Well Pump Horsepower & Flow Rate Calculator
Calculate the required brake horsepower (BHP) for a well pump given flow rate and total dynamic head, or determine the flow rate from a known horsepower. Uses the standard hydraulic horsepower formula with pump and motor efficiency factors.
Formulas Used
Water Horsepower (WHP) — the theoretical power needed to move water:
WHP = (GPM × TDH × SG) / 3960
Where 3960 is a unit-conversion constant (derived from 1 HP = 550 ft·lbf/s and 1 gallon of water = 8.34 lb).
Brake Horsepower (BHP) — shaft power required at the pump, accounting for pump losses:
BHP = WHP / ηpump
Motor Horsepower (MHP) — electrical input power required, accounting for motor losses:
MHP = BHP / ηmotor = (GPM × TDH × SG) / (3960 × ηpump × ηmotor)
Rearranged for Flow Rate:
GPM = (MHP × ηpump × ηmotor × 3960) / (TDH × SG)
Wire-to-Water Efficiency:
ηw2w = WHP / MHP = ηpump × ηmotor
Total Dynamic Head (TDH) components:
TDH = Static Lift + Friction Head Loss + Pressure Head + Velocity Head
Assumptions & References
- The constant 3960 is derived from: 1 HP = 550 ft·lbf/s; water density = 8.34 lb/gal; 1 gal/min = 1/60 gal/s → 3960 = (33,000 ft·lbf/min) / 8.34 lb/gal.
- Specific gravity of 1.0 is assumed for fresh water at standard conditions (60°F / 15.6°C).
- Typical submersible well pump efficiencies range from 50–80%; centrifugal pumps 60–85%.
- Typical submersible motor efficiencies range from 85–95%.
- Total Dynamic Head must include: static water level depth, drawdown, surface discharge pressure head, and all pipe friction losses (calculated via Hazen-Williams or Darcy-Weisbach).
- This calculator does not account for NPSH (Net Positive Suction Head) — verify separately for surface pumps.
- Standard motor sizes follow NEMA standards: 0.5, 0.75, 1, 1.5, 2, 3, 5, 7.5, 10, 15, 20, 25, 30, 40, 50, 75, 100 HP.
- A service factor of 1.15 is commonly applied to motor selection — consider choosing the next standard size above the calculated MHP.
- References: Goulds Pumps Engineering Data Book; Grundfos Pump Handbook; AWWA M21 Groundwater; Hydraulic Institute Standards.