This pump horsepower calculator finds both the water horsepower (the theoretical power to move a fluid) and the brake horsepower (the actual motor power required) from flow rate in GPM, total head in feet, fluid specific gravity, and pump efficiency. It's a core sizing tool for selecting pumps and motors in water, HVAC, irrigation, and process applications.
Pump Horsepower Formula
Brake HP = Water HP ÷ Pump Efficiency
Water horsepower (also called hydraulic or fluid horsepower) is the useful power actually delivered to the liquid to lift and move it. Brake horsepower (BHP) is the larger figure the motor must supply to the pump shaft, because no pump is 100% efficient — friction, internal recirculation, and turbulence all consume extra power. The constant 3960 comes from 33,000 ft·lb/min per HP divided by the 8.33 lb weight of a gallon of water.
Understanding Total Dynamic Head
"Head" in the formula means total dynamic head (TDH) — the full resistance the pump works against, not just vertical lift. TDH combines static lift (the height the fluid is raised), friction losses in pipe and fittings, and any pressure the system must overcome at the outlet. Underestimating friction loss is the most common sizing mistake, leaving a pump that can't reach its rated flow. Express head in feet; for pressure in PSI, multiply PSI by 2.31 to get feet of head for water.
Specific Gravity and Efficiency
Specific gravity (SG) scales the result for fluids heavier or lighter than water (SG = 1.0). Pumping a brine or oil at SG 1.2 needs 20% more power for the same flow and head. Pump efficiency typically runs 50–80% for centrifugal pumps depending on size and operating point; always size the motor on brake horsepower, then round up to the next standard motor rating to keep a safety margin.
Pump HP by Flow and Head (water, 70% efficiency)
| Flow (GPM) | Head (ft) | Water HP | Brake HP |
|---|---|---|---|
| 25 | 50 | 0.32 | 0.45 |
| 50 | 100 | 1.26 | 1.80 |
| 100 | 100 | 2.53 | 3.61 |
| 200 | 150 | 7.58 | 10.82 |
| 500 | 200 | 25.3 | 36.1 |
Worked Example
This calculator provides estimates based on standard mathematical formulas. Real-world results will vary based on mechanical condition, environmental factors, and other variables.
Well & Irrigation Pumps: A Worked Sizing Example
Domestic wells and irrigation are the most common real-world use of this math, and they add one wrinkle: total dynamic head (TDH) is the sum of the vertical lift, the pressure-tank requirement converted to feet (1 PSI = 2.31 ft), and pipe friction losses.
Typical efficiencies to divide by: submersible well pumps 45–65%, surface centrifugal 50–75%, positive-displacement 80–90%. Always round up to the next standard motor size, and remember an oversized pump cycling against a small tank wears out faster than a correctly sized one running longer.
Frequently Asked Questions
TDH is the total equivalent height that a fluid is to be pumped, taking into account friction losses in the pipe.
Specific gravity is the ratio of a fluid's density to water. Water is 1.0. Heavy mud might be 1.5, meaning it requires 50% more power to pump.
Hydraulic horsepower is the useful power delivered to the fluid; brake horsepower is what the motor must supply, found by dividing hydraulic HP by pump efficiency.
Most centrifugal pumps run 50–85% efficient. If you don't know the exact figure, 70% is a reasonable starting estimate for sizing.
Higher head (the height or pressure the pump must overcome) increases the horsepower required proportionally, as does higher flow rate.