Volume of a Cube Calculator
Calculate cube volume, surface area, and diagonals using multiple input methods
Calculate Cube Volume
Length of one edge of the cube
Calculation Results
Formula Used
Volume Formula: V = a³
Where: a = 0.0000 cm
Calculation: V = (0.0000)³ = 0.0000 cm³
Example Calculation
Problem
Find the volume of a cube with a side length of 5 cm.
Solution
Given: Side length (a) = 5 cm
Formula: V = a³
Calculation: V = (5)³ = 5 × 5 × 5 = 125 cm³
Answer: Volume = 125 cm³
Cube Properties
6 square faces of equal size
12 edges of equal length
8 vertices (corners)
All angles are 90 degrees
Most regular 3D shape
Key Formulas
Volume:
V = a³
Surface Area:
SA = 6a²
Face Diagonal:
f = a√2
Cube Diagonal:
d = a√3
Reverse Formulas:
a = ∛V
a = √(SA/6)
a = f/√2
a = d/√3
Quick Tips
A cube is a special case of a rectangular prism where all sides are equal
Volume grows with the cube of the side length (V ∝ a³)
Face diagonal is √2 times the side length
Cube diagonal is √3 times the side length
Understanding Cubes and Volume
What is a Cube?
A cube is a three-dimensional geometric shape consisting of six square faces, twelve edges, and eight vertices. All edges have the same length, and all faces are congruent squares. It's one of the five Platonic solids and the most regular 3D shape.
Real-World Examples
- •Dice (gaming cubes)
- •Rubik's Cube
- •Ice cubes
- •Sugar cubes
- •Storage boxes
Why is the Volume Formula V = a³?
The volume formula comes from the basic principle that volume equals length × width × height:
V = l × w × h
Since all sides of a cube are equal (l = w = h = a):
V = a × a × a = a³
Diagonal Relationships
Face Diagonal: Using Pythagorean theorem on a square face:
f² = a² + a² = 2a² → f = a√2
Cube Diagonal: Using Pythagorean theorem in 3D:
d² = a² + a² + a² = 3a² → d = a√3