Volume of a Cube Calculator
Calculate the volume of a cube using side length, surface area, or space diagonal. Get step-by-step solutions with formulas and examples.
Volume
Cube Properties
Formula Used
Cube Diagram
a = Side Length | A = 6a² | V = a³ | d = a√3
Common Cube Volumes
| Side Length | Volume | Surface Area | Space Diagonal |
|---|---|---|---|
| 1 unit | 1 cu unit | 6 sq units | 1.732 units |
| 2 units | 8 cu units | 24 sq units | 3.464 units |
| 3 units | 27 cu units | 54 sq units | 5.196 units |
| 4 units | 64 cu units | 96 sq units | 6.928 units |
| 5 units | 125 cu units | 150 sq units | 8.660 units |
| 10 units | 1000 cu units | 600 sq units | 17.321 units |
Frequently Asked Questions
What is the formula for the volume of a cube?
The formula for the volume of a cube is V = a³ where a is the length of one side. You can also calculate volume using: V = (√(A/6))³ (from surface area) or V = (d/√3)³ (from space diagonal).
How do you calculate the volume of a cube with side length?
Multiply the side length by itself three times: Volume = side × side × side = side³. For example, a cube with side length 5 cm has volume 5 × 5 × 5 = 125 cm³.
What is the volume of a 4x4x4 cube?
A 4x4x4 cube has side length 4 units. Volume = 4 × 4 × 4 = 64 cubic units. Surface area = 6 × 4² = 96 square units.
How to find the volume of a cube from surface area?
Step 1: Find the side length: a = √(Surface Area / 6)
Step 2: Calculate volume: V = a³
Example: Surface Area = 150 cm² → a = √(150/6) = √25 = 5 cm → V = 5³ = 125 cm³
How to find the volume of a cube from diagonal?
Step 1: Find the side length: a = d / √3
Step 2: Calculate volume: V = a³
Example: Space Diagonal = 8.66 cm → a = 8.66 / 1.732 = 5 cm → V = 5³ = 125 cm³
What is the volume of a cube with side 2.5 cm?
Volume = 2.5 × 2.5 × 2.5 = 15.625 cm³. Surface area = 6 × 2.5² = 37.5 cm². Space diagonal = 2.5 × √3 = 4.33 cm.
What is the difference between volume and surface area of a cube?
Volume measures the space inside the cube (cubic units), while surface area measures the total area of all six faces (square units). For a cube with side a: Volume = a³, Surface Area = 6a².
What is a real-world example of cube volume?
Cube volume is used in many real-world applications:
- Shipping container capacity (3m × 3m × 3m = 27 m³)
- Aquarium water capacity (1ft × 1ft × 1ft = 1 ft³ ≈ 7.48 gallons)
- Construction concrete volume (cubic yards)
- Packaging box capacity