What is the formula for the surface area of a cube?

The surface area of a cube is SA = 6s², where s is the side length. A cube has six identical square faces, each with area s². Multiplying by six gives the total surface area. For example, a cube with side length 5 cm has a surface area of 6 × 25 = 150 cm².

What is the formula for the volume of a cube?

The volume of a cube is V = s³, where s is the side length. Because a cube has equal length, width, and height, the volume is simply the side length multiplied by itself three times. For example, a cube with side length 5 cm has a volume of 5 × 5 × 5 = 125 cm³.

How do you find the diagonal of a cube?

A cube has two types of diagonal. The face diagonal runs across one square face and equals s√2 (approximately 1.414 × s). The space diagonal runs from one corner of the cube to the opposite corner through the interior and equals s√3 (approximately 1.732 × s). For a cube with side 5 cm, the face diagonal is 7.071 cm and the space diagonal is 8.66 cm.

Cube Surface Area and Volume Calculator

Enter the side length of a cube in millimetres, centimetres, metres, kilometres, inches, feet or yards to instantly calculate its surface area, volume, face diagonal and space diagonal, with full working shown for each result.

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Standard geometry Formulas based on Euclidean geometry. Valid for any consistent unit of length.

Cube Dimensions

Side length (s)

Please enter a positive number.

Unit of measurement

About a Cube

A cube is a three-dimensional solid with six equal square faces, twelve equal edges, and eight vertices. All sides are equal length. It is a special case of a rectangular box (cuboid) where length = width = height = s.

Key formulas:
Surface area: SA = 6s²
Volume: V = s³
Face diagonal: d₁ = s√2
Space diagonal: d₃ = s√3

Results

Surface Area
150
cm²

Volume
125
cm³

Face Diagonal

7.071

Space Diagonal

8.66

Full Working

Side length (s)5 cm

Surface area: 6 × s² = 6 × 25150 cm²

Volume: s³ = 5 × 5 × 5125 cm³

Face diagonal: s × √2 = 5 × 1.41421…7.071 cm

Space diagonal: s × √3 = 5 × 1.73205…8.66 cm

How to Calculate the Surface Area of a Cube

A cube has six identical square faces. Each face has an area of s² (side length squared). The total surface area is the sum of all six faces:

SA = 6s²

For example, a cube with side length 5 cm has a surface area of 6 × 5² = 6 × 25 = 150 cm². Surface area is measured in square units (cm², m², in², and so on).

How to Calculate the Volume of a Cube

Volume measures how much three-dimensional space the cube occupies. Because all three dimensions of a cube are equal, volume is simply the side length raised to the power of three:

V = s³

A cube with side length 5 cm has a volume of 5 × 5 × 5 = 125 cm³. Volume is measured in cubic units (cm³, m³, in³, and so on).

Diagonals of a Cube

There are two types of diagonal in a cube:

Face diagonal: runs across a single square face from one corner to the opposite corner. By Pythagoras, the face diagonal equals the hypotenuse of a right triangle with both legs equal to s, so the face diagonal = s√2. For a 5 cm cube: 5 × 1.41421 = 7.071 cm.
Space diagonal (body diagonal): runs from one corner of the cube to the diagonally opposite corner, passing through the interior. It equals s√3. You can derive this by applying Pythagoras twice: first to find the face diagonal (s√2), then treating that as one leg and s as the other to find the space diagonal: √((s√2)² + s²) = √(2s² + s²) = √(3s²) = s√3. For a 5 cm cube: 5 × 1.73205 = 8.66 cm.

Worked Example

A cube has a side length of 5 cm.

Property	Formula	Calculation	Result
Surface area	6s²	6 × 5² = 6 × 25	150 cm²
Volume	s³	5 × 5 × 5	125 cm³
Face diagonal	s√2	5 × 1.41421	7.071 cm
Space diagonal	s√3	5 × 1.73205	8.66 cm

Common Applications

Cube calculations appear in many practical contexts: estimating how much paint is needed to coat a box (surface area), calculating the capacity of a storage container (volume), determining whether a cube-shaped object will fit through a doorway (space diagonal), and in engineering when specifying cubic components.

Related Calculators

Maths and Stats Calculators: full list of geometry and statistics tools.
Volume Calculator: volume for multiple solid shapes.
Surface Area Calculator: surface area for multiple solid shapes.
Area of a Triangle Calculator: triangle area using base and height.

Method: Standard Euclidean geometry formulas for a regular hexahedron (cube). Surface area SA = 6s²; Volume V = s³; Face diagonal d₁ = s√2; Space diagonal d₃ = s√3. No external source required: these are universally accepted geometric identities.

This calculator is for educational purposes. Results are exact within floating-point precision. All formulas assume a perfect cube (all sides equal). Displayed values are rounded to three decimal places for surface area and volume, and three decimal places for diagonals.

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