Cube Volume Calculator

Compute volume, surface area, face diagonal, and space diagonal of a cube instantly. Interactive 3D preview with live updates.

Formulas: Volume V = a³   |   Surface Area S = 6a²   |   Face diagonal dface = a√2   |   Space diagonal dspace = a√3

units
Enter a positive number. Decimals allowed.
a = 1
a = 2
a = 3
a = 5
a = 10
a = 0.5
Only for display; values remain same.
Cube Measurements
Cube edges Side length a
Volume = a³ = 27 | Surface area = 6a² = 54
Face diagonal = a√2 = 4.2426 | Space diagonal = a√3 = 5.1962

All About Cubes

A cube is a three‑dimensional solid object bounded by six square faces, with three meeting at each vertex. All sides are equal length. It is a special case of a rectangular prism where length = width = height.

Key properties:

  • Number of faces: 6 (all squares)
  • Number of edges: 12 (all equal)
  • Number of vertices: 8
  • Volume = edge³ (a³)
  • Surface area = 6 × edge² (6a²)
  • Face diagonal = a√2
  • Space diagonal = a√3

Step‑by‑Step Examples

1
Given a = 3 units → Volume = 3³ = 27 cubic units; Surface = 6·3² = 54 square units.
2
Given a = 5 cm → Face diagonal = 5√2 ≈ 7.071 cm; Space diagonal = 5√3 ≈ 8.660 cm.
3
If volume = 64 m³, then side = ∛64 = 4 m.

Real‑World Applications

  • Packaging: Determining box volume and material needed.
  • Construction: Concrete blocks, foundation shapes.
  • Physics: Moment of inertia calculations for cubic objects.
  • Games & design: 3D modelling of cubic voxels.

Frequently Asked Questions

A face diagonal lies on one square face, connecting two opposite corners of that face. The space diagonal goes through the interior of the cube, connecting two opposite vertices (not on the same face).

Take the cube root of the volume: a = ∛V. For example, if volume = 125 cm³, then a = 5 cm.

Yes, simply enter the side length in your preferred unit (cm, m, inches…). The results will be in the same unit cubed for volume, squared for area, and linear for diagonals.

The calculator automatically sets negative values to 0 and shows a warning. Side length must be non‑negative.