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The Surface Area Of A Sphere Calculator

A sphere's surface area is exactly four of its great circles, a result Archimedes was so pleased with that he asked for it on his tombstone.

Surface area

314.1593

Volume
523.5988
Great circle area
78.5398
Surface area to volume ratio
0.6

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

The formula this calculator uses

surface area = 4 x pi x radius^2

A
Surface area of the sphere, in square units
r
Radius, the distance from centre to surface

How to check the result by hand

  1. 1

    Find the radius

    Halve the diameter if that is what you measured. The radius is what gets squared, so using the diameter makes the answer four times too large.

  2. 2

    Square the radius

    A radius of five squares to twenty five. Squaring is the step that turns a length into an area, which is why the unit becomes square.

  3. 3

    Multiply by pi

    Twenty five times pi is about 78.54, which is the area of the great circle, the largest flat slice through the centre.

  4. 4

    Multiply by four

    78.54 times four is about 314.16. The sphere's skin is exactly four of those great circles, no more and no less.

  5. 5

    Keep the unit squared

    Centimetres give square centimetres. If a volume is wanted instead, the formula changes to four thirds pi r cubed and the unit becomes cubic.

For worked examples, common mistakes and the limits of this formula, read the full How To Calculate The Surface Area Of A Sphere page.