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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.

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  1. 1. A rectangular commercial pool measures 60 ft long by 25 ft wide. The bottom runs on a constant slope from 3 ft deep at the shallow end to 9 ft deep at the deep end. Using 7.5 gallons per cubic foot, what is the pool's volume?

    • A.33,750 gallons
    • B.67,500 gallons✓ Answer
    • C.101,250 gallons
    • D.84,375 gallons

    Average depth is (3 + 9) / 2 = 6 ft, so 60 x 25 x 6 = 9,000 cubic feet and 9,000 x 7.5 = 67,500 gallons. The tempting wrong answer is 101,250 gallons, which comes from using the deep-end depth of 9 ft instead of the average depth; 33,750 gallons uses the shallow-end 3 ft, and 84,375 gallons comes from mistakenly plugging the 7.5 conversion factor in as the depth.

    Source: PHTA Pool & Spa Operator Handbook, rectangular pool volume calculationReport a problem with this question

  2. 2. A circular commercial spa-pool is 20 ft in diameter with a uniform depth of 4 ft. Using pi = 3.14 and 7.5 gallons per cubic foot, what is its volume?

    • A.18,840 gallons
    • B.37,680 gallons
    • C.2,355 gallons
    • D.9,420 gallons✓ Answer

    The radius is half the diameter, so 3.14 x 10 x 10 x 4 x 7.5 = 9,420 gallons. The classic error is 37,680 gallons, produced by squaring the 20 ft diameter as if it were the radius; 18,840 gallons multiplies diameter by radius, and 2,355 gallons uses a 5 ft radius, a quarter of the diameter.

    Source: PHTA Pool & Spa Operator Handbook, circular pool volume calculationReport a problem with this question

  3. 3. An operator tops off a rectangular pool that measures 50 ft by 20 ft, raising the water level by 6 inches. Using 7.5 gallons per cubic foot, how much water was added?

    • A.3,750 gallons✓ Answer
    • B.500 gallons
    • C.45,000 gallons
    • D.7,500 gallons

    Six inches is 0.5 ft, so 50 x 20 x 0.5 = 500 cubic feet and 500 x 7.5 = 3,750 gallons. The most tempting error is 45,000 gallons, which treats the 6 inches as 6 feet; 500 gallons stops at cubic feet without applying 7.5 gallons per cubic foot, and 7,500 gallons assumes a full 1 ft rise.

    Source: PHTA Pool & Spa Operator Handbook, volume added by a change in water levelReport a problem with this question

  4. 4. An L-shaped pool is treated as two sections. The main section is 80 ft by 40 ft with an average depth of 4 ft; the wing is 25 ft by 20 ft with an average depth of 3.5 ft. Using 7.5 gallons per cubic foot, what is the total volume?

    • A.13,125 gallons
    • B.97,750 gallons
    • C.96,000 gallons
    • D.109,125 gallons✓ Answer

    Each section is computed separately and then added: 80 x 40 x 4 x 7.5 = 96,000 gallons and 25 x 20 x 3.5 x 7.5 = 13,125 gallons, for 109,125 gallons. The tempting error is 96,000 gallons, which reports only the main section; 13,125 gallons reports only the wing, and 97,750 gallons adds the wing's 1,750 cubic feet without converting them to gallons.

    Source: PHTA Pool & Spa Operator Handbook, volume of irregular pools computed as a sum of sectionsReport a problem with this question

  5. 5. A pool holds 90,000 gallons and the flow meter reads a steady 250 gallons per minute. What is the turnover time?

    • A.360.0 hours
    • B.6.0 hours✓ Answer
    • C.60.0 hours
    • D.0.6 hours

    Turnover in hours is gallons divided by gallons per minute and then divided by 60: 90,000 / 250 = 360 minutes, and 360 / 60 = 6.0 hours. The trap answer is 360.0 hours, which is the minutes figure reported as hours because the divide-by-60 step was skipped; 60.0 hours divides the minutes by 6 instead of 60, and 0.6 hours divides by 600.

    Source: PHTA Pool & Spa Operator Handbook, turnover time calculationReport a problem with this question

  6. 6. A pool contains 108,000 gallons and the health department having jurisdiction requires a 6-hour turnover. What flow rate must the recirculation system deliver?

    • A.1,800 gallons per minute
    • B.18,000 gallons per minute
    • C.3,000 gallons per minute
    • D.300 gallons per minute✓ Answer

    Flow equals volume divided by turnover hours divided by 60: 108,000 / 6 = 18,000 gallons per hour, and 18,000 / 60 = 300 gallons per minute. The tempting error is 18,000 gallons per minute, the hourly figure reported as a per-minute rate; 1,800 gallons per minute divides only by 60 and ignores the 6 hours, and 3,000 gallons per minute divides by 36 because 6 hours was multiplied by 6 instead of 60.

