Pump horsepower formula
Pump horsepower is the power needed to move a liquid at a given flow and head. The water horsepower is flow times head times specific gravity divided by 3960; dividing by efficiency gives the brake horsepower the motor must supply.
Variables
| HP | Water horsepower | hp |
| Q | Flow rate | US gpm |
| H | Total head | ft |
| SG | Specific gravity | 1.0 for water |
| 3960 | Unit constant | – |
Rearranged
Metric: power (kW) = ρ × g × Q × H
Worked example
A pump moves 100 gpm of water to 50 ft of head.
Water HP = 100 × 50 × 1.0 / 3960 = 1.26 hp.
At 70 percent efficiency, brake HP = 1.26 / 0.70 = 1.8 hp.
Water horsepower is the useful power delivered to the fluid; the motor must supply more because pumps are not perfectly efficient. Dividing by the pump efficiency, typically 0.6 to 0.85, gives the brake horsepower. Specific gravity scales the result for liquids heavier or lighter than water.
Working out flow and head first?
See the Flow Rate Formula and the Pressure Drop Formula.
Water horsepower vs brake horsepower
Water horsepower is the power actually added to the liquid, the product of flow and head. Brake horsepower is what the motor must deliver to the pump shaft, always larger because some energy is lost to friction and turbulence inside the pump. The ratio of the two is the pump efficiency, and the motor is sized on the brake figure.
Where 3960 comes from
One horsepower is 33,000 foot-pounds per minute. A gallon of water weighs 8.34 pounds, so converting gallons per minute and feet of head into foot-pounds per minute and then into horsepower folds the constants into 33,000 divided by 8.34, which is 3960. Specific gravity adjusts it for other liquids.
FAQ
What is the pump horsepower formula?
Water horsepower equals flow in gpm times head in feet times specific gravity divided by 3960. Divide by pump efficiency for brake horsepower.
What is the difference between water and brake horsepower?
Water horsepower is the power delivered to the liquid; brake horsepower is the larger power the motor must supply, the difference being pump losses.
Why divide by 3960?
It is the constant that converts gallons per minute and feet of head into horsepower, from 33,000 foot-pounds per minute divided by the 8.34 pound weight of a gallon of water.