Pump Head and Power Calculator

Hydraulic power (also called water power or fluid power) is the useful work actually delivered to the fluid, P_hydraulic = rho g Q H / 1000 in kW. Shaft power (also called brake power) is what the motor must actually supply to the pump shaft, P_shaft = P_hydraulic / efficiency. Shaft power is always larger because the pump loses some energy to mechanical friction, internal recirculation, and leakage before it reaches the fluid.

P_hydraulic (kW) = rho x g x Q x H / 1000, where rho is fluid density in kg/m3, g is 9.81 m/s2, Q is volumetric flow rate in m3/s (convert from L/s by dividing by 1000), and H is total head in metres. This is the rate of useful work done raising and moving the fluid, independent of the pump's internal efficiency.

P_shaft (kW) = P_hydraulic / (efficiency/100). Shaft power, sometimes called brake horsepower in imperial units, is the actual mechanical power the motor delivers to the pump shaft. It is always greater than hydraulic power because no real pump is 100 percent efficient, some input energy is lost to friction, internal recirculation, and leakage.

Select a motor rated at or above the calculated shaft power, then add a safety margin, commonly 10 to 25 percent, to account for startup torque, voltage variation, and operating away from the pump's best efficiency point. For example, a calculated shaft power of 19.6 kW would typically call for a 22 kW or 25 kW standard motor size, not a motor rated at exactly 19.6 kW.

Total head H is the total energy per unit weight of fluid the pump must add, expressed in metres of fluid column. It includes static lift (elevation change), friction losses in pipes and fittings, and any pressure difference between the source and destination, all converted to equivalent metres of head. It is not simply the vertical height between two tanks unless friction losses are negligible.

Hydraulic power is directly proportional to fluid density, so denser fluids need more power to move at the same flow rate and head. A pump moving brine at 1150 kg/m3 needs 15 percent more power than the same pump moving water at 1000 kg/m3 for identical flow rate, head, and efficiency, which is why process engineers always check density before sizing a motor for a non-water fluid.

Centrifugal pump efficiency typically ranges from about 50 percent for small pumps to 85 to 90 percent for large, well-matched industrial pumps operating near their best efficiency point. Efficiency drops significantly when a pump runs far from its design flow rate, either much lower or much higher than the flow at peak efficiency on its pump curve.

Not directly. Pump power depends on flow rate Q and total head H, and pipe diameter only enters indirectly by influencing how much of the head is consumed by friction losses. A narrower pipe increases friction losses in the piping system, which increases the required total head H for a given flow rate, which in turn increases the power the pump must supply.

1 kilowatt equals about 1.341 horsepower (mechanical/imperial hp), so shaft power in kW can be converted by multiplying by 1.341. For example, a shaft power of 19.62 kW is about 26.3 hp. Pump nameplates in the United States commonly quote horsepower, while SI-unit specifications and most of the rest of the world quote kilowatts.

If total head H stays constant, hydraulic power and shaft power both double exactly, since power is directly proportional to flow rate Q in this formula. In practice, however, a real pump's head decreases as flow rate increases along its performance curve, so actual power draw at higher flow does not scale linearly, this calculator's chart assumes constant head across the plotted flow range for illustration.