How to Calculate the Area of a Curved Surface

Example of a sphere
••• sphere-retention image by Jeffrey Zalesny from

Calculating a square area is as easy as multiplying the length by the width. But when you have a curved surface like a sphere or a cylinder, the problem can be puzzling. Luckily, mathematicians have figured out formulas for curved surfaces, so all you have to do is take a couple of simple measurements and plug the measurements into the formulas. For example, if you know the radius of a sphere, you can use the formula 4 pi r^2 to calculate its surface area. The surface area of a cylinder can be calculated with the height and radius using the formula 2 pi r^2 + 2 pi r h.

Surface Area of a Sphere

    Square the radius. For example, if the radius is 5 inches, then: 5 inches * 5 inches = 25 inches squared.

    Multiply Step 1 by pi. Pi * 25 inches squared = 78.54 inches squared.

    Multiply Step 2 by 4: 78.54 inches squared * 4 = 314.16 inches squared.


    Square the radius. For example, if the radius is 2 inches, then: 2 inches * 2 inches = 4 inches squared.

    Multiply Step 1 by 6.28. 6.28 * 4 inches = 25.04 inches.

    Multiply the radius by the height. For example, a radius of 2 inches and a height of 10 inches would give you: 2 inches * 10 inches = 20 inches squared.

    Multiply Step 3 by 6.28: 20 inches squared * 6.28 = 125.6 inches squared.

    Add Step 2 and Step 4 together: 25.04 inches squared + 125.6 inches squared = 150.64 inches.


    • Although 3.14 is a good approximation of pi and will work for most calculations, you can increase the accuracy of your answers by adding more decimal places to pi. For example, use 3.1416 for pi (4 decimal places) and 6.2832 for 2pi.

About the Author

Stephanie Ellen teaches mathematics and statistics at the university and college level. She coauthored a statistics textbook published by Houghton-Mifflin. She has been writing professionally since 2008. Ellen holds a Bachelor of Science in health science from State University New York, a master's degree in math education from Jacksonville University and a Master of Arts in creative writing from National University.

Photo Credits

  • sphere-retention image by Jeffrey Zalesny from