Rectangular Prism Volume & Surface Area Calculator
Find the volume, total surface area, lateral area and space diagonal of a rectangular prism (box) from its length, width and height.
How it works
V = l · w · h · Surface area = 2(lw + lh + wh) · Lateral area = 2h(l + w) · Diagonal = √(l² + w² + h²)
A rectangular prism (a box or cuboid) is bounded by three pairs of identical rectangles. Its volume is simply the product of the three edge lengths, while the surface area sums the six faces — two of each pair. The lateral area counts only the four side faces (excluding top and bottom), and the space diagonal is the straight-line distance between opposite corners, found by extending the Pythagorean theorem into three dimensions.
Worked example
For a box 4 by 3 by 2 units: volume = 4 · 3 · 2 = 24 units³; surface area = 2(4·3 + 4·2 + 3·2) = 2(12 + 8 + 6) = 52 units²; space diagonal = √(16 + 9 + 4) = √29 ≈ 5.385 units.
Frequently asked questions
What is the difference between total and lateral surface area?
Total surface area covers all six faces. Lateral surface area covers only the four vertical side faces and leaves out the top and bottom — useful when, for example, you are wrapping a label around a box but not covering its ends.
How do I find the space diagonal?
The space diagonal is the distance from one corner of the box to the opposite corner. It equals √(l² + w² + h²), which is the 3-D version of the Pythagorean theorem.
Does it matter which edge I call length, width or height?
No. Volume and total surface area are symmetric in the three edges, so any labelling gives the same result. Only the lateral area depends on which edge you treat as the height.
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This calculator is for educational purposes. Double-check important results before acting on them.