Calculate volume, surface area, and diagonal of a cube. Enter side length, volume, surface area, or diagonal to find all properties.
Last updated: April 2026 | By Patchworkr Team
A cube is a three-dimensional solid with six identical square faces. It's one of the five Platonic solids and the most symmetrical 3D shape.
Key properties:
Cubes are ubiquitous: dice, ice cubes, Rubik's cubes, boxes, and the basis for cubic units of volume (cubic meters, cubic feet).
Determine which property you know: side length (a), volume (V), surface area (A), or space diagonal (d). Why: Different starting measurements require different inverse formulas. Knowing which value you have tells the calculator which calculation path to follow.
Why: The side length is the fundamental cube property. All other measurements (volume, surface area, diagonals) are derived from it. Finding the side is usually the first internal step, even if you start with a different measurement.
Why: These three properties define most practical applications: volume for capacity/storage, surface area for material costs, and diagonal for fitting/clearance checks.
Why: These provide additional geometric context. Face diagonal matters for internal space calculations. Face area is useful for surface treatments. Edge perimeter sum helps in frame construction or edge material calculations.
Check that all values are positive and geometrically consistent. Verify: space diagonal d > face diagonal f > side a, and that volume = (side length)³. Apply results to your application: storage capacity, material ordering, construction clearance, or manufacturing specifications. Why: Consistency checks catch calculation errors. Complete verification ensures you have correct values for downstream decisions. All metric relationships must hold—any violation indicates an input or calculation error.
Storage Box Volume
V = a³, where a is the side length. Cube the side length to get the volume.
A cube has 6 faces (all squares), 12 edges (all equal), and 8 vertices (corners).
Face diagonal crosses a square face (length a√2). Space diagonal goes through the interior from one corner to the opposite corner (length a√3).
Take the cube root: a = ∛V. For example, if V = 64, then a = ∛64 = 4.
Yes! A cube is a rectangular prism where all three dimensions (length, width, height) are equal.
A = 6a², which is 6 times the area of one square face. All 6 faces are identical.
The space diagonal of a unit cube equals √3. This ratio appears in 3D geometry and relates to the Pythagorean theorem in 3D.
Calculating storage capacity, packaging design, construction (concrete blocks), dice manufacturing, and any cubic container or structure.