Pump Horsepower Calculator
Enter your pump flow rate, total head (or pressure), fluid specific gravity, and pump efficiency to get water horsepower, brake horsepower, and shaft power instantly. Switch between the water-pump (head-based) and hydraulic-pump (pressure-based) modes, and between metric and imperial units. Results update as you type.
Water horsepower, brake horsepower, and why they differ
Water horsepower (WHP) is the theoretical power needed to move a given volume of fluid through a given head assuming perfect efficiency. No real pump achieves this, so the shaft must deliver more power, called brake horsepower (BHP). BHP equals WHP divided by the pump efficiency expressed as a decimal. If a motor drives the pump, the electrical or fuel power required is higher still because the motor also has losses: total input power equals BHP divided by motor efficiency. A pump rated at 75% efficiency and driven by a 90% efficient motor has an overall wire-to-water efficiency of 67.5%, meaning only two-thirds of the energy drawn from the supply reaches the fluid.
The water horsepower formula explained
In imperial units, WHP = (GPM x head_ft x specific_gravity) / 3,960. The constant 3,960 comes from unit analysis: one horsepower equals 33,000 foot-pounds per minute, and one US gallon of water weighs 8.34 pounds, so 33,000 / 8.34 = 3,957, rounded in practice to 3,960. For fluids heavier or lighter than water, multiply by the specific gravity - a brine with SG 1.2 requires 20% more power than clean water at the same flow and head. In metric, hydraulic power (kW) = rho x g x Q x H / 1,000, where rho is fluid density in kg/m3, g is 9.81 m/s2, Q is flow in m3/s, and H is head in metres.
Hydraulic pump horsepower (pressure-based mode)
Hydraulic circuits are rated by pressure and flow rather than head. The formula is HP = (GPM x PSI) / 1,714, and the constant 1,714 converts psi-gallons-per-minute to horsepower. Dividing by the pump overall efficiency (volumetric x mechanical) gives the actual input power required. For example, a pump moving 20 GPM at 2,000 PSI with 85% efficiency needs (20 x 2,000) / (1,714 x 0.85) = 27.5 hp. In metric, the equivalent is kW = (L/min x kPa) / 60,000 divided by efficiency.
How to choose the right motor size
Motor sizing should start with the total input power from this calculator, then apply a service factor. For most pumping applications, choose a motor 10-15% above the calculated requirement. Standard motor ratings jump in increments (0.5, 0.75, 1, 1.5, 2, 3, 5, 7.5, 10, 15, 20, 25, 30, 40, 50, 60, 75, 100 hp and so on), so select the next standard size above your calculated need plus the service margin. Starting current for squirrel-cage induction motors can be 6-8 times running current, so verify the supply can handle the inrush before commissioning.
Typical pump efficiency ranges by pump type
| Pump type | Typical efficiency range | Common application |
|---|---|---|
| Centrifugal (small, < 5 HP) | 40-60% | Domestic water supply, sump pumps |
| Centrifugal (medium, 5-50 HP) | 60-80% | HVAC, irrigation, process water |
| Centrifugal (large, > 50 HP) | 75-90% | Municipal water, industrial process |
| Axial flow | 80-90% | High flow, low head (flood control, cooling) |
| Positive displacement (gear) | 80-92% | Hydraulic systems, viscous fluids |
| Positive displacement (piston) | 85-95% | High-pressure hydraulics |
| Submersible | 50-75% | Well pumps, wastewater |
| Vertical turbine | 70-85% | Deep wells, irrigation |
Overall efficiency includes hydraulic, volumetric, and mechanical losses. Actual values depend on operating point relative to the best efficiency point (BEP).
Frequently asked questions
What is the difference between water horsepower and brake horsepower?
Water horsepower (WHP) is the ideal, loss-free power required to move fluid through a given head. Brake horsepower (BHP) is the actual shaft power the pump must receive from its driver, which is always higher because real pumps have internal hydraulic, volumetric, and mechanical losses. The ratio of WHP to BHP is the pump efficiency. For example, if WHP is 10 hp and the pump is 75% efficient, BHP is 10 / 0.75 = 13.3 hp.
Why does specific gravity affect horsepower?
Horsepower is a power (force times velocity) measure. A denser fluid weighs more per gallon, so the pump must do more work to move the same volume to the same height. A fluid with SG 1.5 requires exactly 50% more horsepower than water at identical flow rate and head conditions. Use the specific gravity input when pumping seawater (SG approx. 1.025), brines, acids, slurries, or fuels.
What is the 3,960 constant in the water horsepower formula?
One mechanical horsepower equals 33,000 foot-pounds per minute. One US gallon of water at standard conditions weighs 8.34 pounds. Dividing 33,000 by 8.34 gives 3,957, which is rounded to 3,960 in the standard pump formula. It converts (GPM x feet) into horsepower when the fluid is water (SG = 1.0).
What is the 1,714 constant in the hydraulic pump formula?
One horsepower equals 6,600 inch-pounds per second, and one gallon per minute of fluid at one psi pressure difference delivers a specific rate of work. Working through the unit conversions, (GPM x PSI) / 1,714 yields horsepower. It is the hydraulic equivalent of the 3,960 constant used for head-based centrifugal pump calculations.
How do I account for pipe friction losses?
Include friction losses in the total head input. Total dynamic head (TDH) equals static lift plus friction head plus velocity head minus any inlet pressure benefit. Use the Darcy-Weisbach equation or Hazen-Williams tables to calculate friction head for your pipe diameter, material, length, and flow rate, then add it to the static head before entering the value here.
What pump efficiency should I assume if I do not know mine?
A conservative starting assumption for a mid-size centrifugal pump (5-50 hp) is 70-75% efficiency. Small pumps under 5 hp often run at 50-65%, while large industrial centrifugal pumps at their best efficiency point (BEP) can reach 85-90%. If you are still in the design phase, use 70% as a planning figure and confirm with the manufacturer pump curve before final motor selection.