Surface Area Calculator — Free Online

Surface area is the total area of all the faces (or surfaces) of a three-dimensional object. It is measured in square units (e.g. cm squared, m squared).

For a cube with side length a, every face is an identical square. Since a cube has 6 faces, the surface area is SA = 6a squared. A rectangular prism generalises this: SA = 2(lw + lh + wh), accounting for three pairs of rectangular faces.

For a sphere, the surface area formula SA = 4 pi r squared was first proved by Archimedes. A cylinder combines two circular ends (2 pi r squared) with a lateral surface that unwraps into a rectangle (2 pi r h), giving SA = 2 pi r squared + 2 pi r h.

A cone's surface area includes the circular base (pi r squared) and a lateral surface that unwraps into a sector. The lateral area depends on the slant height l = sqrt(r squared + h squared), giving a lateral area of pi r l. A triangular prism has two triangular faces and three rectangular faces, so SA = 2 times the triangle area plus the perimeter times the prism length.