Surface Area Calculator
Total surface area for a cube, box, sphere, cylinder or cone — pick a shape, enter the dimensions, and see the formula worked out.
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Total surface area
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Surface area is the total area of every outer face of a shape, measured in square units. It is what you would paint or wrap — quite different from volume, which is the space inside. This tool covers the five most common shapes; the formula updates as you type.
The formulas
| Shape | Surface area | Made of |
|---|---|---|
| Cube | 6a² | Six equal squares |
| Box | 2(lw + lh + wh) | Three pairs of rectangles |
| Sphere | 4πr² | One curved surface |
| Cylinder | 2πr(r + h) | Two circles + a curved side |
| Cone | πr(r + l) | Base circle + curved side, l = √(r²+h²) |
Worked example — a cylinder
A cylinder with radius 3 cm and height 10 cm:
That is the two ends (2 × π × 9 = 56.5 cm²) plus the curved wall (2 × π × 3 × 10 = 188.5 cm²).
Why surface area matters
Surface area decides how much paint, cladding, wrapping or coating a shape needs, and how fast it loses or gains heat. The relationship between surface area and volume — captured in the surface-area-to-volume ratio — explains why small animals lose heat quickly and why crushed ice melts faster than a single block.
Frequently asked questions
What is the formula for surface area of a box?
Surface area = 2(lw + lh + wh), where l, w and h are the length, width and height. It is the sum of the areas of all six rectangular faces.
What is the surface area of a sphere?
Surface area = 4πr². A sphere of radius 5 cm has a surface area of 4 × π × 25 = 314.2 square centimetres.
How is surface area different from volume?
Surface area measures the total area of an object's outer faces, in square units. Volume measures the space inside it, in cubic units. Paint covers surface area; water fills volume.
What is the surface area of a cylinder?
Surface area = 2πr(r + h), which is the two circular ends (2πr²) plus the curved side (2πrh).