Surface area calculator
Total surface area of a cube, box, cylinder, sphere, cone, pyramid or prism.
About this calculator
This surface area calculator works out the total outside area of common 3D shapes, from cubes and boxes to cylinders, spheres, cones, pyramids and prisms.
It shows the formula, the lateral area without the ends, the base area and the volume, in any unit.
How it works
The total surface area adds up the area of every face. Curved shapes use π: a sphere is 4πr², and a cylinder is two circles plus the side, 2πr² + 2πrh. The lateral area leaves out the top and bottom.
Last reviewed:
Worked example
- Shape: Cylinder
- Unit: Centimetres
- Radius: 5
- Height: 10
Surface area: 471.238898038 cm²
Common questions
What is the surface area of a cylinder?
2πr² + 2πrh: two circular ends plus the curved side. With r = 5 and h = 10, it is about 471.24.
What is the difference between surface area and volume?
Surface area is the outside covering, in square units. Volume is the space inside, in cubic units.
What is lateral surface area?
The area of the sides only, without the top and bottom. For a cylinder it is 2πrh, the size of the label around a can.
Sources and further reading
The story behind it
Where the idea came from: Archimedes proved that a sphere's surface is exactly four times the area of its largest circle, 4πr², and asked for a sphere inside a cylinder to be carved on his tomb.
He showed that the sphere has two thirds of the surface and volume of the cylinder around it. Cicero found the carving on his tomb in Sicily about 140 years after his death.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
After 15 years as a mathematics educator, I built CalculStore to give students, teachers, professionals and anyone working with numbers simple, reliable tools.
Meet the founder