Water operator math tutorial
Tank Volume in Gallons
Find the volume of a cylindrical tank from diameter and water depth.
Tank volume feeds detention time, chemical dosing for tank disinfection, and storage planning.
A cylindrical tank is a circle area times the water depth, then a conversion from cubic feet to gallons.
The formula
volume (gal) = 0.785 × diameter² (ft²) × depth (ft) × 7.48 gal/ft³
| Variable | Unit |
|---|---|
| Tank diameter | ft |
| Water depth | ft |
| Result: Volume | gal |
Conversion factors used: 7.48 gal per cubic foot.
Applies to: Water Treatment, Water Distribution, Wastewater Treatment.
Common exam tip: Use water depth, not the tank's total height.
Calculator
Volume
234,991 gal
- 1. Area = π × 40² ÷ 4 = 1,256.6 ft²
- 2. 1,256.6 ft² × 25 ft = 31,416 ft³
- 3. 31,416 ft³ × 7.48 = 234,991 gal
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 40 ft diameter tank holds 25 ft of water.
- Area = π × 40² ÷ 4 = 1,256.6 ft²
- 1,256.6 ft² × 25 ft = 31,416 ft³
- 31,416 ft³ × 7.48 = 234,991 gal
Answer: 234,991 gal
Example 2
A 60 ft diameter tank holds 30 ft of water.
- Area = π × 60² ÷ 4 = 2,827.4 ft²
- 2,827.4 ft² × 30 ft = 84,823 ft³
- 84,823 ft³ × 7.48 = 634,476 gal
Answer: 634,476 gal
Common mistakes
Wrong result: 939,965 gal
using π × d² and forgetting to divide by 4
Wrong result: 31,416 gal
reporting cubic feet instead of gallons
Practice questions
1. 30 ft diameter, 20 ft deep. Gallons?
- A105,746 gal
- B422,984 gal
- C14,137 gal
- D1,057,460 gal
Show answer and explanation
Correct answer: A. Area = π × 30² ÷ 4 = 706.9 ft² 706.9 ft² × 20 ft = 14,137 ft³ 14,137 ft³ × 7.48 = 105,746 gal Answer: 105,746 gal. A common slip is using π × d² and forgetting to divide by 4, which gives 422,984 gal.
2. 80 ft diameter, 35 ft deep. Gallons?
- A5,263,801 gal
- B1,315,950 gal
- C175,929 gal
- D13,159,500 gal
Show answer and explanation
Correct answer: B. Area = π × 80² ÷ 4 = 5,026.5 ft² 5,026.5 ft² × 35 ft = 175,929 ft³ 175,929 ft³ × 7.48 = 1,315,950 gal Answer: 1,315,950 gal. A common slip is using π × d² and forgetting to divide by 4, which gives 5,263,801 gal.
3. 50 ft diameter, 18 ft deep. Gallons?
- A1,057,460 gal
- B35,343 gal
- C264,365 gal
- D2,643,650 gal
Show answer and explanation
Correct answer: C. Area = π × 50² ÷ 4 = 1,963.5 ft² 1,963.5 ft² × 18 ft = 35,343 ft³ 35,343 ft³ × 7.48 = 264,365 gal Answer: 264,365 gal. A common slip is using π × d² and forgetting to divide by 4, which gives 1,057,460 gal.
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
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