Surface area calculator
Total outside area of seven solids, including the ends. Slant heights are worked out for you from the vertical height.
54 cm²
SA = 6a² · a = 3
in m²0.0054
in ft²0.058125116
in in²8.3700167
Surface area formulas
| Solid | Formula |
|---|---|
| Cube | SA = 6a² |
| Rectangular box | SA = 2(lw + lh + wh) |
| Cylinder | SA = 2πr² + 2πrh |
| Sphere | SA = 4πr² |
| Cone | SA = πr² + πr√(r² + h²) |
| Square pyramid | SA = a² + 2a√((a/2)² + h²) |
| Hemisphere (closed) | SA = 3πr² |
Unroll a cylinder’s side and you get a rectangle: its width is the circle’s circumference 2πr and its height h, which is where 2πrh comes from.
Questions people ask
What is surface area?
The total area of all the outside faces of a 3D solid, as if you unfolded it flat (its net). It tells you how much paint, wrapping or sheet material you need.
What is slant height?
For cones and pyramids, the distance from the apex down the side to the base edge. This calculator asks for the vertical height and works out the slant height with the Pythagorean theorem.
Does the cylinder formula include the top and bottom?
Yes: 2πr² covers the two circular ends and 2πrh the curved side. For an open tube, use only 2πrh (lateral area).