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How to Calculate Volume of a Round Pond

Updated April 17, 2017

Math calls the volume of a round pond a spherical cap. Imagine a sphere with the round pond fitting in the bottom of it. You can calculate the volume of this spherical cap, or pond, by measuring the depth of the water and the radius of the surface of the pond.

Measure the radius ("r") of the surface of the pond. Have an assistant stand on one edge of the pond and firmly hold the tape measure. Take the tip of the measuring tape and pull it while walking around the pond. One the other side of the pond, where the measuring tape extends the furthest distance, record this measurement in inches. Divide by 12 to give you the diameter in feet. Divide this result by two to give the radius of the pond.

Measure the depth ("d") of the pond. If the pond is small enough, wade out and use the measuring tape to measure the deepest part of the pond. Record this measurement in inches. Divide by 12 to give you the depth in feet. If the pond is larger, measure the depth from a boat. In either case, make sure you are measuring the actual depth to the bottom, and not to an object on the bottom, such as a large rock or tree branch.

Use a calculator or spreadsheet to calculate the volume "v" with this mathematical formula:

v = (3.1416_d)/6) * (3_r^2 + d^2). The calculation gives you the volume of the pond in cubic feet.

Tip

Make sure the measuring tape remains straight during measurements. If the measuring tape bends, the measurements will be too large.

Warning

Do not attempt to measure the depth of the pond unless you are a good swimmer and have an assistant watching and ready to help. Be careful using online websites that purport to automatically calculate the "partial volume of a sphere." This volume is actually the volume of the entire sphere minus the spherical cap. Be careful using online websites that purport to automatically calculate the "spherical cap." These often ask for a radius, but usually refer to the radius of the entire sphere, not the radius of the surface of the pond.

Things You'll Need

  • Measuring tape in inches
  • Calculator or spreadsheet
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About the Author

Byron Berger is a licensed attorney and registered civil engineer. Since 1998, he has contributed articles to legal and engineering periodicals, including "ADC Comment" and "Philosophical Magazine." Berger holds a B.S. in materials engineering from Michigan Technological University, as well as a J.D. from the University of the Pacific, McGeorge School of Law.