How to use the surface area calculator
This calculator finds the surface area of a sphere, a cone, a regular tetrahedron or a regular n-gonal prism. Choosing a solid leaves only the inputs it needs, and alongside the total it reports the values that went into it, such as base area, lateral area and slant height.
The formula in use is printed with your values on the formula line: 4πr² for a sphere, πr² + πrl with slant height l = √(r² + h²) for a cone, √3 a² for a regular tetrahedron, and twice the base n a² ÷ (4 tan(π/n)) plus the lateral area n a h for a prism.
The prism accepts any number of base sides from 3 to 100, so triangular, hexagonal and octagonal prisms are all handled on one screen. A value of n that is not a whole number or is below 3 cannot form a prism and produces a message, as does any length or height of 0 or less.
Values involving π or √3 are irrational and cannot be written exactly as finite decimals. Every step runs on unrounded values and rounding to six decimal places happens only as the number is printed, so no error creeps in from intermediate rounding. Areas are in the square of whatever length unit you entered.
Frequently Asked Questions
A sphere has S = 4πr². A cone adds the base πr² to the lateral area πrl, giving πr(r + l), where the slant height l is √(r² + h²).
The regular n-gon base has area n a² ÷ (4 tan(π/n)), and the sides are n rectangles totalling n × a × h. Because there are two bases, the total is twice the base area plus the lateral area.
It is bounded by four equilateral triangles of side a, and one such triangle has area √3 a² ÷ 4, so four of them come to √3 a².