How to Estimate Pool and Spa Gallons

Why this matters

Every chemical label in pool service is written per gallon or per 10,000 gallons, so the volume on the customer's account is a multiplier on every dose the route ever puts in that water. A volume 20 percent high means every shock, every acid addition and every stabilizer dose runs 20 percent strong, every visit, until somebody re-measures. Most account volumes were typed in once, from a guess or from the previous company, and never checked. This card is the three formulas, the one input that carries most of the error (average depth), and a meter check that proves the number before it goes on the account.

The three formulas and their constants

POOL GALLONS (all dimensions in feet)
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RECTANGLE   L x W x avg depth x 7.48
ROUND       D x D x avg depth x 5.9
OVAL        L x W x avg depth x 5.9
            (true ellipse only, see below)

AVERAGE DEPTH, UNIFORM SLOPE
            (shallow + deep) / 2
AVERAGE DEPTH, BROKEN FLOOR
            sum of (section length x its avg)
            / total length

GALLONS PER INCH OF WATER = surface sq ft x 0.623
--------------------------------------------------

7.48 is gallons per cubic foot, owned by The Water Constants 7.48, 8.34 and 231. Length times width times depth is cubic feet; times 7.48 is gallons.

5.9 is 7.48 x 0.7854 (pi / 4) = 5.875, rounded up. A circle covers 0.7854 of the square drawn around its diameter, so a round pool holds 0.785 of the box it fits in. The rounding costs 0.4 percent, which is far inside the error of any depth measurement. For the mistake of feeding a radius into a diameter formula, see related: The Pool Dose Figured From the Diameter as the Radius.

For an ellipse, the same 5.9 works because an ellipse covers 0.7854 of its bounding rectangle, exactly as a circle covers its square. That only holds for a true ellipse, and many pools called oval are not one.

0.623 is 7.48 / 12, the gallons in one square foot of surface 1 in deep. It drives the meter check at the end.

The steps

1. Measure the water, not the pool. Length and width at the water line, inside the walls. Depth from the water surface to the floor, not from the coping. Water normally sits several inches below the deck, and figuring depth from the deck adds that whole band to every section. On a commercial pool the posted depth markers describe the design water level, which may not be where the water is today; measure rather than reading the tile.

Hazard at this step: measure from the deck with a pole, a weighted tape or a telescoping pole marked in inches. Do not enter the water to measure. If the pump is running, keep hands and poles clear of the main drain and skimmer intake, where suction can trap a tool or a limb. If the water is green or cloudy enough that you cannot see the floor, you also cannot see a drop-off or debris, which is another reason to stay out.

2. Find where the floor changes slope, and measure each section. This is the step that sets the accuracy. A pool floor is rarely one straight ramp. Most have a flat shallow section, a transition slope, and a deep section. Walk the deck with the pole and take depth at the shallow wall, at the start of the transition, at the end of the transition and at the deep point. Write the distance along the pool between each reading.

3. Weight the depths by section length. For a floor that genuinely slopes uniformly from end to end, (shallow + deep) / 2 is correct. For anything else, multiply each section's length by its average depth, add them, and divide by the total length. That is a weighted mean, the right average when the pieces are different sizes; see related: Averaging Readings: Mean, Median and Weighted.

4. Pick the formula from the shape, not the name. A rectangle with radius corners can be figured as a rectangle; the corners take out well under 1 percent on a residential pool. A "kidney," an L, a pool with a sun shelf or a spa spillover gets broken into pieces, each with its own area and its own depth, and the pieces added. The method of breaking a shape into rectangles, triangles and circle pieces is owned by How to Find the Area of an Irregular Room by Decomposition.

5. Run the meter check before the number goes on the account. At the next top-off, read the water meter (or a hose flow meter) before and after raising the water a measured number of inches. Surface area x 0.623 x inches added is what should have gone in. If the meter and the math agree within about 10 percent, the surface area is right, and the surface area is half of the volume problem.

6. Write the inputs on the account, not just the total. Dimensions, section lengths and depths, the formula used and the date. The next tech can then re-check one input instead of re-measuring everything, and a total with no inputs behind it is how bad numbers survive for years.

Worked example 1: the uniform-slope rectangle

A 16 by 32 ft pool runs from 3 ft deep at the shallow wall to 6 ft deep at the deep wall on a single even slope. The pole readings in between fall on the straight line, which confirms the slope is uniform.

Line  Item                         Value      Unit
1     Length                        32.0      ft
2     Width                         16.0      ft
3     Surface = L1 x L2            512.0      sq ft
4     Avg depth = (3 + 6) / 2        4.5      ft
5     Volume = L3 x L4           2,304        cu ft
6     Gallons = L5 x 7.48       17,234        gal
7     Per inch = L3 x 0.623        319        gal/in

The pool holds about 17,200 gallons. Line 7 is the meter-check figure: a top-off that raises the level 2 in should register close to 638 gallons on the meter (319 x 2).

Worked example 2: same outline, broken floor

Now take a different 16 by 32 ft pool, the common residential shape. The poles find a flat 3.5 ft shallow section 20 ft long, a 6 ft transition from 3.5 to 8 ft, and a 6 ft deep section at 8 ft.

