The body diagonal is a part of a right triangle composed of a unit cell edge and a face diagonal. We can calculate the length using the Pythagorean Theorem.

The face diagonal is part of a right triangle with two unit cell edges.

Thus the body diagonal can be found from three unit cell edges.

The body diagonal is four times the atomic radius (d = 4R) so:

For the BCC metal iron:
a = 287 pm, R = 124 pm

Click the links on the right to view this process step-by-step.