Calculate hydraulic (water) power, brake power at the shaft, and electrical motor input — in HP and kW — from flow, head, specific gravity, and efficiencies.
US + metric
Formula shown
Shareable results
Pump Power
ft
SG
%
%
%
Brake Power18hp(13.5 kW)
Power
hp
kW
Hydraulic (water)
12.6
9.42
Brake (shaft)
18
13.5
Motor input (electrical)
20
14.9
Nearest standard motor at or above the 18 hp brake power: 20 hp. Allow for the manufacturer’s recommended margin.
K = 3960 for Q in gpm and H in ft (result in hp), or 367 for Q in m³/h and H in m (result in kW), for water at SG = 1. 3960 ≈ 33,000 ft·lbf/min per hp ÷ 8.34 lb/gal.
For preliminary sizing and educational use. Verify final design against manufacturer performance curves and applicable codes; final designs should be reviewed by a licensed professional engineer.
Pump power comes in three figures, each larger than the last. Hydraulic (water) power is the useful power delivered to the fluid; brake power is what the shaft must supply, found by dividing hydraulic power by pump efficiency; and motor input power is the electrical draw, found by dividing brake power by motor (and any drive) efficiency. Water horsepower equals flow times head times specific gravity divided by 3960 in US units, or by 367 for kilowatts in SI.
Worked example
Pumping 500 gpm of water (SG = 1.0) against 100 ft of total head, with a pump efficiency of 70% and a motor efficiency of 90% (direct drive):
Nearest standard motor at or above the brake power: 20 hp
Where does 3960 come from?
One horsepower is 33,000 ft·lbf per minute, and a US gallon of water weighs about 8.34 lb. Dividing 33,000 by 8.34 gives 3956 ≈ 3960, the divisor that turns gpm × ft into water horsepower. In SI the equivalent divisor is 367: it folds in 3600 seconds per hour and g = 9.81 m/s², so m³/h × m ÷ 367 gives hydraulic power in kilowatts. Multiply by specific gravity for fluids other than water.
When to use — and when not to
Use brake power to select the pump driver and to check the operating point against the motor’s service factor. Size the motor at or above the brake power at the worst-case point on the curve — often end-of-curve (maximum flow), not the design point. For lifecycle running cost rather than nameplate sizing, use the energy cost calculator; to see how power changes with speed, use the affinity laws calculator.
Variables
Symbol
Meaning
US unit
SI unit
Q
Flow rate
gpm
mu00b3/h
H
Total head
ft
m
SG
Specific gravity of the fluid
-
-
u03b7_p
Pump (hydraulic) efficiency
%
%
u03b7_m
Motor efficiency
%
%
u03b7_d
Drive efficiency (belt/VFD, optional)
%
%
K
Power constant (3960 for gpmu00b7ftu2192hp, 367 for mu00b3/hu00b7mu2192kW)
