Cuboid Calculator — Volume, Surface Area & Diagonal
Enter the length, width and height of a cuboid to find its volume, total and lateral surface areas, space diagonal and all three face diagonals.
units
units
units
V = l × w × h
- 1
Length × width (base area)
8 × 5 = 40 - 2
Base area × height (Volume)
40 × 3 = 120V = l × w × h — the number of unit cubes that fit inside.
How does this calculator work?
For a cuboid with length l, width w and height h: Volume = l × w × h, Total surface area = 2(lw + lh + wh), Space diagonal = √(l² + w² + h²). Enter the three edge lengths in any unit — the output is in the cube and square of that unit.
Formula
How this is calculated
A cuboid (also called a rectangular prism or box) is a three-dimensional shape with six rectangular faces, twelve edges and eight corners. It is fully defined by three perpendicular edge lengths: length l, width w and height h, in any consistent unit.
Volume is l × w × h — the number of unit cubes that fit inside. Total surface area sums the areas of all six faces: there are two l×w faces (top and bottom), two l×h faces (front and back) and two w×h faces (left and right), giving SA = 2(lw + lh + wh). Lateral surface area counts only the four side faces (excluding top and bottom): 2(l + w) × h, useful for calculating the wall area of a room.
The space diagonal is the longest straight line through the interior, from one corner to the opposite corner: √(l² + w² + h²), derived from Pythagoras applied twice in 3-D. Each face also has its own diagonal: the base face has √(l² + w²), the front face √(l² + h²) and the side face √(w² + h²). All these formulas assume a perfect right-angle box; no approximations are used.
Frequently asked questions
A cube is a special cuboid where all three dimensions are equal (l = w = h). A cuboid has three potentially different dimensions, so every cube is a cuboid but not every cuboid is a cube.
The space diagonal d = √(l² + w² + h²). It is the 3-D version of Pythagoras: first find the base diagonal √(l² + w²), then treat that as one leg and h as the other to get √(l² + w² + h²).
Lateral surface area covers the four side faces only, excluding the top and bottom. It equals 2(l + w) × h and is useful when calculating the amount of paint or wall material needed for a room, ignoring the floor and ceiling.
Also known as
TG we-Calculate Editorial Team. (2026). Cuboid Calculator — Volume, Surface Area & Diagonal [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/cuboid-calculator
TG we-Calculate Editorial Team. "Cuboid Calculator — Volume, Surface Area & Diagonal." TG we-Calculate. 2026. https://we-calculate.com/calculator/cuboid-calculator.
TG we-Calculate Editorial Team, "Cuboid Calculator — Volume, Surface Area & Diagonal," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/cuboid-calculator
@misc{wecalculate_cuboid_calculator, title = {Cuboid Calculator — Volume, Surface Area & Diagonal}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/cuboid-calculator}}, year = {2026}, note = {TG we-Calculate} }
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