Brake horsepower (BHP) is the power the motor actually delivers to the pump shaft — larger than the useful “water horsepower” because no pump is perfectly efficient. For a centrifugal pump it follows one compact relationship, and this calculator works it in whichever direction you need: enter any four of flow, head, specific gravity, efficiency, and brake power, and it returns the fifth.

The formula and where 3960 comes from

In US units, BHP = Q × H × SG / (3960 × η), with flow Q in gpm, head H in feet, specific gravity SG, and pump efficiency η as a decimal. The 3960 is not arbitrary: one horsepower is 33,000 ft·lbf per minute, and a US gallon of water weighs about 8.34 lb, so 33,000 ÷ 8.34 ≈ 3960. In metric units the same physics gives brake power in kilowatts as P = Q × H × SG / (367 × η) with Q in m³/h and H in m. Toggle US/Metric and the calculator swaps the constant and the units for you.

Solve in any direction

Because it is one equation in five variables, knowing four fixes the fifth. Pick what you want from the “Solve for” menu:

Brake power — the usual case: size the motor for a known duty.
Efficiency — back it out from a measured motor draw to see how a pump is really performing (a solved efficiency above 100% means the numbers don’t add up — usually the entered power is too low).
Flow or head — find the duty a given brake power can support.
Specific gravity — check the fluid a measured power implies.

Worked example

500 gpm at 100 ft of head, water (SG 1.0), 70% pump efficiency: BHP = 500 × 100 × 1.0 / (3960 × 0.70) ≈ 18.0 hp (13.5 kW). That is the shaft power; the motor should be the next standard size above it, with the manufacturer’s recommended margin — see the motor sizing calculator. For the full hydraulic → brake → electrical breakdown, use the pump power calculator.