The short formula for gallons in a round pool is:
Diameter * Diameter * Height * 5.9.
Note that Diameter and Height are both in feet, and Height is the height of the water, not the pool wall.
So if you have a 4' high pool, your water is probably 3.5 to 3.75 feet high or between 6" to 3" below the rail.
The LONG formula is from your high school geometry:
Pi*R-squared*height*7.48
7.48 is the number of gallons in a cubic foot of water.

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I had to look at your byline to see that it wasn't posted by ChemGeek
Happy swimming!