Cuboid Calculator

A cuboid, also known as a rectangular prism, is a three-dimensional geometric shape bounded by six rectangular faces. To determine its various properties, our calculator relies on three core algebraic formulas based on side lengths length (a), width (b), and height (height). The volume is found by multiplying all three dimensions together: Volume = a * b * height. The total surface area is calculated by summing the areas of all six rectangular faces using the formula: Area = (2 * a * b) + (2 * height * b) + (2 * a * height). Finally, the interior space diagonal—the longest straight line passing through the center from one corner to the opposite vertex—is derived from the three-dimensional Pythagorean theorem: Diagonal = sqrt(a^2 + height^2 + b^2).

Imagine you need to find the spatial properties of a storage box where side a is 5 meters, side b is 3 meters, and the height is 4 meters. First, calculate the volume by multiplying the dimensions: Volume = 5 * 3 * 4 = 60 cubic meters. Next, compute the total surface area by evaluating the face pairs: Area = (2 * 5 * 3) + (2 * 4 * 3) + (2 * 5 * 4) = 30 + 24 + 40 = 94 square meters. Finally, find the space diagonal by squaring each dimension, summing them up, and taking the square root: Diagonal = sqrt(5^2 + 4^2 + 3^2) = sqrt(25 + 16 + 9) = sqrt(50) is approximately 7.07 meters.

Always ensure that all measurements use the exact same unit of length—such as centimeters or meters—before plugging them into the calculator to avoid severe conversion errors. When calculating packaging or shipping capacities, remember that volume dictates physical storage limits, while surface area dictates material required for construction or wrapping. Double-check your diagonal calculation if you are fitting rigid long items inside a container to ensure they clear the interior corners.