Surface Area Calculator guide
Surface Area Calculator: 3D Shapes Explained
Use our surface area calculator to find the total surface area of a cube, cuboid, cylinder, cone, sphere and other 3D shapes.
By the AllCalculator editorial teamUpdated 16 October 20261 min read
The surface area of a 3D shape is the total area of all its faces, like the amount of paper you'd need to wrap it. Our Surface Area Calculator works it out for 12 common shapes.
How to use the calculator (Surface Area Calculator)
- Choose a shape.
- Enter its measurements and choose your units.
You'll see the surface area in square units, square metres and square feet, plus the volume.
Surface area formulas
| Shape | Surface area |
|---|---|
| Cube | 6a² |
| Cuboid | 2(lw + lh + wh) |
| Cylinder | 2πr(r + h) |
| Cone | πr(r + s), where s is the slant height |
| Sphere | 4πr² |
| Hemisphere | 3πr² (including the flat face) |
A worked example
With the calculator's default settings, a cylinder with a radius of 3cm and a height of 10cm:
- Two circular ends: 2 × π × 3² = 56.55cm²
- The curved side: 2 × π × 3 × 10 = 188.50cm²
- Total: 245.04cm²
Frequently asked questions
Does the surface area include the bottom?
Yes, it's the total area of every face. For an open-topped shape, subtract the area of the missing face.
How is surface area used in real life?
To work out how much paint, insulation, cladding or wrapping you need.
Is surface area the same as area?
Area is for flat 2D shapes. Use our Area Calculator for those. For the space inside a shape, see the Volume Calculator.
Sources and further reading
- GOV.UK: National curriculum in England – mathematicsgov.uk
- Wolfram MathWorld: Surface areamathworld.wolfram.com
Links open official and independent websites in a new tab.
This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.