Pump Power Calculator
Sizing a pump correctly starts with the power it must deliver to move a fluid against a given head. The hydraulic power, the useful power added to the fluid, equals the fluid density times gravitational acceleration times the volumetric flow rate times the head. Real pumps are not perfect, so the shaft power the motor must supply is the hydraulic power divided by the pump efficiency, which accounts for friction, leakage and other losses. This calculator takes the fluid density, the flow rate in cubic meters per second, the total head in meters and the pump efficiency as a decimal, then returns the required shaft power in watts to two decimal places. Using SI units throughout keeps the answer in watts, which you can divide by 745.7 to convert to mechanical horsepower if you prefer. The formula is the standard one used in fluid mechanics and pump selection, and it underpins the energy estimates engineers make when specifying equipment. Mechanical power conventions and related engineering standards are published by US federal agencies including the National Highway Traffic Safety Administration. Every figure is computed deterministically from the formula, shown below, with a worked example that reconciles exactly to the calculator so you can check each step yourself.
Shaft power equals hydraulic power divided by efficiency: P = rho g Q H / eta. Pumping water (1,000 kg/m3) at 0.05 m3/s against a 20 m head at 70% efficiency needs 14,014.29 W (about 14.01 kW).
Pump power formula
P = rho g Q H / eta
P = required shaft power (W)
rho = fluid density (kg/m3), g = 9.81 m/s^2
Q = flow rate (m3/s), H = head (m), eta = efficiency
The product rho g Q H is the hydraulic power, the useful power added to the fluid. Dividing by the efficiency eta accounts for losses inside the pump, giving the larger shaft power the motor must actually provide. Gravitational acceleration g is taken as 9.81 m/s^2.
Worked example
A pump moves water (density 1,000 kg/m3) at a flow rate of 0.05 m3/s against a total head of 20 m, with a pump efficiency of 0.70.
- Hydraulic power: 1,000 x 9.81 x 0.05 x 20 = 9,810 W
- Divide by efficiency: 9,810 / 0.70 = 14,014.29 W
- That is about 14.01 kW of shaft power
- To convert to horsepower: 14,014.29 / 745.7 = 18.79 hp
So the pump requires about 14,014.29 W (14.01 kW) of shaft power. These are the calculator's default inputs, so the result above matches the widget exactly.
Pump Power Calculator: frequently asked questions
How do you calculate pump power?
The shaft power is P = rho g Q H / eta, where rho is fluid density, g is 9.81 m/s^2, Q is volumetric flow rate, H is total head and eta is pump efficiency. The product rho g Q H is the hydraulic power; dividing by efficiency gives the shaft power the motor must supply.
What is the difference between hydraulic and shaft power?
Hydraulic power, rho g Q H, is the useful power transferred to the fluid. Shaft power is larger because real pumps lose energy to friction and leakage; it equals the hydraulic power divided by the pump efficiency. The motor must deliver the shaft power.
What head should I use?
Use the total dynamic head, which combines the static lift, the pressure head and friction losses through the pipework and fittings. The total head is the actual height-equivalent the pump must overcome, not just the vertical rise.
How do I convert watts to horsepower?
Divide the power in watts by 745.7 to get mechanical horsepower. For example, 14,014.29 W divided by 745.7 is about 18.79 hp.
What is the pump power formula?
Required shaft power equals P = rho g Q H / eta, with the hydraulic power being rho g Q H.
Official sources
- Mechanical power and engineering standards reference: US National Highway Traffic Safety Administration (NHTSA). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.