Rectangular Prism Calculator
Find a rectangular prism's volume, surface area, and space diagonal from its length, width, and height.
Volume
24
Volume = l × w × h. A 4 × 3 × 2 box holds 24 cubic units.
Surface area
52
Space diagonal
5.3852
Surface area = 2(lw + lh + wh); the space diagonal that runs corner to corner is √(l² + w² + h²). A 4 × 3 × 2 box has a surface area of 52 and a diagonal of about 5.39.
How it works
A rectangular prism — a box or cuboid — is defined by three measurements: length, width, and height. Once you have those, the volume, the outside surface area, and the longest internal diagonal all follow directly.
Volume is length × width × height. Surface area adds up the six rectangular faces, which pair off into 2(lw + lh + wh). The space diagonal, the straight line from one corner to the opposite corner through the middle of the box, comes from the 3-D Pythagorean rule: √(l² + w² + h²).
This covers moving boxes, aquariums, rooms, and shipping crates. A 4 × 3 × 2 box, for instance, holds 24 cubic units, has 52 square units of surface, and a corner-to-corner diagonal of about 5.39.
Frequently asked questions
How do I find the volume of a rectangular prism?
Multiply the three dimensions together: volume = length × width × height. The units come out cubed, so meters give cubic meters and inches give cubic inches.
What's the surface area formula?
Surface area = 2(lw + lh + wh). A box has three pairs of matching faces, so you find the area of one of each pair, add them, and double the total.
What is the space diagonal?
It's the longest straight line inside the box, running from one corner to the diagonally opposite corner. It equals √(l² + w² + h²) — the same Pythagorean idea as a flat rectangle's diagonal, extended into three dimensions.