Squaring of Circle | Ellipse | Rectangle | Polygon || Square Multiplication

Cubing of Sphere | Ellipsoid | Cuboid || Cube Multiplication

Cubing the Cuboid - Calculator

Name: Cubing the Cuboid - Calculator
Author: Jürgen Kummer

Calculator for the edge lengths of a cube and of a cuboid, if both have the same surface area or volume. The cubing of the cuboid is the three-dimensional equivalence to the squaring of the rectangle. Please specify, if surface area or volume should be equal. Then enter three of the four lenghts, the other values will be calculated.

equal surface areas equal volumes

	Cube	Cuboid
Length:
Width:
Height:
Diagonal:
Surface area:
Volume:

Round to decimal places.

The unit is the same for lengths, width and height. The surface area has this unit squared, the volume has this unit to the power of three. For example, length in centimeters, area in square centimeters, volume in cubic centimeters. The diagonal is the space diagonal between two opposite vertices. The diagonal of a cuboid is always longer than that of a cube with the same volume or same surface area.

Example: cube and cuboid with almost equal volumes. The edge length of the cube is 100 pixels, the dimensions of the cuboid are 120 x 100 x 83 pixels, because there are no fractions of pixels. Cubes and cuboids are distorted by perspective. Lines receding into the distance appear shorter. In a square, of course all edges are the same length. The edges receding into the distance of the cuboid are proportionally sized to those of the cube. This cube has one million pixels, this cuboid 996,000. A pixel is typically a unit of area, but in this case, it is interpreted spatially. Therefore, the pixel unit is not written as a power of three.

The same principle applies to the cubing of the cuboid as to the squaring of the rectangle, since the faces of a cuboid are all rectangles or squares. There are a total of six faces, of which at most three can be different. Opposite faces are equal in size. These rectangles can be constructed if they have constructible side lengths.

Last updated on 01/23/2026. Author: Jürgen Kummer

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