Surface Area Calculator

What surface area means

The surface area of a solid is the total area of everything on its outside: every face of a box, the curved wall and both ends of a can, the skin of a ball. It is measured in square units such as cm², m² or ft², and it answers practical questions like how much paint, wrapping paper, sheet metal or insulation an object needs.

This calculator returns the total surface area, meaning all faces together. Some textbooks also talk about lateral area, which leaves out the top and bottom. If you only need the sides, subtract the end areas listed in the sections below.

How to use the calculator

1. Pick the shape under Surface area of.
2. Choose the Metric, the unit in which you want the answer. The result is given in the matching square unit.
3. Fill in the measurements that appear. Each has its own unit selector, so a length in meters and a height in inches can be entered as they are.
4. Press Calculate Surface Area. Whole-number answers appear bare, other answers with up to six decimals.

Round shapes are described by their diameter, not the radius, because that is what you can measure with a ruler or tape. The calculator halves it internally. The cone and cylinder also take a vertical height; for the cone this is the straight-up height, not the sloping side.

Surface area of a rectangular box

A box has three pairs of identical rectangles. Add the three distinct face areas and double the total.

A = 2 × (width × length + width × height + length × height)

Example: a cabinet is 0.6 m wide, 0.4 m long and 0.3 m high. The faces are 0.6 × 0.4 = 0.24, 0.6 × 0.3 = 0.18 and 0.4 × 0.3 = 0.12 m², which sum to 0.54. Doubled, the area is 1.08 m². A shipping carton of 45 × 30 × 20 cm has 2 × (1,350 + 900 + 600) = 5,700 cm² of cardboard on its faces, before overlaps and flaps.

Surface area of a cube

All six faces of a cube are squares with the same side a.

A = 6 × a²

Example: a cube with an edge of 5 cm has six faces of 25 cm², so the surface area is 150 cm², or 0.015 m². Doubling the edge quadruples the area: a 10 cm cube has 600 cm².

Surface area of a cylinder

A closed cylinder is made of two circular ends and a curved wall that unrolls into a rectangle. The rectangle is as tall as the cylinder and as wide as the circle's circumference.

A = 2πr² + 2πr × h = 2πr × (r + h)

Example: a food can is 7.4 cm across and 10.8 cm tall, so r = 3.7 cm. The two ends take 2π × 3.7² ≈ 86.02 cm² and the wall takes 2π × 3.7 × 10.8 ≈ 251.08 cm². Together that is about 337.09 cm² of metal and label.

Surface area of a sphere

A = 4πr² = πd²

A sphere needs just one measurement, so the diameter is all you enter. Example: a ball 10 cm across has an area of π × 10² ≈ 314.16 cm². If you need more than the area, the sphere calculator also returns the radius and volume.

Surface area of a cone

A cone has a circular base and a curved side. The side depends on the slant height s, the distance from the rim to the tip, which follows from the Pythagorean theorem.

s = √(r² + h²)

A = πr² + πr × s = πr × (r + s)

Example: r = 3 cm and h = 4 cm give s = √(9 + 16) = 5 cm. The base is π × 9 ≈ 28.27 cm², the curved side is π × 3 × 5 ≈ 47.12 cm², and the total is 75.40 cm². Enter the diameter (6 cm) and the vertical height (4 cm); the slant height is found for you.

Surface area of a triangular prism

A triangular prism has two identical triangular ends joined by three rectangles. For the ends, the calculator uses the triangle's base and its perpendicular height; the other two sides of the triangle are Width₁ and Width₂; Length is how far the prism runs.

A = base × height + (base + width₁ + width₂) × length

The first term is the two triangles (2 × ½ × base × height) and the second is the three rectangles, whose combined width equals the triangle's perimeter. Example: a right triangle with base 6, height 8 and hypotenuse 10 forms a prism 12 long. Ends: 6 × 8 = 48. Rectangles: (6 + 8 + 10) × 12 = 288. Total: 336 square units.

Practical uses and tips

• Painting and coating: surface area times the number of coats gives the area to cover. Subtract doors, windows or any face that will not be painted.
• Packaging and wrapping: add an allowance for overlaps and seams; the calculated value is the exact geometric area.
• Heat and insulation: heat loss scales with exposed area, so the surface area is a first step before applying an insulation rating.
• Open containers: a tank without a lid has one face less. Subtract the top area from the total.

Square units convert with the square of the length factor. One square meter is 10,000 cm², and one square foot is 144 in². One square meter is about 10.7639 ft². The area unit converter handles other pairs.

Related tools: the area calculator for flat shapes and the volume calculator for the space a solid encloses.