    Source: PHTA Pool & Spa Operator Handbook, flow rate required for a given turnoverReport a problem with this question

  7. 7. A 144,000-gallon pool recirculates at a measured 400 gallons per minute and the pump runs continuously. How many complete turnovers occur in 24 hours?

    • A.4.0 turnovers✓ Answer
    • B.0.1 turnovers
    • C.6.0 turnovers
    • D.24.0 turnovers

    One turnover takes 144,000 / 400 = 360 minutes, or 6 hours, so 24 / 6 = 4.0 turnovers per day. The most attractive error is 6.0 turnovers, which is the turnover time in hours mistaken for a count; 0.1 turnovers comes from skipping the divide-by-60 and treating 360 as hours, and 24.0 turnovers assumes one turnover every hour.

    Source: PHTA Pool & Spa Operator Handbook, turnovers per dayReport a problem with this question

  8. 8. A high-rate sand filter with 12 square feet of filter surface area is passing 240 gallons per minute. What is the filtration rate?

    • A.0.05 gallons per minute per square foot
    • B.2,880.00 gallons per minute per square foot
    • C.20.00 gallons per minute per square foot✓ Answer
    • D.40.00 gallons per minute per square foot

    Filtration rate is flow divided by filter area: 240 / 12 = 20.00 gallons per minute per square foot. The tempting error is 2,880.00, which multiplies flow by area instead of dividing; 0.05 inverts the fraction as area over flow, and 40.00 halves the area to 6 square feet, a habit carried over from grid filters that are counted on two sides.

    Source: PHTA Pool & Spa Operator Handbook, filtration rate as flow divided by filter surface areaReport a problem with this question

  9. 9. A diatomaceous earth filter holds 24 grid elements. Each grid presents 2.5 square feet of surface on each of its two faces, and water is filtered through both faces. What is the filter's effective surface area?

    • A.30.00 square feet
    • B.120.00 square feet✓ Answer
    • C.48.00 square feet
    • D.60.00 square feet

    Both faces of every grid filter, so the area is 24 x 2.5 x 2 = 120.00 square feet. The most common mistake is 60.00 square feet, which counts only one face per grid; 48.00 square feet counts two faces but uses 1 square foot per face instead of 2.5, and 30.00 square feet divides the one-sided figure by 2 instead of doubling it.

    Source: PHTA Pool & Spa Operator Handbook, effective filter area of a diatomaceous earth grid element arrayReport a problem with this question

  10. 10. A cartridge filter bank must pass 375 gallons per minute, and the manufacturer's design filtration rate is 0.375 gallons per minute per square foot. How much filter surface area is required?

    • A.140.63 square feet
    • B.100.00 square feet
    • C.500.00 square feet
    • D.1,000.00 square feet✓ Answer

    Required area equals flow divided by filtration rate: 375 / 0.375 = 1,000.00 square feet. The tempting error is 140.63 square feet, from multiplying 375 by 0.375 instead of dividing; 100.00 square feet is a decimal slip that divides by 3.75, and 500.00 square feet doubles the stated rate to 0.75 before dividing.

    Source: PHTA Pool & Spa Operator Handbook, required filter surface area from flow and design filtration rateReport a problem with this question

  11. 11. A 20,000-gallon pool must be heated from 68 degrees F to 82 degrees F. Using 8.33 pounds per gallon and the rule that one BTU raises one pound of water one degree F, how many BTUs are required?

    • A.233,240 BTU
    • B.280,000 BTU
    • C.2,332,400 BTU✓ Answer
    • D.166,600 BTU

    BTUs equal gallons x 8.33 x the temperature rise, and the rise is 82 - 68 = 14 degrees: 20,000 x 8.33 x 14 = 2,332,400 BTU. The tempting error is 280,000 BTU, which multiplies gallons by the rise but drops the 8.33 pounds per gallon; 166,600 BTU omits the temperature rise entirely, and 233,240 BTU is a decimal slip of one factor of ten.

    Source: PHTA Pool & Spa Operator Handbook, heater BTU sizing calculationReport a problem with this question

  12. 12. A dosage chart states that 2 ounces of a granular chlorine product per 10,000 gallons raises free chlorine by 1 ppm. An operator must raise free chlorine by 3 ppm in a 45,000-gallon pool. Using 16 ounces per pound, how much product is needed?

