Cube Volume Calculator
This calculator finds the volume, total surface area, face diagonal, and space diagonal of a cube based on the length of its edge (side).
Enter the edge length (a) of the cube below to calculate its properties. Ensure you use consistent units for your input.
Enter Cube Dimension
Understanding Cube Volume & Formulas
What is a Cube?
A cube is the three-dimensional analog of a square. It is a regular solid object bounded by six equal square faces, with three faces meeting at each vertex. All angles are right angles, and all edges have the same length. It's a special type of rectangular prism where length, width, and height are equal.
The Cube Volume Formula
The formula for cube volume is found by multiplying the edge length (a) by itself three times (cubing the edge length):
V = a * a * a = a³
Where:
- V is the Volume
- a is the length of one edge (side) of the cube
This simple cube volume equation calculates the 3D space inside the cube.
Other Cube Formulas
- Total Surface Area (SA): A cube has 6 identical square faces, each with an area of a².
SA = 6 * a² - Face Diagonal (df): The diagonal distance across one square face of the cube. Found using the Pythagorean theorem on a face.
df = √(a² + a²) = √(2a²) = a√2≈ 1.414 * a - Space Diagonal (ds): The diagonal distance through the interior of the cube from one vertex to the opposite vertex.
ds = √(a² + a² + a²) = √(3a²) = a√3≈ 1.732 * a
Example Calculation (Provided in Original Text)
EX: Bob has a cubic suitcase with edge lengths (a) of 2 feet. Calculate the volume:
V = a³ = (2 ft)³ = 2 * 2 * 2 = 8 cubic feet (ft³).
Real-Life Cube Volume Examples
Click on an example to see the step-by-step calculation:
Example 1: Standard Die Volume
Scenario: Calculate the volume of a standard six-sided die.
1. Known Value: Typical Edge Length (a) ≈ 1.6 cm.
2. Formula: V = a³
3. Calculation: V = (1.6)³ = 1.6 * 1.6 * 1.6
4. Result: V = 4.096 cubic cm.
Conclusion: A standard die has a volume of about 4.1 cubic centimeters.
Example 2: Sugar Cube Volume
Scenario: Find the volume of a common sugar cube.
1. Known Value: Edge Length (a) ≈ 1.5 cm.
2. Formula: V = a³
3. Calculation: V = (1.5)³ = 1.5 * 1.5 * 1.5
4. Result: V = 3.375 cubic cm.
Conclusion: A sugar cube typically has a volume of about 3.4 cubic centimeters.
Example 3: Rubik's Cube Volume
Scenario: Calculate the total volume occupied by a standard 3x3 Rubik's Cube.
1. Known Value: Edge Length (a) ≈ 5.7 cm.
2. Formula: V = a³
3. Calculation: V = (5.7)³ = 5.7 * 5.7 * 5.7
4. Result: V ≈ 185.19 cubic cm.
Conclusion: A Rubik's Cube occupies roughly 185 cubic centimeters of space.
Example 4: Cubic Foot Box Volume
Scenario: Find the volume of a shipping box described as "one cubic foot".
1. Known Value: Edge Length (a) = 1 foot.
2. Formula: V = a³
3. Calculation: V = (1)³ = 1 * 1 * 1
4. Result: V = 1 cubic foot.
Conclusion: By definition, a box with 1-foot edges has a volume of 1 cubic foot.
Example 5: Ice Cube Volume
Scenario: Calculate the volume of a single ice cube from a tray making cubic cubes.
1. Known Value: Edge Length (a) = 1 inch.
2. Formula: V = a³
3. Calculation: V = (1)³ = 1 * 1 * 1
4. Result: V = 1 cubic inch.
Conclusion: Each ice cube has a volume of 1 cubic inch.
Example 6: Wooden Building Block Volume
Scenario: Find the volume of a standard cubic wooden block for children.
1. Known Value: Edge Length (a) = 3 cm.
2. Formula: V = a³
3. Calculation: V = (3)³ = 3 * 3 * 3
4. Result: V = 27 cubic cm.
Conclusion: The building block has a volume of 27 cubic centimeters.
