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Surface area of a sphere

Excel formula: Surface area of a sphere
Generic formula 
=4*PI()*A1^2
Summary 

To calculate the surface area of a sphere, you can use the PI function together with the exponent operator (^). In the example shown, the formula in C5, copied down, is:

=4*PI()*B5^2

which calculates the surface area of a sphere with the radius given in column B. Units are indicated generically with "u", and the result is units squared (u2).

Explanation 

In geometry, a sphere is defined as the set of points that are all the same distance (r) from a given point in a three-dimensional space. The formula for calculating the surface area of a sphere is: 

 

The Greek letter π ("pi") represents the ratio of the circumference of a circle to its diameter. In Excel, π is represented in a formula with the PI function, which returns the number 3.14159265358979, accurate to 15 digits:

=PI() // returns 3.14159265358979

To square a number in Excel, you can use the exponentiation operator (^):

=A1^2

Or, you can use the POWER function:

=POWER(A1,2)

Rewriting the formula using Excel's math operators we get:

=4*PI()*B5^2

Or, with the POWER function:

=4*PI()*POWER(B5,2)

For example, with a radius of 5 hardcoded into the formulas we have:

=4*PI()*5^2 // returns 314.16
=4*PI()*POWER(5,2) // returns 314.16 

and both formulas return the same result. Following Excel's order of operations, exponentiation will occur before multiplication.

Author 
Dave Bruns

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