Line  Section        Length   Avg depth   Length x depth
1     Shallow flat    20 ft    3.50 ft      70.0 ft x ft
2     Transition       6 ft    5.75 ft      34.5 ft x ft
3     Deep section     6 ft    8.00 ft      48.0 ft x ft
4     Totals          32 ft                152.5 ft x ft
5     Weighted avg = 152.5 / 32 = 4.77 ft
6     Gallons = 512 x 4.766 x 7.48 = 18,251 gal
7     Shortcut (3.5 + 8) / 2 = 5.75 ft
8     Shortcut gallons = 512 x 5.75 x 7.48 = 22,021 gal

The shortcut puts 3,770 more gallons on the account (22,021 minus 18,251), which is 21 percent too high (22,021 / 18,251 = 1.21). Every dose from that number runs about a fifth strong, and on a chemical like acid that is the difference between a correction and an overshoot. The transition's 5.75 ft average on line 2 is itself the uniform-slope rule applied to one section, which is the right place for it.

The deep section is treated as flat here. A real hopper has sloped sides, so it holds somewhat less than a flat-bottomed box of the same length, which means 18,251 is still a little high and a dose figured from it runs slightly strong. For a chemical where excess does harm, dose a little under the computed amount and test up to target; step 6 of How to Figure the Volume of a Round or Rectangular Tank states that rounding rule.

Worked example 3: the round pool and the oval that is not an ellipse

Round. A 24 ft round above-ground pool with water 4 ft deep across a flat floor:

• 24 x 24 = 576 sq ft
• 576 x 4 ft = 2,304
• 2,304 x 5.9 = 13,594 gallons, about 13,600

Check from the box: 24 x 24 x 4 x 7.48 = 17,234 gallons for the square box, and 0.785 of that is 13,529. The gap of about 65 gallons is the 5.875-to-5.9 rounding plus the 0.785, both well under 1 percent. (Note that the box for this round pool holds exactly what the rectangle in example 1 holds, because 576 x 4 and 512 x 4.5 are both 2,304 cubic feet. That is a coincidence of these dimensions, not a rule.)

Oval. A 15 by 30 ft above-ground "oval," 4 ft deep. The oval formula gives 15 x 30 x 4 x 5.9 = 10,620 gallons. But most above-ground ovals are not ellipses. They are straight-sided: a rectangle with a half circle on each end, which a measuring tape along the side shows immediately because the long walls run parallel. Figured as that shape:

• Rectangle between the ends: 15 ft wide x 15 ft long (30 ft overall minus the two 7.5 ft half-circle ends) = 225 sq ft
• Two half circles of 15 ft diameter make one full circle: 0.7854 x 15 x 15 = 176.7 sq ft
• Surface = 225 + 176.7 = 401.7 sq ft
• Gallons = 401.7 x 4 x 7.48 = 12,019

The ellipse formula on a straight-sided pool undercounts by 1,399 gallons (12,019 minus 10,620), 13 percent of the ellipse figure. Here the error runs low, so every dose is about 12 percent weak (10,620 / 12,019 = 0.88), which shows up as a pool that never quite holds its chlorine.

Spas and the shapes you cannot measure

A spa is the worst candidate for geometry. Seats, footwells, steps and a contoured shell mean the water is nothing like a box: a 7 by 7 ft spa with 3 ft of water would figure as 49 x 3 x 7.48 = 1,100 gallons as a box, and the real volume is well below that once the molded seats are taken out. Two better sources, in order:

1. The maker's stated water capacity, on the spa's spec label, in the owner's manual or in its documentation. For a portable spa this is the number to use.
2. A metered fill. On a spa drained for service, read the water meter or a hose flow meter before and after the refill to the operating level. That measures the real water, shell contours included. A timed fill from a measured hose flow works the same way: see related: How to Measure Flow With a Bucket and a Stopwatch.

For an in-ground spa attached to a pool, figure the pool and the spa separately and record both. They are often dosed together through one system but they are serviced, drained and heated separately, and one combined number helps with none of those jobs.

What changes the answer

• The water level is off normal. After a storm or a leak the level can be inches high or low. On the 16 by 32 ft pool each inch is 319 gallons, so a level 3 in below normal holds about 957 gallons less than the account number. For dosing, figure from where the water is.
• The floor was resurfaced or the pool was remodeled. Added plaster, a new sun shelf or a filled-in deep end all change the volume. A remodel is a re-measure, not an adjustment.
• A vinyl-liner floor is not where the drawing says. Liner floors are hand-troweled and settle, so the depth points come from the pole, never from the original plans.

How to verify you got this right

1. The meter check closes. Surface area x 0.623 x inches raised is within about 10 percent of what the meter recorded.
2. The average depth came from measured sections, and the account shows them.
3. The shape was confirmed with a tape. Parallel long walls mean straight-sided, not ellipse.
4. The box check agrees for round and oval pools, within the rounding of the constants.
5. The first dose behaves. A chemical added at the label rate for the computed volume should move the test reading by about what the label predicts. A pool that consistently over- or under-responds to correct doses is telling you the volume is wrong.

References

• See related: The Water Constants 7.48, 8.34 and 231
• See related: How to Find the Area of an Irregular Room by Decomposition
• See related: Averaging Readings: Mean, Median and Weighted
• See related: The Pool Dose Figured From the Diameter as the Radius
• Spa manufacturer specification labels and owner's manuals for stated water capacity