

SG = Specific Gravity (1 for water)

η = pump efficiency

### Example - Power pumping Water

1 m3/h of water is pumped a head of 10 m. The theoretical pump power can be calculated as

Ph(kW) = (1 m3/h) (1000 kg/m3) (9.81 m/s2) (10 m) / (3.6 106)

= 0.027 kW

### Shaft Pump Power

The shaft power - the power required transferred from the motor to the shaft of the pump - depends on the efficiency of the pump and can be calculated as

Ps(kW) Ph(kW) / η                                     (3)

where

Ps(kW)  = shaft power (kW)

η = pump efficiency

### Online Pump Calculator - SI-units

The calculator below can used to calculate the hydraulic and shaft power of a pump:

q - flow (m3/h)

ρ - density of fluid (kg/m3)

g - gravity (m/s2)

η - pump efficiency

### Online Pump Calculator - Imperial units

The calculator below can used to calculate the hydraulic and shaft power of a pump using Imperial units:

q - flow capacity (gpm)

γ - specific weight of fluid (lb/ft3)

g - gravity (ft/s2)

η - pump efficiency

### Related Mobile Apps from The Engineering ToolBox

- free apps for offline use on mobile devices.  ## Related Topics

• Pumps - Piping systems and pumps - centrifugal pumps, displacement pumps - cavitation, viscosity, head and pressure, power consumption and more.

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## Citation

• Engineering ToolBox, (2003). Pumps - Power Calculator. [online] Available at: https://www.engineeringtoolbox.com/pumps-power-d_505.html [Accessed Day Mo. Year].

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