A rectangular prism — also called a box or cuboid — is one of the most common three-dimensional shapes in everyday life, from shipping boxes to storage bins to the rooms in a house. This calculator finds three key measurements from just three inputs: length, width, and height.
How the Rectangular Prism Calculator works
Volume (V = l × w × h) measures the space enclosed by the box — how much it can hold. Surface area (SA = 2(lw + lh + wh)) measures the total area of the six flat faces covering the box — how much material wraps around it. The space diagonal (d = √(l² + w² + h²)) is the straight-line distance from one corner to the opposite corner, derived by applying the Pythagorean theorem twice: once across the base, and once from the base diagonal up to the top corner.
Inputs and what they mean
Enter length, width, and height in any consistent unit — inches, feet, centimeters, or meters. The three labels are interchangeable; what matters is that all three measurements use the same unit before you calculate. Volume grows fastest with dimension changes (cubic relationship), so a small increase in any one side has an outsized effect on capacity — doubling the height alone doubles the volume, while doubling all three dimensions multiplies volume by eight.
Limits and edge cases
This calculator assumes a perfect rectangular prism with right angles at every corner — it will not give accurate results for boxes with beveled edges, rounded corners, or non-rectangular cross-sections. All three dimensions must be positive numbers; a zero or negative input means the shape is degenerate and has no defined volume. For a box where all sides are equal, use the dedicated Cube Calculator, which is a simplified version of the same formulas.