Cuboid Volume Calculator

About this calculator

For a cuboid (rectangular box) with length l, width w, and height h, the volume is V = l·w·h, the total surface area is SA = 2(lw + lh + wh) — the sum of the areas of all six rectangular faces — and the space diagonal (the longest straight line that fits inside the box, corner to opposite corner) is d = √(l² + w² + h²), an extension of the Pythagorean theorem into three dimensions.

Geometry students use these formulas as a foundational 3D-measurement exercise, while shipping and logistics companies use volume calculations to determine how many boxes fit in a container or truck and to compute dimensional (volumetric) weight for freight pricing. Packaging designers use surface area to estimate material needed for a box, and carpenters, cabinet makers, and DIY furniture builders use the space diagonal to check whether a piece will fit through a doorway or stairwell during a move.