Surface Area Calculator — cube, box, sphere, cylinder

How it works

Surface area is the combined area of all the outer faces of a three-dimensional solid, measured in square units. It's what you'd paint, wrap or plate. Each solid has a standard formula:

• Cube: six equal square faces = 6a²
• Box (rectangular prism): two of each face = 2(ab + bc + ca)
• Sphere: 4πr² — exactly four times the area of its "great circle"
• Cylinder: the curved side (2πrh) plus the two circular ends (2πr²) = 2πr(r + h)

Like area, surface area is a square measure, so it scales with the square of a linear size — double the dimensions and the surface area quadruples (while the volume grows eightfold).

Worked example

A box 4 × 3 × 2 has three distinct face sizes — 4×3, 3×2 and 2×4 — each appearing twice: SA = 2(12 + 6 + 8) = 52 square units. A cube of side 3 has SA = 6 × 3² = 54. A sphere of radius 3 has SA = 4π × 9 = 36π ≈ 113.1. And a cylinder of radius 2, height 5 has SA = 2π × 2 × (2 + 5) = 28π ≈ 87.96.

Frequently asked questions

How do I find the surface area of a box?

Add the areas of its three distinct faces and double the total: 2(ab + bc + ca), where a, b and c are the edge lengths. A 4-by-3-by-2 box gives 2(12 + 6 + 8) = 52. A cube is the case where all edges match, so its surface area is 6 × side².

How do I find the surface area of a cylinder?

Add the curved side to the two circular ends: 2πrh + 2πr², which factors to 2πr(r + h). For radius 2 and height 5 that's 2π × 2 × 7 = 28π ≈ 87.96. The curved part alone (the label on a can) is the lateral surface area, 2πrh.

How does a sphere's surface area relate to a circle?

A sphere's surface area, 4πr², is exactly four times the area of a circle of the same radius (πr²). So a sphere of radius 3 has surface area 36π, four times the 9π area of the flat circle through its centre. It's a surprisingly clean result.

What's the difference between surface area and volume?

Surface area is the outside skin (a square measure — how much wrapping or paint); volume is the inside capacity (a cubic measure — how much it holds). As a solid grows, its volume outpaces its surface area, which is why large animals lose heat more slowly and why small particles react faster: it's the surface-area-to-volume ratio.

What units does surface area use?

Square units of whatever you measured — square metres (m²) if the dimensions are in metres, cm² if in centimetres. This calculator treats the dimensions as plain numbers, so keep every dimension in the same unit and read the surface area in that unit squared.

Why does surface area grow with the square of size while volume grows with the cube?

Because surface area covers two dimensions and volume three. Scaling a solid by a factor multiplies its surface area by that factor squared and its volume by the factor cubed — so bigger objects have proportionally less surface for their bulk. That shrinking surface-area-to-volume ratio shapes everything from cooling rates to biology.