    • A.0.56 pounds
    • B.1.69 pounds✓ Answer
    • C.0.11 pounds
    • D.27.00 pounds

    The dose is (45,000 / 10,000) x 3 ppm x 2 ounces = 27 ounces, and 27 / 16 = 1.69 pounds. The classic trap is 27.00 pounds, the ounce figure reported as pounds because the divide-by-16 was skipped; 0.56 pounds forgets to multiply by the 3 ppm change, and 0.11 pounds divides by 16 a second time.

    Source: PHTA Pool & Spa Operator Handbook, chemical dosage chart per 10,000 gallonsReport a problem with this question

  13. 13. A chart states that 10.7 fluid ounces of a liquid chlorine product per 10,000 gallons raises free chlorine by 1 ppm. An operator must raise free chlorine by 2 ppm in a 60,000-gallon pool. Using 128 fluid ounces per gallon, how much product is needed?

    • A.1.00 gallons✓ Answer
    • B.128.40 gallons
    • C.0.50 gallons
    • D.8.03 gallons

    The dose is (60,000 / 10,000) x 2 ppm x 10.7 = 128.4 fluid ounces, and 128.4 / 128 = 1.00 gallon. The tempting error is 128.40 gallons, the fluid-ounce figure reported as gallons; 8.03 gallons divides by 16 as if the product were dry, and 0.50 gallons forgets to multiply by the 2 ppm change.

    Source: PHTA Pool & Spa Operator Handbook, converting a liquid chemical dose from fluid ounces to gallonsReport a problem with this question

  14. 14. A chart figure of 2 ounces per 10,000 gallons per 1 ppm assumes a product of 100 percent strength. The product on hand is 65 percent available chlorine. How much of it raises free chlorine by 1 ppm in a 40,000-gallon pool?

    • A.12.31 ounces✓ Answer
    • B.8.00 ounces
    • C.123.10 ounces
    • D.5.20 ounces

    At full strength the dose is (40,000 / 10,000) x 1 ppm x 2 = 8 ounces, and a weaker product requires dividing by its decimal strength: 8 / 0.65 = 12.31 ounces. The tempting error is 8.00 ounces, which skips the strength adjustment entirely; 5.20 ounces multiplies by 0.65 instead of dividing, and 123.10 ounces misplaces the decimal by dividing by 0.065.

    Source: PHTA Pool & Spa Operator Handbook, adjusting a chemical dose for product strengthReport a problem with this question

  15. 15. A pool tests at 4.2 ppm total chlorine and 1.0 ppm free chlorine. The operator will breakpoint chlorinate by raising free chlorine to ten times the combined chlorine. By how many ppm must free chlorine be raised?

    • A.3.2 ppm
    • B.42.0 ppm
    • C.31.0 ppm✓ Answer
    • D.10.0 ppm

    Combined chlorine is total minus free, 4.2 - 1.0 = 3.2 ppm; ten times that is a 32.0 ppm target, and the pool already holds 1.0 ppm, so the increase is 31.0 ppm. The tempting error is 42.0 ppm, from multiplying total chlorine by ten instead of combined chlorine; 10.0 ppm multiplies the free chlorine by ten, and 3.2 ppm reports the combined chlorine itself.

    Source: PHTA Pool & Spa Operator Handbook, breakpoint chlorination calculation, with CDC Healthy Swimming guidance on combined chlorineReport a problem with this question

  16. 16. A 24,000-gallon pool needs its free chlorine raised by 10 ppm to reach breakpoint. The chart figure is 10.7 fluid ounces of liquid chlorine per 10,000 gallons per 1 ppm, and there are 128 fluid ounces in a gallon. How much liquid chlorine is required?

    • A.2.01 gallons✓ Answer
    • B.16.05 gallons
    • C.256.80 gallons
    • D.0.20 gallons

    The dose is (24,000 / 10,000) x 10 ppm x 10.7 = 256.8 fluid ounces, and 256.8 / 128 = 2.01 gallons. The tempting error is 256.80 gallons, the fluid-ounce total reported as gallons; 16.05 gallons divides by 16 instead of 128, and 0.20 gallons uses a 1 ppm change instead of the 10 ppm the breakpoint demands.

    Source: PHTA Pool & Spa Operator Handbook, chemical dosing at breakpoint chlorinationReport a problem with this question

  17. 17. A pool's cyanuric acid measures 150 ppm. The operator drains 40 percent of the water and refills with fill water that contains no cyanuric acid. What will the cyanuric acid level be after the pool is mixed?

