Rectangular Prism Volume Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
The volume of a rectangular prism (cuboid) is calculated as V = length × width × height. For a box measuring 3 m × 4 m × 12 m, the volume is 144 m³.
Explanation
A rectangular prism (also called a cuboid) is a solid whose six faces are rectangles, like a box, a room, or a brick — the special case where all three dimensions are equal is a cube. In addition to volume, this calculator gives the total area of its six faces (useful for estimating an amount of paint or packaging cardboard) and its interior diagonal — the longest straight line that can be drawn inside the prism, from one corner to the opposite one. This diagonal is calculated by generalizing the Pythagorean theorem to three dimensions, D = √(L² + W² + H²): the same principle used elsewhere in this catalog for distances between two points, a rectangular prism and a set of coordinates sharing the same distance formula in space. For the same underlying two-dimensional building blocks, see our rectangle area and perimeter calculator.
Example: a box measuring 3 m × 4 m × 12 m
Inputs
Length: 3 m. Width: 4 m. Height: 12 m.
Calculation
Volume = 3 × 4 × 12 = 144 m³. Total area = 2 × (3×4 + 3×12 + 4×12) = 2 × (12+36+48) = 2 × 96 = 192 m². Diagonal = √(3² + 4² + 12²) = √(9+16+144) = √169 = 13 m.
Result
This box has a volume of 144 m³, a total surface area of 192 m², and an interior diagonal of 13 m.
Frequently asked questions
What's the difference between a rectangular prism and a cube?
A cube is a special case of a rectangular prism where all three dimensions (length, width, height) are equal. All of this calculator's formulas remain valid for a cube: just enter the same value for all three fields, which simplifies the volume to side³ and the total area to 6 × side².
How is a rectangular prism's interior diagonal calculated?
By applying the Pythagorean theorem twice: first on the base to get the diagonal of the rectangle formed by the length and width, then a second time by combining this base diagonal with the height. The result simplifies directly to D = √(L² + W² + H²), the three-dimensional generalization of the Pythagorean theorem.
What is this calculator's total area used for?
It corresponds to the combined surface of the prism's six faces, useful for example to estimate the amount of paint needed to cover a room (excluding floor/ceiling if needed), the amount of cardboard needed to make a box, or the packaging required for a parcel of given dimensions.