Calculate the Volume of a Kidney Shaped Pool

A "how to" calculate the volume of a kidney-shaped pool. If you look online you will find several ways on how to approach this. It is not an exact science, but when the range of the various results has a difference of over 4000 gallons for the volume of the pool, well that is a lot of water!

If you look at the above image we will add some lengths with the conversion to decimal values.
length A = 22' = 22'
diameter B = 11'-4"= 11.33'
diameter C = 10'-4" = 10.33'
length d = 7'-6" = 7.5'
height = 1'-7" = 1.58'
average pool depth = 4'.6" = 4.5'

formula's used:
Circle: area = p r²
Trapezoid: area = (a+b) / 2*h
p = 3.14159

Solving for circle with diameter B:

diameter = 11.33 radius = 5.56 (half of the diameter)
3.14159 * 5.56² = 3.14159 *30.9136 = 97.12
Area of this circle = 97.12 sq ft

Solving for circle with diameter C:

diameter = 10.33 radius = 5.165 (half of the diameter)
3.14159 * 5.165² = 3.14159 * 26,667 = 83.92
Area of this circle = 83.92 sq ft

If you look at the above image, the ends represent half circles. To get the combined area for the two divide the full circle areas in half and add them together.
97.12 / 2 plus 83.92 / 2 = 48.56 + 41.96 = 90.52
The area of the two half circles = 90.52 sq ft

Next, you need to calculate the area in between these two half circles. This area represents a trapezoid.
A trapezoid is a four-sided shape with at least one set of parallel sides
side ab runs parallel to side cd
side ab is the same length as diameter B ab = 11.33'
side cd is the same length as diameter C cd = 10.33'

the total length of the pool = 22'
since the lengths ab and cd run parallel to each other there is one distance measurement you have to work with.
to get this length you have to subtract half of diameter B and half of diameter C from the total length.
22 - 5.56 - 5.165 = 11.275
the distance between the two parallel lines = 11.275

then using the trapezoid formula for area:
(11.33 + 10.33) / 2 * 11.275 = 122.108
the area of the trapezoid = 122.108sq ft

the total area then = 90.52 + 122.108 = 212.628 sq ft

If you look at the above image again you see a grey section at the bottom. It is included in thre calculation since it is within the red line area, This grey section needs to be subtracted from the pool square footage.

Here it represents a segment of a circle with;
length d = 7'-6" = 7.5' and a height of = 1'-7" = 1.58'
using a calculator, the area of this segment = 8.2 sq ft

subtract this from the total area from above:
212.628 - 8.2 = 204.4

The surface area for this Kidney shaped pool is 204.4 sq feet

Multiply this amount by the average pool depth of 4.5' to get the pool volume in cubic feet
204.4 * 4.5 = 918 cubic feet.

1 cubic foot = 7.48 US gallons
1 cubic foot = 6.23 Imperial gallons
1 cubic foot = 28.32 litres

Pool volume:
918 * 7.48 = 6866.64 US gallons
918 * 6.23 = 5719
918 * 28.32 = 25997.76 litres

Note:

If you plug the same values into the calculator the results will be slightly different. This how to uses rounded of numbers while the calculator uses all the digits.

Links:

Kidney Shaped Pool Volume Calculator
Metric Kidney Shaped Pool Volume Calculator