Calculating the capacity a pool or spa requires the volume and surface area of the pool or spa. Calculating a pool's area in square meters or feet is the first step in determining information including meters cubed or gallons, maximum capacity of swimmers and other critical information about your pool.
Geometric Formulas
We can use a few simple formulas to calculate pool size. Following are the basic formulas and calculations to determine surface areas:
Legend
- A = Area
- L = Length
- W = Width
- H = Height
- r = Radius
- d = Diameter
- Pi (π) = 3.14 constant
- Area of a square or rectangle: A = L x W
- Area of a right triangle: A = (L x W)/2
- Area of a circle: A = π x r x r
How to Calculate Volume
Calculated the cubic volume by including the surface area and depth of the pool. For accurate calculations, the pool should be divided into various areas according to the depth.
Constant Depth Pools: Square or Rectangular
Length x width x average depth = volume (in meters cubed)
Length x width x depth x 7.5 = volume (in gallons)
Length times width gives the surface area of the pool. Multiplying that by the depth gives the volume in cubic meters.
If you’d like to find the pool volume in gallons, multiply your results by 7.5, as there are 7.5 gallons for each cubic foot.
Variable Depth Pools: Square and Rectangular
Length x width x average depth = volume (in meters cubed)
Length x width x average depth x 7.5 = volume (in gallons)
Length times width gives the surface area of the pool. Multiplying that by the average depth gives the volume in cubic meters.
If you’d like to find the pool volume in gallons, multiply your results by 7.5, as there are 7.5 gallons for each cubic foot.
Measure the length, width, and average depth of the pool, rounding each measurement off to the nearest meter.
If the shallow end is 0.5 m and the deep end is 1 m, and assuming the slope of the pool bottom is gradual and even, then the average depth is 0.75 m
- Average depth = (Depth at the shallow end + Depth at the deep end) / 2
- Average depth = ( 0.5 + 1 ) / 2 = 0.75 m
If the majority the pool is shallow and then drops off suddenly to a deep end, you will have a different average depth. In such a case, you might want to treat the pool as two parts. Measure the length, width, and average depth of the shallow section, then take the same measurements for the deeper section. Calculate the volume of the shallow portion and add that to the volume you calculate for the deeper portion.
Make sure to use the actual water depth in your calculations, not the depth of the container. Calculating the accurate volume is crucial, as it could mean serious errors when adding chemicals, which are added based on the volume of water.
Circular Pools
The formula: π x radius squared x average depth = volume
The number 3.14, refers to pi, which is a mathematical constant. The radius is half of the diameter, so measure the distance across the widest part of the circle and divide it by 2 to find the radius. Squared means the number is multiplied by itself, so multiply the radius by itself.
For example, if the diameter is 3 m, we can half this value for a radius of 1.5 m. Now to find the radius squared, multiply 1.5 m by itself to arrive at 2.25 m2.
With this information, you can return to the formula:
π x radius squared x average depth = volume
3.14 x 2.25 m squared x 0.75 m = 150 m3
In measuring the capacity of a spa, you might need to calculate two or three sections within the hot tub and add them together to arrive at a total volume due to the seats. Therefore, you might want to treat it as two separate volumes-the volume above the seat line and the volume below.
Irregular Shapes
In order to find the capacity of irregular shaped pools, imagine the hot tub or pool as a grouping of smaller, regular shapes. Take the measurements of these areas and refer to the above calculation to find the area of each square, rectangle, or circle. Add the volumes together to determine the total capacity.
