22 Pool Math & Calculations Practice Questions & Answers
Every Pool Math & Calculations practice question from the Pool Operator (CPO) Practice Test, with the correct answer and a short explanation.
Start practice test →1. A rectangular pool is 60 ft long and 30 ft wide, with a shallow end 3 ft deep and a deep end 8 ft deep and a constant slope between them. Using 7.5 gallons per cubic foot, what is the pool volume in gallons?
- A.74,250 gallons✓ Answer
- B.108,000 gallons
- C.40,500 gallons
- D.9,900 gallons
With a constant slope the average depth is (3 + 8) ÷ 2 = 5.5 ft, so the volume is 60 × 30 × 5.5 = 9,900 cubic feet, and 9,900 × 7.5 = 74,250 gallons. Multiplying length by width by depth gives cubic feet, and only the final step converts cubic feet to gallons.
Source: PHTA Pool & Spa Operator Handbook, essential calculations chapter (rectangular pool volume and average depth)Report a problem with this question
2. A circular pool is 30 ft in diameter with a uniform depth of 4 ft. Using 3.14 for pi and 7.5 gallons per cubic foot, what is the volume in gallons?
- A.84,780 gallons
- B.5,299 gallons
- C.21,195 gallons✓ Answer
- D.2,826 gallons
The radius is half the diameter, 15 ft, so the surface area is 3.14 × 15 × 15 = 706.5 sq ft; 706.5 × 4 = 2,826 cubic feet, and 2,826 × 7.5 = 21,195 gallons. Using the diameter in place of the radius quadruples the area and is the most common error here.
Source: PHTA Pool & Spa Operator Handbook, essential calculations chapter (circular pool volume)Report a problem with this question
3. A pool is 100 ft long and 40 ft wide. The first 75 ft of its length slopes at a constant grade from 3 ft deep to 7 ft deep; the remaining 25 ft is a diving well of constant 12 ft depth. Using 7.5 gallons per cubic foot, what is the total volume in gallons?
- A.202,500 gallons✓ Answer
- B.225,000 gallons
- C.150,000 gallons
- D.112,500 gallons
A pool with two different bottom profiles must be split into sections and the sections added: the sloped swim area averages (3 + 7) ÷ 2 = 5 ft, giving 75 × 40 × 5 × 7.5 = 112,500 gallons, and the constant-depth well gives 25 × 40 × 12 × 7.5 = 90,000 gallons, for 202,500 gallons total. Averaging the shallowest and deepest points across the whole pool overstates the volume because the diving well does not slope.
Source: PHTA Pool & Spa Operator Handbook, essential calculations chapter (multi-section pool volume)Report a problem with this question
4. An oblong pool consists of a rectangle 40 ft long and 20 ft wide with a half-circle added at each end, each half-circle having a diameter of 20 ft. The depth is a uniform 4 ft. Using 3.14 for pi and 7.5 gallons per cubic foot, what is the volume in gallons?
- A.28,710 gallons
- B.61,680 gallons
- C.33,420 gallons✓ Answer
- D.24,000 gallons
Two half-circles of the same diameter combine into one full circle of radius 10 ft, so the area is (40 × 20) + (3.14 × 10 × 10) = 800 + 314 = 1,114 sq ft; 1,114 × 4 = 4,456 cubic feet, and 4,456 × 7.5 = 33,420 gallons. Counting only the rectangle, or only one of the two ends, leaves out real water.
Source: PHTA Pool & Spa Operator Handbook, essential calculations chapter (oblong pool surface area and volume)Report a problem with this question
5. A pool has a water surface 50 ft by 25 ft. The operator must raise the water level by 3 inches. Using 0.0833 ft per inch and 7.5 gallons per cubic foot, approximately how many gallons must be added?
- A.2,343 gallons✓ Answer
- B.312 gallons
- C.781 gallons
- D.28,125 gallons
Water added or lost equals surface area times the depth change in feet times 7.5: 50 × 25 = 1,250 sq ft, 3 inches = 3 × 0.0833 = 0.2499 ft, so 1,250 × 0.2499 = 312.4 cubic feet and 312.4 × 7.5 = about 2,343 gallons. Treating the 3 as feet instead of inches inflates the answer twelvefold.
Source: PHTA Pool & Spa Operator Handbook, essential calculations chapter (water volume per inch of depth)Report a problem with this question
6. A pool holds 240,000 gallons. The health code having jurisdiction requires a 6-hour turnover. What flow rate in gallons per minute is required to meet that turnover?
