How this calculator works
A rectangular prism, also called a cuboid, is a box with six rectangular faces. Its volume is length times width times height. The total surface area adds the areas of all six faces in three matching pairs, and the lateral area counts only the four upright sides. The space diagonal is the longest straight line through the inside, found by applying the Pythagorean theorem twice, once across the base and again up through the height.
Formula
V = lwh; total area = 2(lw + lh + wh); lateral area = 2h(l + w); base area = lw; space diagonal = √(l² + w² + h²).
Worked example
A box 4 m long, 3 m wide and 2 m high has a volume of 24 m³ and a base area of 12 m². Its total surface area is 2 × (12 + 8 + 6) = 52 m², its lateral area is 2 × 2 × 7 = 28 m², and its space diagonal is √29 ≈ 5.385 m.
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Frequently asked questions
How is this different from a cube?
A cube is a rectangular prism whose three edge lengths are equal. Every cube is a rectangular prism, but a rectangular prism only becomes a cube when length, width and height match.
What does the lateral area leave out?
It leaves out the top and bottom faces and counts only the four side walls. Use it for paint or cladding on the sides; use the total surface area when covering the whole box.
Can I solve for a missing edge from a volume?
Yes. Choose the edge to find, enter the volume and the other two edges, and the calculator divides the volume by their product. A zero or negative edge is rejected because it would not form a solid.