Space Diagonal of a Cuboid

The space diagonal is the straight-line distance from one corner of a rectangular box to the opposite corner inside the box. It works because you can first find the diagonal across the base using the Pythagorean theorem, then combine that with the height using the same idea again, which simplifies to d = \sqrt{l^2 + w^2 + h^2}. In other words, the three perpendicular edges contribute independently to the final distance.

Use this formula when you need the longest internal distance across a rectangular prism, such as in packaging, construction, or 3D geometry problems. It is also useful when checking whether a long object will fit inside a box or container.

• Adding the side lengths first instead of squaring them first
• Using only two dimensions and forgetting the third dimension
• Confusing the space diagonal with a face diagonal on one side of the box