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Calculate all properties of a cube from any single measurement. Enter the side length, volume, surface area, or space diagonal.
A cube is a three-dimensional solid with six identical square faces. It is one of the five Platonic solids and is also known as a regular hexahedron. Every edge has the same length, and all angles are 90°.
A cube has two types of diagonals:
The space diagonal formula comes from the 3D Pythagorean theorem: d² = s² + s² + s² = 3s², so d = s√3.
A face diagonal lies entirely on one face of the cube (like a 2D diagonal of a square), while a space diagonal passes through the interior of the cube, connecting two vertices that are not on the same face. The space diagonal is always longer: s√3 vs s√2.
A cube is a special case of a rectangular prism (box) where all three dimensions are equal. In a cube, length = width = height = s. A rectangular prism can have three different dimensions.
Take the cube root of the volume: s = ∛V. For example, if V = 27, then s = ∛27 = 3.
A cube has 6 identical square faces, each with area s². The total surface area is 6 times one face: SA = 6s².
Common cube-shaped objects include dice, Rubik's cubes, sugar cubes, ice cubes (approximately), and some storage boxes. Perfect cubes are less common in nature.
A cube has 12 face diagonals (2 per face × 6 faces) and 4 space diagonals (connecting opposite vertices through the interior). That's 16 diagonals total.