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Water horsepower equals flow in gallons per minute (gpm) times total dynamic head in feet, divided by 3,960. Brake horsepower is water horsepower divided by the pump efficiency, and motor horsepower is brake horsepower divided by the motor efficiency, each efficiency as a decimal.
water horsepower (WHP) = gpm × total dynamic head (TDH) (ft) ÷ 3,960 · brake horsepower (BHP) = WHP ÷ pump eff. · motor horsepower (MHP) = BHP ÷ motor eff.
| Term | Meaning | Units |
|---|---|---|
| gpm | pump flow | gal/min |
| TDH | total dynamic head the pump works against | ft of water |
| 3,960 | 33,000 ft·lb/min per horsepower ÷ 8.34 lb/gal | gpm·ft per hp |
| Efficiency | pump or motor efficiency as a decimal | unitless |
All three sheets give water and brake horsepower; the drinking water sheet also gives motor horsepower and wire-to-water efficiency. Official sheets: Exam Conversion Sheet (revised 4/30/2026) (State Water Resources Control Board, Drinking Water Operator Certification Program; Water Treatment and Water Distribution exams); Equivalents and Formulas Sheet, Version 1 (State Water Resources Control Board, Wastewater Operator Certification Program; Wastewater Treatment Plant Operator exams); Equivalents and Formulas Sheet, Version 2 (State Water Resources Control Board, Wastewater Operator Certification Program; Wastewater Treatment Plant Operator exams).
Pump horsepower · Original practice item, not a real exam question.
A booster pump delivers 1,650 gpm against 145 ft of TDH. The pump is 78 percent efficient and its motor 92 percent. Find WHP, BHP and MHP.
1,650 gpm × 145 ft ÷ 3,960 = 60.4 hp60.4 hp ÷ 0.78 = 77.5 hp77.5 hp ÷ 0.92 = 84.2 hpAnswer: WHP 60.4 hp, BHP 77.5 hp, MHP 84.2 hp
One horsepower is 33,000 ft·lb/min and a gallon of water weighs 8.34 lb, so 33,000 ÷ 8.34 = 3,957, rounded to 3,960 for gpm and feet of head.
Pump efficiency times motor efficiency: 0.78 × 0.92 = 71.8 percent here. Water horsepower divided by it gives motor horsepower directly.
Multiply by 0.746 kW per hp: 84.2 hp × 0.746 = 62.8 kW, which times hours run and the price per kilowatt-hour gives the power cost.
The free study app has a step-by-step lesson on this calculation, with fraction-tile unit cancellation and graded practice problems.
Open the pump horsepower lessonFormulas follow the official sheets linked above, which are the reference at the exam. The worked example and the mistakes are original practice material written for this page; they are not real exam questions, which are confidential. Written by the site's author.
Questions, flashcards, and explanations are AI-written under a sourcing policy that builds on the exam content outlines and candidate materials each certifying body publishes without restriction and the regulations and technical references they cite, and that excludes actual exam questions, recollections of any exam sat by the author, other study products, and any handbook or document released under a confidentiality agreement. Any item found outside that policy is rewritten from primary sources or removed. Content is then put through repeated review — regulatory values checked against primary sources, every calculation recomputed, and errors corrected — plus spot checks by the author, who holds California water operator certifications and a California civil engineering license. Those spot checks are sampling, not a professional review: nothing here is stamped, sealed, or offered as engineering advice, and not every item has been individually verified, so mistakes can still slip through.
Not affiliated with or endorsed by the State Water Resources Control Board (SWRCB), its Division of Drinking Water (DDW) or Wastewater Operator Certification Program (WWOCP), the California-Nevada American Water Works Association (CA-NV AWWA), the California Water Environment Association (CWEA), the National Council of Examiners for Engineering and Surveying (NCEES), the California Board for Professional Engineers, Land Surveyors, and Geologists (BPELSG), the Contractors State License Board (CSLB), or the American Public Works Association (APWA). All questions, flashcards, and references are independent study aids; verify against the official exam materials.