Surface Area Calculator

Surface Area Formulas for Common Solids

Surface area measures the total area covering the outside of a three-dimensional solid, the sum of every face’s area added together. Unlike volume, which is measured in cubic units and describes the space a shape contains, surface area is measured in square units, the same kind used for flat, two-dimensional shapes, because it is really just the area of every flat or curved surface that wraps around the solid. Knowing a shape’s surface area matters whenever you need to cover, paint, wrap, or manufacture its outside, rather than fill its inside.

Shapes built from flat faces add those faces directly. A cube has six identical square faces, so its surface area is 6s². A rectangular prism has three pairs of matching rectangles, front and back, top and bottom, left and right, giving SA = 2(lw + lh + wh). A sphere has no flat faces at all, yet its curved surface still reduces to a clean formula, 4πr², exactly four times the area of a circle with the same radius. A cylinder combines both ideas: two circular bases, each πr², plus a curved side that unrolls into a rectangle of width 2πr and height h, giving 2πr² + 2πrh altogether.

Cones and pyramids need one extra measurement first: the slant height, the distance along the sloped surface from the base to the apex, which is different from the shape’s vertical height and must be found using the Pythagorean theorem. Once the slant height is known, a cone’s lateral surface unrolls into a sector with area πrl, added to its circular base for a total of πr² + πrl. A square pyramid’s four triangular faces each have area (1/2)bl, adding up to 2bl, plus the square base b². The calculator above computes each slant height automatically before applying these formulas.