Surface Area Of A Cube Calculator

What this calculator does

The surface area of a cube is the total area of its six square faces, the whole of its outside. How much paper it would take to wrap it, or how much paint to coat it. Because a cube is so even, one number does it: the edge.

Type the edge and you have the area of the outside.

Using the calculator

1. Type the edge length.
2. Press Calculate.

The edge has to be positive. There is no unit setting, so the result is a plain number in square units of whatever unit you used.

The formula | surface area = 6 × edge²

The surface area of a cube is:

surface area = 6 × edge²

A cube has six faces, and every one is an identical square with area edge × edge, which is edge². Six identical squares, so you work out one and multiply by six. That is all the formula is saying.

Unfolding the cube into six squares

Here is the picture that makes it obvious. Take a cube, cut along enough of its edges, and lay it out flat. You get a net, often shaped like a cross, made of six equal squares. The surface area is simply those six squares added up. Seeing the cube opened out is the clearest way to understand why six faces, each edge², gives 6 × edge².

Surface area or volume? Two different things

A cube has both, and they answer different questions. The surface area is the skin, 6 × edge², and because each face is flat, with two dimensions, it is measured in square units. The volume is the space inside, edge³, and because that has three dimensions, it is measured in cubic units. They are easy to mix up but easy to keep apart once you see it: 6 × edge² covers the cube, edge³ fills it. For the space inside, see the volume of a cube calculator.

The unitless, square answer

This tool does not ask for a unit, so it reports a bare number. Work in whatever unit you like, and read the answer in that unit squared: an edge in centimetres gives a surface area in square centimetres, cm². The squaring is built into the edge² in the formula, since every face is an area.

A worked example | a 10 cm edge

Say the edge is 10 cm.

1. Area of one face: 10² = 100.
2. Six faces: 6 × 100 = 600.

So the surface area is 600 cm². For contrast, the same cube's volume is 10³ = 1,000 cm³, the space inside rather than the skin around it, and in cubic units rather than square.

A cube is a special box

A cube is the special case of a box, or rectangular prism, where every edge is equal. A box's surface area is 2 × (width × length + length × height + width × height), and when all three are the same edge that collapses to 2 × (3 × edge²), which is 6 × edge². For boxes with unequal sides, see the surface area of a rectangular prism calculator, and for other shapes the surface area calculator.

Questions people ask

What is the surface area of a cube with a 10 cm edge?

It is 600 cm². Find one face, 10² = 100, and multiply by the six faces.

What is the formula?

Surface area = 6 × edge², since a cube has six identical square faces each of area edge².

Why six?

Because a cube has six faces, all the same size. You find the area of one and multiply by six.

What is the difference between surface area and volume?

Surface area is the outside skin, 6 × edge², in square units. Volume is the inside space, edge³, in cubic units.

What unit is the answer in?

Whatever unit you used, squared. The tool shows a plain number, so an edge in centimetres gives cm².

References

A note on the idea behind it. The surface area of a cube is the sum of its six identical square faces, found neatly by unfolding the cube into a flat net of six squares. Representing solids as nets to find their surface area is a standard approach in geometry. For further reading, see Cube.

1. The net of a cube, six equal squares, whose total area, 6 × edge², is the cube's surface area.