Things You'll Need
If you are between feet when you measure, round up to the nearest foot.
Record the measurements and your calculations with each step. This allows you to double check your work.
When considering the sand depth, leave room for the children and their shovels, buckets and other toys.
Figuring out how many bags of sand are needed to fill a sandbox requires only a straightforward volume calculation. Which formula you use depends on the shape of the sandbox -- square, rectangular or circular. Since sandbox sand typically comes in 50-pound bags that contain half a cubic foot, your calculations should be made in cubic feet. Another option is to buy the sand in bulk, which would require your calculations to be made in cubic yards. With accurate measurements and careful calculations, the exact amount of sand can easily be determined.
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Square or Rectangular Box
Take two initial measurements for a square or rectangular sandbox -- the interior length and width. Have an assistant hold the end of a tape measure on the inner left side of the box and pull it to the inner right side of the box and take a reading. If the box is rectangular, repeat the process to take an inner width measure.
Multiply the first measurement by itself for a square box. For example, for an 8-foot square box: 8 times 8 equals 64. If it's a rectangular box, multiply the first measurement by the second. For example, if the box measures 8 feet long and 6 feet wide: 8 time 6 equals 48.
Take the result of your area calculation and multiply this number by the desired depth of the sand to find the volume. For example, if you want the sand to be 1 foot deep in the 8-foot square box, the volume of sand is 64 times 1, for 64 cubic feet. Since each bag fills up half a cubic foot, this example would require 128 bags of sand.
Convert cubic feet to cubic yards, if you are buying bulk, by dividing the number of cubic feet by 27. For the 8-foot square box: this would be 64 divided by 27, for a result of 2.37 cubic yards.
Measure the diameter of a circular sandbox. Have an assistant hold the end of a tape measure at one side inside of the box. Pull the tape straight across to the opposite inside of the box and take a reading.
Divide this number by 2 to get the radius -- a key component of the volume formula. For example, if the diameter is 8 feet, the radius is 4 feet.
Square the radius -- multiply it by itself -- with your calculator. Multiply this number by pi -- 3.14 -- and then multiply the result by the desired depth of the sand to get the volume. For example, if the sandbox has a radius of 4 feet, and you want the sand to be 1 foot deep, you will need a little more than 50 cubic feet of sand: 4 times 4 times 3.14 times 1 equals 50.24. This example would require just over 100 bags of sand since each bag fills up half a cubic foot. In cubic yards: 50.24 divided by 27 equals 1.86.
Michele M. Howard
Michele M. Howard began writing professionally in 2009, producing sports, fitness, home improvement and gardening articles for various websites. In addition to writing, Howard is a United States Professional Tennis Association tennis instructor and a professional racket stringer. Howard holds a Bachelor of Arts in mathematics from Southern Connecticut State University.