Cube Surface Area Calculator

A cube has six identical square faces, twelve equal edges and eight corners. Since every face is the same, the whole calculation is one square area multiplied by six. That is useful for wrapping a gift box, painting a block, or working out how much acrylic a display case needs. If the sides are not all equal, the shape is a cuboid, and the cuboid surface area calculator is the right tool.

Formula

A = 6 × s²

A

the total surface area

s

the length of one edge

Surface area from the edge

Square the edge to get one face, then multiply by six. A cube with 4 cm edges has faces of 16 cm² and a surface of 96 cm². A storage box with 30 cm edges has 6 × 900 = 5,400 cm² of cardboard on the outside, which is 0.54 m², not counting the flaps.

Surface area from the face diagonal

The face diagonal runs corner to corner across one square. By the Pythagorean theorem its square is 2s², so one face has half the diagonal squared and all six faces have three times it. A face diagonal of 10 gives 3 × 100 = 300, with an edge of about 7.07. There is no need to work out the edge first.

• s = f ÷ √2
• A = 3 × f²

Surface area from the space diagonal

The space diagonal runs through the middle of the cube, from one corner to the opposite one. It forms a right triangle with an edge and a face diagonal, so its square is s² + 2s² = 3s². The surface is therefore twice the diagonal squared. A space diagonal of 9 gives 2 × 81 = 162, with an edge of about 5.20.

This is the longest straight line that fits inside a cube, so it tells you whether a rod or a poster tube will fit. A box with 30 cm edges takes a rod of up to about 51.96 cm when laid corner to corner.

• s = d ÷ √3
• A = 2 × d²

Surface area and volume

Surface area is measured in square units and volume in cubic units, so the two numbers cannot be compared directly. The 4 cm cube has a surface of 96 cm² and a volume of 64 cm³. The volume calculator handles other solids if you need to compare capacities.

• V = s³

What happens when you cut a cube

Cutting a solid exposes new surface while its volume stays put. Take a 6 cm cube with a surface of 216 cm² and a volume of 216 cm³. Slice it into eight 3 cm cubes and the volume is still 8 × 27 = 216 cm³, but the surface doubles to 8 × 54 = 432 cm². This is why crushed ice cools a drink faster than a single block and why chopped vegetables cook sooner than whole ones.

Frequently asked questions