It depends on two other factors viz;-
#1 How deep is the pool
#2 Rate of flow of the inflowing water.
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29,952 GALLONS
a pool is a cylinder. the volume is the surface area times the depth. the surface area is pi ( 3.14) times the radius squared which in your case is 3.14 x 12 x12 =462 square feet. multiply the depth in feet 4 feet ( you don't fill it right to the top) =1848 cubic feet. there are 8 gallons in a cubic foot of water therefore you need 14,784 gallons of water to fill a 24 by 52 foot round pool
about 45,000 Gal
Assuming that 24' is the diameter of the pool, then the volume of the pool is 3,387,491.39 cubic inches. There are 231 cubic inches in a gallon, so the pool holds 14,664.46 gallons of water.
If this is a round pool that is 27 feet across by 52 inches tall and you fill it with 4 feet (48 inches) of water, the total volume would be 17,204 gallons of water.