- A.40,000 gpm
- B.667 gpm✓ Answer
- C.4,000 gpm
- D.1,333 gpm
Required flow equals volume divided by turnover hours divided by 60 minutes per hour: 240,000 ÷ 6 = 40,000 gallons per hour, and 40,000 ÷ 60 = about 667 gpm. Dropping the division by 60 leaves an hourly figure, not the gpm the flow meter reads.
Source: PHTA Pool & Spa Operator Handbook, water circulation chapter (turnover and required flow rate)Report a problem with this question
7. A pool holds 189,000 gallons and the flow meter reads a steady 700 gallons per minute. How many hours does one complete turnover take?
- A.2.25 hours
- B.7.5 hours
- C.270 hours
- D.4.5 hours✓ Answer
Turnover time in hours equals volume divided by gpm divided by 60: 189,000 ÷ 700 = 270 minutes, and 270 ÷ 60 = 4.5 hours. The 270 figure is minutes, so reporting it as hours is a unit error rather than an arithmetic one.
Source: PHTA Pool & Spa Operator Handbook, water circulation chapter (turnover time calculation)Report a problem with this question
8. A spa holds 900 gallons and its circulation pump moves 30 gallons per minute. How many minutes does one complete turnover of the spa water take?
- A.0.5 minutes
- B.15 minutes
- C.30 minutes✓ Answer
- D.60 minutes
Volume divided by flow in gallons per minute gives the turnover directly in minutes: 900 ÷ 30 = 30 minutes. No division by 60 is needed here because the question asks for minutes, and dividing by 60 anyway would give the answer in hours.
Source: PHTA Pool & Spa Operator Handbook, spa and therapy operations chapter (spa turnover calculation)Report a problem with this question
9. A pool holds 300,000 gallons and the circulation system runs 24 hours a day at 1,000 gallons per minute. How many complete turnovers does the system achieve in 24 hours?
- A.4.8 turnovers✓ Answer
- B.288 turnovers
- C.5 turnovers
- D.0.21 turnovers
The system pumps 1,000 × 60 × 24 = 1,440,000 gallons in a day, and 1,440,000 ÷ 300,000 = 4.8 turnovers. The value 5 is the turnover time in hours (300,000 ÷ 1,000 ÷ 60), which answers a different question than the one asked.
Source: PHTA Pool & Spa Operator Handbook, water circulation chapter (turnovers per day)Report a problem with this question
10. A pool circulates at 480 gallons per minute. The filter selected will be operated at a filtration rate of 15 gallons per minute per square foot. How much filter surface area is required?
- A.3.2 sq ft
- B.7,200 sq ft
- C.64 sq ft
- D.32 sq ft✓ Answer
Required filter area equals flow rate divided by the filtration rate: 480 ÷ 15 = 32 square feet. Multiplying instead of dividing gives 7,200, a figure with the wrong units, since gpm divided by gpm per square foot must leave square feet.
Source: PHTA Pool & Spa Operator Handbook, filtration chapter (filter area and filtration rate)Report a problem with this question
11. A diatomaceous earth filter contains 6 grids, each measuring 3 ft by 5 ft, and each grid filters water through both of its faces. If the filter is operated at 1.5 gallons per minute per square foot, what is the maximum flow it can handle?
- A.270 gpm✓ Answer
- B.180 gpm
- C.540 gpm
- D.135 gpm
Each grid presents 3 × 5 = 15 sq ft per face, and because both faces filter, each grid contributes 30 sq ft, so 6 grids give 180 sq ft; 180 × 1.5 = 270 gpm. Counting only one face of each grid halves the area and produces the 135 gpm answer.
Source: PHTA Pool & Spa Operator Handbook, filtration chapter (diatomaceous earth grid area and flow capacity)Report a problem with this question
12. A cartridge filter has 320 square feet of media surface area and is passing 120 gallons per minute. What filtration rate is the filter operating at?
- A.0.19 gpm per sq ft
- B.0.375 gpm per sq ft✓ Answer
- C.2.67 gpm per sq ft
- D.38,400 gpm per sq ft
Filtration rate equals flow divided by filter area: 120 ÷ 320 = 0.375 gallons per minute per square foot. Inverting the division gives 2.67, which describes square feet per gallon and is not a filtration rate.
