Diagonal of a cube calculator

A cube has two kinds of diagonal. A face diagonal runs across one face, and since a face is a square, it is the same length as the diagonal of a square. A space diagonal runs right through the cube from one corner to the furthest one. It is the hypotenuse of a right-angled triangle whose two shorter sides are the face diagonal and a vertical edge.

How it works

For a cube with edge a, the face diagonal is

$$d_f=a\sqrt{2}$$

and the space diagonal is

$$d_s=\sqrt{{\left(a\sqrt{2}\right)}^2+a^2}=\sqrt{3a^2}=a\sqrt{3}$$

For a solid whose edges have different lengths, use the calculator for the diagonal of a cuboid.