Start with the shape, then the depth, then the conversion
All three shapes here work the same way: get the surface area in square feet, multiply by the average depth in feet to get cubic feet, then multiply by 7.4805 to get US gallons.
| Shape | Surface area |
|---|---|
| Rectangular | length × width |
| Round | π × radius², or 0.7854 × diameter² |
| Oval (true ellipse) | 0.7854 × length × width |
The 7.4805 comes from 1,728 cubic inches in a cubic foot divided by 231 cubic inches in a gallon. You will see 7.5 used everywhere, and for a pool it is close enough — it overstates by about a quarter of a percent, which on a 20,000 gallon pool is 52 gallons, well inside the error in your depth measurement. This page uses the exact figure because it costs nothing to.
A 16 by 32 foot rectangular pool averaging 5 feet deep works out at 2,560 cubic feet, which is 19,150 gallons. If you have seen 19,200 for the same pool, that is the 7.5 rounding. Both are fine; neither is more accurate than your estimate of the average depth.
Average depth is where the error lives
Everything above is arithmetic that cannot be wrong. The average depth is a measurement, and it is usually the weakest number in the calculation.
Averaging the shallow end and the deep end gives the right answer only for a floor that slopes evenly from one to the other, which is the common case in a simple vinyl-liner pool and the rare case in a gunite one. A typical built pool has a flat shallow shelf that runs for a third or half of the length, then a slope, then a deep hopper that occupies less area than people picture. Take the two extremes on a pool like that and you will overstate the volume, often by a tenth.
The fix costs ten minutes. Walk the length with a pole marked in feet, take the depth every few feet, and average those readings. It is a crude integration and it is far more honest than averaging two numbers. If the pool has an odd outline as well, break it into rectangles and part-circles, work each one out, and add them.
The other check available to almost everyone is the water meter. Note the reading before you fill, note it after, and the difference is the volume with no geometry involved at all. If your calculated figure and your metered figure differ by more than a few percent, trust the meter.
Turnover, and what the number means
Turnover time is the volume divided by the filtration flow rate — how long the pump takes to move a quantity of water equal to the whole pool through the filter. A pool of 20,000 gallons with 60 GPM through the filter turns over in about 5.6 hours.
What it is not is a guarantee that all the water has been filtered. The pool is not a queue. Filtered water returns and mixes with unfiltered water immediately, so after one nominal turnover a good fraction of the original water has still never been through the filter. The usual estimate is that one turnover processes on the order of two thirds of it, and it takes several turnovers to get most of the way. This is why the target sits at more than one turnover a day rather than exactly one.
Six to ten hours is the range most residential pools are designed around, with commercial and high-bather-load water treated much more aggressively. The flow to enter is the flow through the filter with the system as it stands — the pump's rated flow is measured at a head the plumbing does not provide, and a dirty filter drops it further. If you want the real number, read it off a flow meter or work it back from the filter pressure and the pump curve.
Volume as the basis for dosing
Parts per million is a mass ratio: one part of something per million parts of water. Since water weighs about 8.345 lb per gallon, the pounds of active ingredient needed for a given ppm change comes out as gallons times 8.345 times ppm divided by a million. For 10,000 gallons and 1 ppm, that is 0.083 lb, or about 1.34 ounces. If the product is not pure, divide by its percentage strength.
Every part of that is arithmetic and none of it is chemistry. Real pool products do not all deliver their active ingredient one-for-one — some consume it in side reactions, some raise other things you did not want raised, some behave differently at different pH. The dose arithmetic here gives you the mass a perfect product would need, which is the correct starting point and the wrong finishing point. The label on the container is the finishing point. Dose in stages, test between them, and never add two products at once.
Where this calculation earns its keep is in showing you how sensitive dosing is to the volume estimate. If you have been treating a pool as 20,000 gallons and it is really 17,500, every dose you have ever added was fourteen percent heavy, which is exactly the kind of persistent bias that makes chemistry feel unpredictable when it is actually being perfectly consistent about the wrong number.
Questions people ask
How many gallons is a 16 by 32 foot pool?
It depends on the depth, which is the part nobody mentions when they quote a figure. At a constant 4 feet it is 15,320 gallons, at an average of 5 feet it is 19,150, and at an average of 6 feet it is 22,980. The arithmetic is 16 times 32 times the average depth to get cubic feet, times 7.4805 for gallons. If the pool has a shallow end and a deep end, the average depth is not the mean of the two unless the floor slopes evenly for the whole length, and on most built pools it does not. Measure the depth at several points and average those.
Should I use 7.5 gallons per cubic foot?
You can, and almost every pool reference does. The exact figure is 7.4805, so 7.5 overstates the volume by about a quarter of a percent — on a 20,000 gallon pool that is 52 gallons, which is far smaller than the uncertainty in your depth measurement. The rounding is not what will make your chemistry wrong. What will is a pool that is a different shape from the one you assumed, or a depth average taken from two extremes on a floor that is not a simple ramp.
What is a good turnover rate for a residential pool?
Most residential pools are designed around a turnover somewhere in the six to ten hour range, which works out to two to four turnovers a day. That is common practice rather than a universal figure — commercial and public pools are held to considerably more aggressive requirements set by health authorities, and those requirements vary by jurisdiction and by the type of water. The flow rate that matters is what actually passes through the filter with the plumbing you have, not the pump nameplate. Head losses in the suction and return lines, the filter itself and any heater cut the delivered flow substantially below the rated figure, and a loaded filter cuts it further as it loads.
How do I work out the volume of an irregular or kidney-shaped pool?
Break it into shapes you can calculate and add them. A kidney is usually well approximated by two overlapping circles or by a rectangle with a curved bite taken out, and a freeform pool can be treated as a series of rectangles laid along its length with the width measured at the middle of each one. Do the areas first, add them to get one surface area, then apply the average depth to the whole thing. The alternative that beats all of this for accuracy is the water meter: read it before and after a fill, and you have measured the volume rather than estimated it.
Does the volume calculation include the skimmer, the lines and the filter?
No, and for dosing purposes it usually should. The plumbing, pump, filter and heater hold water that is part of the circulating system, and on a pool with long runs to an equipment pad that can be a few hundred gallons. It is a small percentage of a full-size pool and a meaningful one on a small spa. The pipe volume calculator on this site will give you the line volume if you know the size and length of the runs; add it to the pool figure if you want the total in circulation.