Source: PHTA Pool & Spa Operator Handbook, filtration chapter (filtration rate calculation)Report a problem with this question
13. A pool holds 60,000 gallons. The dose chart states that 2.0 ounces of calcium hypochlorite per 10,000 gallons raises free chlorine by 1 ppm. The free chlorine reads 1.0 ppm and the operator wants 3.0 ppm. How many pounds of calcium hypochlorite are needed, using 16 ounces per pound?
- A.0.75 pounds
- B.2.25 pounds
- C.1.5 pounds✓ Answer
- D.24 pounds
The dose is volume ÷ 10,000 × ppm change × chart amount ÷ 16: 6 × 2 × 2.0 = 24 ounces, and 24 ÷ 16 = 1.5 pounds. The ppm change is the difference between the target and the current reading, not the target itself.
Source: PHTA Pool & Spa Operator Handbook, disinfection chapter (chemical dosage formula, per 10,000 gallon basis)Report a problem with this question
14. A pool holds 80,000 gallons. The dose chart states that 10.7 fluid ounces of 12% sodium hypochlorite per 10,000 gallons raises free chlorine by 1 ppm. To raise free chlorine by 1.5 ppm, approximately how many gallons of the liquid are needed, using 128 fluid ounces per gallon?
- A.About 0.5 gallons
- B.About 128 gallons
- C.About 8.0 gallons
- D.About 1.0 gallon✓ Answer
The calculation is 8 × 1.5 × 10.7 = 128.4 fluid ounces, and 128.4 ÷ 128 = about 1.0 gallon. Liquids convert with 128 fluid ounces per gallon; using the 16-ounce dry conversion by mistake yields the 8-gallon distractor.
Source: PHTA Pool & Spa Operator Handbook, disinfection chapter (liquid chlorine dosage and fluid ounce conversion)Report a problem with this question
15. A pool holds 50,000 gallons. The dose chart states that 1.4 pounds of sodium bicarbonate per 10,000 gallons raises total alkalinity by 10 ppm. The total alkalinity reads 70 ppm and the operator's target is 110 ppm. How many pounds of sodium bicarbonate are needed?
- A.77 pounds
- B.7 pounds
- C.28 pounds✓ Answer
- D.280 pounds
The needed change is 110 − 70 = 40 ppm, which is 4 units of the chart's 10 ppm step, so the dose is 5 × 4 × 1.4 = 28 pounds. This chart row is already stated in pounds per 10 ppm, so multiplying by 40 ppm directly, as if the row were per 1 ppm, overdoses by a factor of ten.
Source: PHTA Pool & Spa Operator Handbook, water balance chapter (total alkalinity adjustment dosage)Report a problem with this question
16. A pool holds 30,000 gallons. The dose chart states that 0.9 pounds of 100% pure calcium chloride per 10,000 gallons raises calcium hardness by 10 ppm. The product on hand is only 77% calcium chloride, and the operator needs to raise calcium hardness from 150 ppm to 250 ppm. Approximately how many pounds of the product are needed?
- A.20.8 pounds
- B.27 pounds
- C.350 pounds
- D.35 pounds✓ Answer
For pure product the dose would be 3 × 10 × 0.9 = 27 pounds, but because only 77% of the product is the active ingredient the weight must be divided by 0.77: 27 ÷ 0.77 = about 35 pounds. Dividing by the strength always increases the weight needed; multiplying by it moves the answer the wrong way.
Source: PHTA Pool & Spa Operator Handbook, water balance chapter (calcium hardness dosage adjusted for product purity)Report a problem with this question
17. A pool holds 120,000 gallons. Total chlorine reads 3.4 ppm and free chlorine reads 2.0 ppm. The operator will use the handbook rule that the breakpoint target free chlorine equals combined chlorine times 10. If 2.0 ounces of calcium hypochlorite per 10,000 gallons raises free chlorine 1 ppm, how many pounds are required, using 16 ounces per pound?
- A.288 pounds
- B.18 pounds✓ Answer
- C.21 pounds
- D.2.1 pounds
Combined chlorine is 3.4 − 2.0 = 1.4 ppm, so the target free chlorine is 1.4 × 10 = 14 ppm, and because 2.0 ppm is already present the addition is 14 − 2.0 = 12 ppm: 12 × 12 × 2.0 = 288 ounces ÷ 16 = 18 pounds. The most-missed step is subtracting the existing free chlorine, since the ten-times figure is a target level and not the amount to add.