    • A.105 ppm
    • B.60 ppm
    • C.110 ppm
    • D.90 ppm✓ Answer

    Draining 40 percent leaves 60 percent of the original stabilizer, so 150 x 0.60 = 90 ppm. The tempting error is 60 ppm, which reports 150 x 0.40, the share that was removed rather than what remains; 110 ppm subtracts 40 ppm instead of 40 percent, and 105 ppm applies a 30 percent drain.

    Source: PHTA Pool & Spa Operator Handbook, dilution by partial drain and refillReport a problem with this question

  18. 18. A pool measures 2,800 ppm total dissolved solids. The operator drains one quarter of the water and refills with fill water measuring 200 ppm total dissolved solids. What is the resulting level after mixing?

    • A.2,150 ppm✓ Answer
    • B.700 ppm
    • C.2,100 ppm
    • D.2,600 ppm

    Three quarters of the old water remains and one quarter is new: (0.75 x 2,800) + (0.25 x 200) = 2,100 + 50 = 2,150 ppm. The tempting error is 2,100 ppm, which ignores the dissolved solids the fill water brings in; 700 ppm reports only the quarter removed, and 2,600 ppm subtracts 200 ppm outright instead of blending.

    Source: PHTA Pool & Spa Operator Handbook, dilution of dissolved solids by partial drain and refillReport a problem with this question

  19. 19. Water moves through a suction pipe whose cross-sectional area is 0.0884 square feet at a velocity of 6 feet per second. Using 7.5 gallons per cubic foot, what is the flow rate?

    • A.119.3 gallons per minute
    • B.31.8 gallons per minute
    • C.238.7 gallons per minute✓ Answer
    • D.4.0 gallons per minute

    Area times velocity gives 0.0884 x 6 = 0.5304 cubic feet per second; times 7.5 is 3.978 gallons per second, and times 60 is 238.7 gallons per minute. The tempting error is 4.0 gallons per minute, which is the per-second figure reported per minute; 31.8 gallons per minute omits the 7.5 gallons per cubic foot, and 119.3 gallons per minute uses only half the stated pipe area.

    Source: PHTA Pool & Spa Operator Handbook, flow from velocity and pipe cross-sectional areaReport a problem with this question

  20. 20. A commercial spa holds 1,500 gallons and averages 25 bathers per day. Using the interval formula of spa gallons divided by 3, then divided by average users per day, how often should the water be replaced?

    • A.6.7 days
    • B.20.0 days✓ Answer
    • C.60.0 days
    • D.180.0 days

    Applying the formula, 1,500 / 3 = 500, and 500 / 25 = 20.0 days. The tempting error is 60.0 days, which divides gallons straight by bathers and skips the divide-by-3 step; 6.7 days divides by 3 a second time, and 180.0 days multiplies by 3 instead of dividing.

    Source: PHTA Pool & Spa Operator Handbook, spa water replacement interval formulaReport a problem with this question

  21. 21. A pool is 75 ft by 30 ft, with a constant slope from 3.5 ft deep to 8.5 ft deep. The code having jurisdiction requires a 6-hour turnover. Using 7.5 gallons per cubic foot, what flow rate is needed?

    • A.164.1 gallons per minute
    • B.281.3 gallons per minute✓ Answer
    • C.28.1 gallons per minute
    • D.46.9 gallons per minute

    Average depth is (3.5 + 8.5) / 2 = 6 ft, so the volume is 75 x 30 x 6 x 7.5 = 101,250 gallons, and 101,250 / 6 / 60 = 281.3 gallons per minute. The tempting error is 164.1 gallons per minute, which uses the shallow-end 3.5 ft as if it were the average depth; 46.9 gallons per minute divides by 36 after multiplying 6 hours by 6, and 28.1 gallons per minute divides by 600 instead of 60.

    Source: PHTA Pool & Spa Operator Handbook, average depth and required flow rate for a stated turnoverReport a problem with this question

  22. 22. A round commercial spa is 8 ft in diameter with an average water depth of 3.5 ft. Using pi = 3.14 and 7.5 gallons per cubic foot, what is its volume?

    • A.659 gallons
    • B.176 gallons
    • C.1,319 gallons✓ Answer
    • D.330 gallons

    The radius is 4 ft, so 3.14 x 4 x 4 x 3.5 = 175.84 cubic feet and 175.84 x 7.5 = 1,319 gallons. The tempting error is 176 gallons, the cubic-foot figure reported as gallons because the 7.5 conversion was skipped; 330 gallons uses a 2 ft radius, a quarter of the diameter, and 659 gallons averages the already-average depth down to 1.75 ft.

    Source: PHTA Pool & Spa Operator Handbook, circular spa volume calculationReport 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 →