Find the surface area and volume of a box, cube, cylinder, sphere or cone. Pick a shape, enter its measurements in any one unit, and see both results. Free, private, and runs entirely in your browser.
Surface area is the total area of all the outer faces of a solid. Each shape has its own formula built from its measurements, and the volume is calculated alongside it.
What is surface area used for? It tells you how much material covers a solid, such as paint, wrapping, insulation or sheet metal.
Is surface area the same as volume? No. Surface area is measured in square units and volume in cubic units.
A box measures 4 by 3 by 2. Surface area = 2(4×3 + 4×2 + 3×2) = 2(12 + 8 + 6) = 52 square units, and the volume is 24 cubic units. A cylinder with radius 3 and height 5 has surface area 2π × 3 × (3 + 5) ≈ 150.80 and volume π × 9 × 5 ≈ 141.37.
How do I find the surface area of a cone? Add the circular base πr² to the curved part πr times the slant height, where the slant height is √(r² + h²).
Does the calculator include the open top of a container? No. It gives the total closed surface. Subtract the open face if the shape has no lid.
Archimedes proved in the 3rd century BC that the surface area of a sphere equals four times the area of its great circle, and that its volume is two-thirds that of the cylinder around it. He considered the result among his greatest and asked for it to be shown on his tomb. The formulas for boxes, cylinders and cones follow from unfolding the solid into flat pieces.
Use this calculator to estimate paint for a tank, wrapping for a gift box, sheet metal for a duct or insulation for a pipe. A cube with 5 cm sides has a surface area of 150 square centimeters. For other shapes and more options, see the 3D shape calculator.
How do I find the surface area of a rectangular prism? Use 2(lw + lh + wh). The box option does this.
What is lateral surface area? It is the area of the sides only, excluding the top and bottom. For a cylinder it is 2πrh.