Example 7: Cubic Ottoman Volume
Scenario: Calculate the volume of space occupied by a cubic ottoman.
1. Known Value: Edge Length (a) = 16 inches.
2. Formula: V = a³
3. Calculation: V = (16)³ = 16 * 16 * 16
4. Result: V = 4096 cubic inches (or 2.37 cubic feet).
Conclusion: The ottoman takes up 4096 cubic inches of space.
Example 8: Fabric Storage Cube Volume
Scenario: Find the internal storage volume of a common fabric cube.
1. Known Value: Internal Edge Length (a) ≈ 11 inches.
2. Formula: V = a³
3. Calculation: V = (11)³ = 11 * 11 * 11
4. Result: V = 1331 cubic inches.
Conclusion: The storage cube holds about 1331 cubic inches.
Example 9: Large Storage Box Volume
Scenario: Calculate the volume of a large cubic plastic storage box.
1. Known Value: Edge Length (a) = 50 cm (or 0.5 meters).
2. Formula: V = a³
3. Calculation: V = (50)³ = 125,000 cubic cm OR V = (0.5)³ = 0.125 cubic meters.
4. Result: V = 125,000 cm³ (which is 125 Liters or 0.125 m³).
Conclusion: The large box has a volume of 0.125 cubic meters.
Example 10: Voxel Volume (Conceptual)
Scenario: In computer graphics, a voxel is like a 3D pixel. Find the volume if it's a cube.
1. Known Value: Edge Length (a) = 1 unit (e.g., 1 mm, 1 pixel unit).
2. Formula: V = a³
3. Calculation: V = (1)³ = 1
4. Result: V = 1 cubic unit.
Conclusion: A single cubic voxel has a volume of 1 cubic unit relative to its edge length unit.
Understanding Volume Measurement
Volume is the quantification of the three-dimensional space a substance occupies...
Common Volume Units Reference
Ensure your input edge length uses a consistent unit...
Frequently Asked Questions about Cube Volume
1. What is the formula for volume of a cube?
The volume (V) of a cube is calculated by cubing the length of one edge (a): V = a³ (or side * side * side).
2. How is cube volume related to a square?
A cube is made of 6 square faces. The volume extends the 2D area of one square face (a²) into the third dimension by multiplying by the edge length again (a² * a = a³).
3. How do I calculate the volume if I only know the surface area (SA)?
The surface area is SA = 6a². First, find the edge length 'a' by rearranging: a = √(SA / 6). Then, calculate the volume using V = a³.
4. How do I find the volume from the face diagonal (df)?
The face diagonal is df = a√2. Rearrange to find the edge: a = df / √2. Then calculate volume: V = a³ = (df / √2)³.
5. How do I find the volume from the space diagonal (ds)?
The space diagonal is ds = a√3. Rearrange to find the edge: a = ds / √3. Then calculate volume: V = a³ = (ds / √3)³.
6. What is the formula for the surface area of a cube?
The total surface area (SA) is the sum of the areas of the 6 square faces: SA = 6 * a², where 'a' is the edge length.
7. What's the difference between a face diagonal and a space diagonal?
A face diagonal goes across one flat square face of the cube. A space diagonal goes through the interior of the cube from one corner to the furthest opposite corner.
8. What units will the results be in?
If you enter the edge length in meters (m), the volume will be in cubic meters (m³), the surface area in square meters (m²), and the diagonals in meters (m).
9. What if my object is box-shaped but not a perfect cube?
If the length, width, and height are different, it's a rectangular prism (or cuboid). Its volume is calculated as V = length * width * height.
10. How does the volume change if I double the edge length?
Since volume is V = a³, if you double the edge length (to 2a), the new volume becomes V = (2a)³ = 2³ * a³ = 8 * a³. The volume increases by a factor of 8.
11. Is a die a perfect cube?
Usually very close, but the rounded corners/edges and the indented pips slightly reduce the actual volume compared to a perfect mathematical cube of the same nominal edge length.
