Surface area calculator for boxes, cylinders, cones, spheres and more

How to use the surface area calculator

1. Choose the Shape: cube, cuboid (box), cylinder, sphere, hemisphere, cone, rectangular pyramid, triangular prism, frustum of a cone, torus or ellipsoid.
2. Fill in the boxes that appear, such as Radius and Height. Each value must be above zero.
3. Set the Unit of the lengths. The answer is labelled in that unit squared, such as cm².
4. Read Surface area and the extra figures under it, then check Formula and working.

What it does and when to use it

Surface area tells you how much material covers a solid: card for a gift box, sheet metal for a tank, fabric for a cushion, or paint for a ball. The tool counts every face, so the cylinder, hemisphere, cone and frustum are treated as closed. Where it helps, it also gives the side area alone: the lateral surface of a cylinder or cone, and the curved surface of a hemisphere.

For the space inside the same shapes, use the volume calculator. For a full breakdown of one solid, the cylinder calculator and cone calculator list several measurements at once.

How it works

The formulas the tool applies:

• Cube: SA = 6s²; cuboid: SA = 2(lw + lh + wh)
• Cylinder: SA = 2πr(r + h), with side 2πrh
• Sphere: SA = 4πr²; closed hemisphere: SA = 3πr² (curved 2πr² plus the flat circle πr²)
• Cone: SA = πr(r + s), where the slant height s = √(r² + h²)
• Rectangular pyramid: SA = lw + l√((w/2)² + h²) + w√((l/2)² + h²)
• Triangular prism: two triangle ends by Heron’s formula plus L × (a + b + c)
• Frustum: SA = π(R + r)√((R − r)² + h²) + πR² + πr²
• Torus: SA = 4π²Rr
• Ellipsoid: Thomsen’s approximation with p = 1.6075

Worked examples

A shoe box, step by step. Length 30 cm, width 20 cm, height 10 cm.

1. Find one of each pair of faces: 30 × 20 = 600, 30 × 10 = 300, 20 × 10 = 200.
2. Add them: 600 + 300 + 200 = 1,100.
3. Each face has a twin on the opposite side, so double it: 2 × 1,100 = 2,200.

The tool shows Surface area: 2,200 cm².

A tin can. Radius 4 cm, height 12 cm. Total surface is 402.1238597 cm², and the label alone needs Lateral surface: 301.5928947 cm².

A 3-4-5 prism. Triangle sides 3, 4 and 5 cm and length 10 cm. Each end has area 6 cm², and the three side faces total 10 × 12 = 120 cm², so the tool gives Surface area: 132 cm².

Limits and tips

• Enter radius, not diameter. Halve a diameter first.
• For the torus the tube radius cannot exceed the major radius, and prism sides must form a real triangle.
• The unit menu labels the answer only. Put all lengths in one unit before you start; to show the answer in a different unit, use the area converter.
• Real objects have seams, lips and overlaps, so add a margin when buying material.