Water operator math tutorial
Water Horsepower
Compute the power a pump delivers to the water from flow and head.
Water horsepower is the useful power the water receives, before any losses in the pump or motor.
The constant 3,960 comes from converting gpm and feet of head into horsepower. Memorize it with the formula.
The formula
WHP = flow (gpm) × head (ft) ÷ 3,960
| Variable | Unit |
|---|---|
| Flow | gpm |
| Total head | ft |
| Result: Water horsepower | hp |
Conversion factors used: 3,960 = 33,000 ft·lb/min per hp ÷ 8.34 lb/gal.
Applies to: Water Treatment, Water Distribution, Wastewater Treatment, Collection Systems.
Common exam tip: Water horsepower has no efficiency in it. Efficiency enters in the next formula.
Calculator
Water horsepower
24.24 hp
- 1. 800 gpm × 120 ft ÷ 3,960 = 24.24 hp
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Worked examples
Example 1
A pump delivers 800 gpm against 120 ft of head.
- 800 gpm × 120 ft ÷ 3,960 = 24.24 hp
Answer: 24.24 hp
Example 2
A booster moves 1,500 gpm against 85 ft.
- 1,500 gpm × 85 ft ÷ 3,960 = 32.2 hp
Answer: 32.2 hp
Common mistakes
Wrong result: 2.91 hp
using 33,000 instead of 3,960 for gpm and feet
Wrong result: 32.32 hp
dividing by an efficiency when only water horsepower was asked
Practice questions
1. 500 gpm against 60 ft of head. Water horsepower?
- A0.91 hp
- B10.1 hp
- C7.58 hp
- D75.8 hp
Show answer and explanation
Correct answer: C. 500 gpm × 60 ft ÷ 3,960 = 7.58 hp Answer: 7.58 hp. A common slip is using 33,000 instead of 3,960 for gpm and feet, which gives 0.91 hp.
2. 1,200 gpm against 150 ft of head. Water horsepower?
- A5.45 hp
- B60.61 hp
- C454.5 hp
- D45.45 hp
Show answer and explanation
Correct answer: D. 1,200 gpm × 150 ft ÷ 3,960 = 45.45 hp Answer: 45.45 hp. A common slip is using 33,000 instead of 3,960 for gpm and feet, which gives 5.45 hp.
3. 2,000 gpm against 40 ft of head. Water horsepower?
- A20.2 hp
- B2.42 hp
- C26.94 hp
- D202 hp
Show answer and explanation
Correct answer: A. 2,000 gpm × 40 ft ÷ 3,960 = 20.2 hp Answer: 20.2 hp. A common slip is using 33,000 instead of 3,960 for gpm and feet, which gives 2.42 hp.
Where this formula applies
This calculation can appear in the disciplines below. Exact exam coverage depends on your state, certification level, and official exam outline.
Water Treatment
Water Distribution
Wastewater Treatment
Collection Systems
Study guides
Keep going with the full guide
Water Operator Math Made Simple walks through operator math step by step and includes printable references plus a full practice exam.
Water Operator Math Made Simple
A Step-by-Step Guide to the Math Every Water Operator Needs to Know