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Pump power calculator: horsepower from flow and head

Calculate the hydraulic power and the motor power a pump needs from flow rate, total head and efficiency, with the energy use and running cost.

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Results

Motor power needed

1.81 hp

Electricity cost per year

$354

In kW
1.35 kW
Hydraulic power
943 W
Energy per year
1,967 kWh

From water to watts

A pump adds energy to water: it lifts it and pushes it through pipes against friction. The power that ends up in the water is the hydraulic power. Because pumps and motors lose energy as heat, the electrical power drawn is higher.

The formulas

  • Hydraulic power (W) = ρ × g × Q × H, with ρ = 1,000 kg/m³ × specific gravity, g = 9.80665 m/s², Q in m³/s and H in meters
  • Water horsepower = gpm × ft × SG ÷ 3,960
  • Motor power = hydraulic power ÷ overall efficiency
  • Energy per year = motor power × hours per day × 365

Worked example

A well pump delivers 50 gpm against a total head of 100 ft with an overall efficiency of 70%:

  1. Water horsepower = 50 × 100 ÷ 3,960 ≈ 1.26 hp, or 943 W hydraulic.
  2. Motor power = 943 ÷ 0.70 ≈ 1,347 W = 1.81 hp (1.35 kW).
  3. Running 4 hours a day: 1.347 × 4 × 365 ≈ 1,967 kWh per year.
  4. At $0.18 per kWh, that costs about $354 per year.

A standard 2 hp motor would be the usual choice.

What counts in total head

Total dynamic head is the sum of:

  • Static lift: vertical distance from the water level (in a well, the pumping level, not the static level) to the highest discharge point.
  • Friction losses in pipes, elbows, valves and filters, which rise with the square of flow.
  • Pressure head needed at the outlet: 1 psi = 2.31 ft of water. A pressure tank set to 50 psi adds about 115 ft.

Typical efficiencies

Pump type Overall efficiency
Small submersible or jet pump 30–50%
Residential centrifugal pump 40–60%
Commercial centrifugal pump 60–75%
Large industrial pump at best efficiency point 75–90%

Specific gravity

Enter 1 for clean water. Use about 1.03 for seawater, 0.7 to 0.9 for many oils and fuels, and up to 1.5 for some slurries. Viscous liquids also reduce pump efficiency, which this simple model does not include.

Saving energy

  • Choose a pump whose best efficiency point matches your normal flow and head.
  • Avoid throttling with a valve; a variable-speed drive cuts power roughly with the cube of speed.
  • Reduce friction with larger pipes and fewer fittings: halving friction head can cut the power more than a premium motor would.
  • Oversize the motor by only 10% to 20% over the calculated power.

Frequently asked questions

How do you calculate pump horsepower?

Water horsepower = flow (gpm) × head (ft) × specific gravity ÷ 3,960. Divide by the overall efficiency to get the motor power. 50 gpm at 100 ft and 70% efficiency needs about 1.8 hp.

What is total head?

The vertical lift from the water surface to the outlet plus friction losses in pipes and fittings and any pressure required at the outlet (2.31 ft of head per psi).

What efficiency should I use?

Small pumps with motors often reach only 40% to 60% overall; larger centrifugal pumps reach 70% to 85% at their best efficiency point. Check the pump curve when you can.

Should I choose a bigger pump to be safe?

Not by much. An oversized pump runs far from its best efficiency point, wastes energy and can cycle on and off. Add a margin of about 10% to 20% to the calculated power.

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Results are estimates provided for information purposes. They do not replace professional advice.

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