Source: PHTA Pool & Spa Operator Handbook, disinfection chapter (breakpoint chlorination calculation)Report a problem with this question
18. A pool holds 100,000 gallons and needs a 2 ppm increase in free chlorine. The dose chart is built on a calcium hypochlorite that is 65% available chlorine and calls for 2.0 ounces per 10,000 gallons per 1 ppm. The operator instead has a 78% available chlorine product. Using 16 ounces per pound, approximately how much of the 78% product is needed?
- A.2.5 pounds
- B.2.1 pounds✓ Answer
- C.33.3 pounds
- D.3.0 pounds
With the 65% product the dose would be 10 × 2 × 2.0 = 40 ounces, and a stronger product supplies the same chlorine in less weight, so the weight scales by 65 ÷ 78: 40 × 0.833 = 33.3 ounces ÷ 16 = about 2.1 pounds. Required weight varies inversely with available chlorine, so scaling by 78 ÷ 65 instead moves the answer the wrong direction.
Source: PHTA Pool & Spa Operator Handbook, disinfection chapter (percent available chlorine and dosage scaling)Report a problem with this question
19. A liquid sanitizer is labeled 12.5% available chlorine. Using the conversion that 1% equals 10,000 parts per million, what concentration does that label represent in ppm?
- A.1,250 ppm
- B.12,500 ppm
- C.125,000 ppm✓ Answer
- D.1,250,000 ppm
Percent and ppm are both ratios, and the stated factor makes the conversion a single multiplication: 12.5 × 10,000 = 125,000 ppm. Keeping the relationship straight explains why a few ppm in a pool is an extremely dilute solution compared with the concentrate in the drum.
Source: PHTA Pool & Spa Operator Handbook, essential calculations chapter (percent to parts per million conversion)Report a problem with this question
20. A 250,000-gallon pool has a cyanuric acid reading of 80 ppm. The operator drains 25% of the water and refills with fresh water that contains no cyanuric acid, then mixes thoroughly. Assuming nothing else changes the reading, what will the cyanuric acid level be?
- A.20 ppm
- B.80 ppm
- C.40 ppm
- D.60 ppm✓ Answer
Draining and refilling removes the dissolved substance in the same proportion as the water removed, so 75% of the original reading remains: 80 × 0.75 = 60 ppm. Dilution is the only practical way to lower a stable dissolved level like cyanuric acid, and the reading falls in direct proportion to the fraction of water replaced.
Source: PHTA Pool & Spa Operator Handbook, water balance chapter (dilution by partial drain and refill)Report a problem with this question
21. An operator uses the handbook interval for spa water replacement: days between replacements equals spa gallons divided by 3, then divided by the average number of bathers per day. A 750-gallon spa averages 25 bathers per day. How many days does the formula give?
- A.90 days
- B.30 days
- C.10 days✓ Answer
- D.3.3 days
Applying the formula in order gives 750 ÷ 3 = 250, then 250 ÷ 25 = 10 days. Both divisions matter: skipping the division by 3 triples the interval and understates how quickly a small, heavily used volume accumulates dissolved material.
Source: PHTA Pool & Spa Operator Handbook, spa and therapy operations chapter (spa water replacement interval formula)Report a problem with this question
22. Water flows at 300 gallons per minute through a pipe whose internal cross-sectional area is 0.0884 square feet. Using 7.5 gallons per cubic foot and 60 seconds per minute, what is the velocity of the water in feet per second?
- A.7.5 ft per second✓ Answer
- B.0.13 ft per second
- C.452 ft per second
- D.3.8 ft per second
Convert flow to cubic feet per minute, 300 ÷ 7.5 = 40, then divide by the pipe area to get 40 ÷ 0.0884 = 452 feet per minute, and 452 ÷ 60 = about 7.5 feet per second. Velocity is volume flow divided by cross-sectional area, so the same flow speeds up in a smaller pipe and slows down in a larger one.
Source: PHTA Pool & Spa Operator Handbook, water circulation chapter (flow, pipe area and water velocity)Report a problem with this question
Practice questions based on the Pool & Hot Tub Alliance (PHTA) Pool & Spa Operator Handbook and public CDC healthy-swimming guidance. CPO and Certified Pool/Spa Operator are marks of the Pool & Hot Tub Alliance; this site is not affiliated with or endorsed by PHTA. Water-quality limits, turnover requirements and bather loads are set by the health code where your facility operates — always follow that code and your local health department, and confirm current course requirements before testing. About the CPO certification →