Cube Calculator

Calculate volume, surface area, and diagonals of a cube from its side length.

What is a Cube?

A cube is a three-dimensional solid shape with six identical square faces, twelve equal edges, and eight vertices (corners). It is the most symmetrical of all three-dimensional shapes - every face, edge, and vertex is geometrically equivalent to every other. Mathematically, a cube is a regular hexahedron, one of only five Platonic solids.

Because all sides of a cube are equal, there is only one measurement needed to fully describe it: the side length (s). From this single dimension, the volume, surface area, face diagonal, and space diagonal can all be derived precisely.

The volume of a cube (s³) represents how much three-dimensional space it encloses. The term “cubing” a number in mathematics - raising it to the power of three - comes directly from the cube’s volume formula. The surface area (6 × s²) represents the total area of all six square faces, telling you how much material would be needed to construct or coat the cube’s exterior.

The face diagonal is the diagonal drawn across a single square face, connecting two non-adjacent corners on that face. Since each face is a square with side s, the face diagonal = s√2 (by the Pythagorean theorem applied to the right triangle formed by two sides and the diagonal of the square face). The space diagonal connects two diagonally opposite corners of the entire cube, passing through its center. Its length is s√3, derived by applying the Pythagorean theorem in three dimensions: space diagonal = √(s² + s² + s²) = s√3.

Cubes appear throughout everyday life: dice, Rubik’s cubes, ice cubes, and cubic units of volume measurement (cm³, m³, ft³) all derive from or relate to the cube. In chemistry, many crystalline substances adopt cubic lattice structures. In computing, three-dimensional arrays of data are sometimes called “data cubes.”

Formula

Volume of a Cube:

V = s³

s = Side length

V = Volume (cubic units)

Surface Area of a Cube:

SA = 6 × s²

SA = Surface Area (square units, from 6 identical square faces each with area s²)

Face Diagonal and Space Diagonal:

Face Diagonal = s × √2 Space Diagonal = s × √3

Face diagonal: Pythagorean theorem across one square face → √(s² + s²) = s√2

Space diagonal: Pythagorean theorem in 3D → √(s² + s² + s²) = s√3

How to Use This Calculator

Enter the side length of your cube. All sides are equal, so only one value is needed.
Click Calculate to compute all four measurements simultaneously.
Read the results - volume in cubic units, surface area in square units, and both diagonals in linear units matching your input.
Application tip - if you know the volume and want the side length, compute s = ∛V manually and then enter that value to verify all other measurements.

Example Calculations

Example 1 - Dice (Side = 2 cm)

A standard casino die has a side length of approximately 2 cm.

s = 2 cm

Volume = 2³ = 8 cm³

Surface Area = 6 × 2² = 6 × 4 = 24 cm²

Face Diagonal = 2 × √2 = 2.828 cm

Space Diagonal = 2 × √3 = 3.464 cm

Volume = 8 cm³ | Surface Area = 24 cm² | Face Diagonal = 2.8284 cm | Space Diagonal = 3.4641 cm

Try this example →

Example 2 - Shipping Crate (Side = 1.2 m)

A cubic shipping crate has a side of 1.2 m. Find its capacity and material needed.

s = 1.2 m

Volume = 1.2³ = 1.728 m³ = 1,728 litres capacity

Surface Area = 6 × 1.44 = 8.64 m² (material to build all 6 faces)

Space Diagonal = 1.2 × √3 = 2.078 m (longest object that fits inside the crate)

Volume = 1.728 m³ | Surface Area = 8.64 m² | Space Diagonal = 2.0785 m

Try this example →

Frequently Asked Questions

What is the formula for the volume of a cube?+

Volume = s³, where s is the side length. A cube with side 4 cm has volume = 4³ = 64 cm³. This is why the term 'cubing' a number means raising it to the third power.

What is the surface area of a cube?+

A cube has 6 identical square faces. Surface Area = 6 × s². For a cube with side 4 cm, Surface Area = 6 × 16 = 96 cm².

What is the difference between a face diagonal and a space diagonal?+

A face diagonal connects two opposite corners of a single square face: its length = s√2. A space diagonal connects two opposite corners of the entire cube, passing through the center: its length = s√3. A cube with side 5 cm has face diagonal = 5√2 ≈ 7.07 cm and space diagonal = 5√3 ≈ 8.66 cm.

How is a cube different from a cuboid (rectangular box)?+

A cube is a special case of a cuboid (also called rectangular parallelepiped) where all three dimensions - length, width, and height - are exactly equal. Every cube is a cuboid, but a cuboid with unequal dimensions is not a cube.

What are real-world examples of cubes?+

Dice, Rubik's cubes, sugar cubes, ice cubes, and some shipping boxes are cube-shaped or approximately cubic. The cubic metre and cubic foot units of volume derive their names from the cube's volume formula (side³).

How do you calculate the volume of a cube?+

Volume of a cube = side^3 (side cubed). Example: a cube with side length 5 cm has volume = 5^3 = 125 cm^3. Volume is always in cubic units. If you know the surface area instead: side = sqrt(surface area / 6), then volume = side^3. If you know the space diagonal d: side = d / sqrt(3), then volume = (d / sqrt(3))^3.

What is the difference between face diagonal and space diagonal of a cube?+

The face diagonal connects two opposite corners of one face of the cube. Face diagonal = side x sqrt(2). The space diagonal (or main diagonal) connects two opposite corners of the entire cube, passing through the interior. Space diagonal = side x sqrt(3). Example: a cube with side 6 cm: face diagonal = 6 x 1.414 = 8.49 cm, space diagonal = 6 x 1.732 = 10.39 cm.

How many faces, edges, and vertices does a cube have?+

A cube has: 6 faces (all squares), 12 edges (all equal length), and 8 vertices (corners). It is one of the five Platonic solids. Each face is perpendicular to its four adjacent faces. Each vertex connects exactly 3 edges. These properties make the cube the most symmetric 3D shape, which is why it appears in architecture, engineering, packaging, and games (dice).