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Surface Area Calculator
Find the total outside area of a 3D shape: pick a cube, box, cylinder, sphere, cone or pyramid, enter its dimensions and see the total, lateral and base areas with every step of the formula shown.
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Enter your values to see the result.
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How to use the Surface Area Calculator
- Select the shape and the unit you measured in.
- Enter the dimensions: radius or diameter for round shapes, length, width and height for boxes and pyramids.
- For a cylinder, choose closed, open top or open tube.
- Read the total surface area and the lateral and base areas.
- Check the steps or the table of other units, then copy the results.
Surface area formulas
| Shape | Total surface area | Lateral area | Example |
|---|---|---|---|
| Cube | 6s² | 4s² | s = 10 → 600 |
| Box | 2(lw + lh + wh) | 2h(l + w) | 30 × 20 × 10 → 2,200 |
| Cylinder | 2πr² + 2πrh | 2πrh | r = 5, h = 12 → 534.07 |
| Sphere | 4πr² | (all curved) | r = 11 → 1,520.53 |
| Cone | πr² + πrℓ, ℓ = √(r² + h²) | πrℓ | r = 3, h = 4 → 75.40 |
| Rectangular pyramid | lw + l·√((w/2)² + h²) + w·√((l/2)² + h²) | the four triangles | 6 × 6, h = 4 → 96 |
Surface area vs volume
Surface area measures the outside skin of an object in square units; volume measures the space inside in cubic units. When a shape grows, its surface area increases with the square of its size but its volume with the cube. Double every dimension of a box and it needs 4 times as much wrapping paper but holds 8 times as much.
Surface area is what you need for paint, labels, insulation, heat loss and material costs. Volume is what you need for capacity, fill and weight. The Volume Calculator covers the inside.
Frequently asked questions
What is surface area?
Surface area is the total area of all the outside faces or surfaces of a 3D object, measured in square units. It tells you how much material would cover the object, such as paint, wrapping paper or sheet metal.
What is the difference between lateral and total surface area?
Lateral surface area counts only the sides: the curved surface of a cylinder or cone, or the four side faces of a box or pyramid. Total surface area adds the base(s), such as the top and bottom circles of a cylinder.
What is the surface area formula for a cylinder?
SA = 2πr² + 2πrh. The two circular ends contribute 2πr² and the curved side, which unrolls into a rectangle of width 2πr and height h, contributes 2πrh. For an open cup use πr² + 2πrh.
How do you find the surface area of a cone?
Add the base circle and the curved side: SA = πr² + πrℓ, where the slant height ℓ = √(r² + h²). For r = 3 and h = 4, ℓ = 5 and SA = 9π + 15π = 24π ≈ 75.40.
How do you find the surface area of a pyramid?
Add the base area and the four triangular faces. For a rectangular base l × w and height h, the faces on the length sides have slant height √((w/2)² + h²) and those on the width sides √((l/2)² + h²): SA = lw + l·√((w/2)² + h²) + w·√((l/2)² + h²).
Why is a sphere's surface area 4πr²?
Archimedes showed that a sphere's surface equals the curved side of the cylinder that just encloses it: 2πr × 2r = 4πr². That is exactly four times the area of the sphere's great circle (πr²).
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