Cube Calculator

Calculate volume, surface area & edge length of any cube instantly

Calculation Results

Enter a cube measurement to calculate all properties.

Cube Diagram

a = 0 V = 0 S = 0 f = 0 d = 0

The Cube: A Perfect 3D Shape

A cube is a three-dimensional geometric shape with six equal square faces, twelve equal edges, and eight vertices. All internal angles are 90°, and every face is a square.

Key Properties of a Cube

  • Edge Length (a) - The length of any side of the square face.
  • Surface Area (A) - Total area of all six square faces (A = 6a²).
  • Volume (V) - The amount of 3D space the cube occupies (V = a³).
  • Diagonals - Each face has a diagonal (d_face = √2a); the space diagonal is longer (d_space = √3a).
  • Faces, Edges, Vertices - 6 faces, 12 edges, and 8 vertices.

Mathematical Equations of a Cube

  • Surface Area
    A = 6a²
  • Volume
    V = a³
  • Face Diagonal
    d_face = √2a
  • Space Diagonal
    d_space = √3a

Why Are Cubes Important?

  • Mathematics – Essential in volume and area calculations, 3D geometry.
  • Engineering – Used in structural and load distribution studies.
  • Technology – Represent pixels in 3D modeling and data visualization.
  • Everyday Life – Boxes, dice, Rubik's cubes – all real-world cubes.

Facts About Cubes

  • The cube is a special case of a rectangular prism where all sides are equal.
  • The cube is one of the five Platonic solids.
  • All cubes are symmetric and have the highest possible number of axes of symmetry for a 3D object.

The cube is a symbol of uniformity and balance. With its perfect symmetry and practical applications, it plays a critical role in geometry, design, architecture, and more.

Cube Formulas

  • Surface Area (A): A = 6a²
  • Volume (V): V = a³
  • Edge Length (a): a = ∛V
  • Face Diagonal: d_face = √2a
  • Space Diagonal: d_space = √3a
a

Edge (a)

A

Surface Area (A)

V

Volume (V)

d

Space Diagonal

How to Use the Cube Calculator

This Cube Calculator computes surface area, volume, edge length, or diagonals based on known values.

1 Select the Input Type

Choose what you know:

  • Edge Length (a)
  • Volume (V)
  • Surface Area (A)

Example: If you know edge = 4, choose edge length.

2 Enter the Known Value

Enter numeric values in the fields.

  • Use only positive values.
  • Use decimals if needed (e.g., 3.5).

Example: Edge = 5

3 Click "Calculate"

The calculator will display:

  • Surface Area
  • Volume
  • Face and Space Diagonals

Example Use Cases

  • Shipping boxes - Estimate capacity or material cost.
  • Game design - Calculate size or space for 3D models.
  • Architecture - Modeling modular structures or volumes.

Example Calculations

  • Example 1: Edge = 3 units

    • Surface Area = 6 × 9 = 54 units²
    • Volume = 27 units³
    • Diagonal ≈ 5.20 units

  • Example 2: Volume = 64 units³

    • Edge = 4 units
    • Surface Area = 96 units²

  • Example 3: Surface Area = 150 units²

    • Edge ≈ 5 units
    • Volume ≈ 125 units³

Frequently Asked Questions

1. What is the volume of a cube?

The volume is calculated by cubing the edge length:

V = a³

2. Is every cube also a square?

No, but every face of a cube is a square. A square is 2D, a cube is 3D.

3. Are all sides and angles of a cube equal?

Yes. All sides are equal in length, and all angles are 90°.

4. Where are cubes used in real life?
  • Packaging: Boxes and containers
  • Games: Dice, Rubik's cubes
  • Construction: Modular components
  • Computing: Voxel-based 3D graphics

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