On This Page
- How to use the Cube Volume Calculator
- Cube volume formula
- How to calculate volume of a cube
- Find side length from cube volume
- Worked examples
- Cube vs. cuboid volume
- Box and solid figure problems
- Cube volume units, liters, and gallons
- Frequently asked questions
How to Use the Cube Volume Calculator
Use this cube volume calculator when all three dimensions are the same and you know one side length. Enter the side, choose the unit, and the page shows volume, face area, surface area, space diagonal, total edge length, liters, gallons, cubic feet, and step-by-step work.
Use it for homework, cube-shaped boxes, dice, classroom models, storage blocks, packaging cubes, and any object where length, width, and height are equal.
Cube Volume Formula
The standard formula for calculating cube volume is:
- V = volume
- s = side length of the cube
- s³ = side × side × side
A cube has equal length, width, and height. That is why a single measurement is enough to calculate the full three-dimensional volume.
How to Calculate Volume of a Cube
To calculate cube volume by hand, identify the side length and multiply it by itself three times. Make sure the side length is in one unit before calculating.
Step 1: Identify the Side Length
The side length is the length of any edge of the cube. Since all edges are equal, you only need one measurement.
Step 2: Square the Side Length
Multiply the side length by itself to find the area of one square face.
Step 3: Multiply by the Side Length Again
Multiplying by the side length a third time gives the space inside the cube.
- Find the side length: s
- Square the side: s²
- Multiply by the side again: s³
- Write the answer in cubic units, such as cm³, m³, or in³
Find Side Length From Cube Volume
Sometimes a problem gives the volume of a cube and asks for the side length. In that case, use the cube root of the volume.
For example, if a cube has volume 1,000 cm³, then s = ∛1,000 = 10 cm.
Worked Cube Volume Examples
Most cube questions follow the same path: find the side length, apply V = s³, and write the answer in cubic units.
Example 1: Classroom Storage Cube
Problem: A classroom storage bin is shaped like a cube. The inside side length is 18 inches. How much space is inside the bin?
- Side length = 18 in
- Use V = s³
- V = 18³ = 18 × 18 × 18
- V = 5,832 in³
Answer: The storage cube has 5,832 cubic inches of internal volume.
Example 2: Aquarium Decoration Cube in Centimeters
Problem: A solid glass decoration is a cube with side length 7 cm. Find the volume of glass used to make the cube.
- Side length = 7 cm
- Volume = 7³
- 7 × 7 × 7 = 343
- V = 343 cm³
Answer: The cube volume is 343 cm³.
Example 3: Find the Missing Edge Length
Problem: A cube-shaped box has a volume of 512 cubic inches. Find the length of one edge.
- Known volume: V = 512 in³
- Use s = ∛V
- s = ∛512
- Since 8 × 8 × 8 = 512, s = 8 in
Answer: Each edge is 8 inches long.
Example 4: Cube Capacity in Liters
Problem: A cube-shaped water container has an inside side length of 0.4 meters. Estimate its capacity in liters. Use 1 m³ = 1,000 liters.
- Side length = 0.4 m
- Volume = 0.4³ = 0.064 m³
- Convert to liters: 0.064 × 1,000 = 64 L
Answer: The container holds about 64 liters.
Example 5: Cube From Space Diagonal
Problem: A cube has a space diagonal of 10.392 cm. Find its approximate volume. Use s = diagonal ÷ √3.
- Side length = 10.392 ÷ √3 ≈ 6 cm
- Volume = 6³
- V = 216 cm³
Answer: The cube volume is about 216 cm³.
Cube or Cuboid: Which Formula Should You Use?
Use the cube formula only when all three dimensions are equal. If the object has different length, width, and height, it is a cuboid or rectangular prism, not a cube.
- Cube: V = s³
- Cuboid: V = length × width × height
For example, a box that is 5 cm by 5 cm by 5 cm is a cube. A box that is 5 cm by 4 cm by 3 cm is a cuboid, so you should multiply all three dimensions.
Box and Solid Figure Problems
Some homework questions say "box," "storage cube," or "solid figure" even when the shape is not a single cube. First decide whether all edges are equal. If they are not equal, use length × width × height for each rectangular prism instead of the cube formula.
Example: Storage Cube With Side 5y Inches
Problem: A storage cube has length, width, and height each labeled 5y inches. Find the volume of the storage cube.
- Side length = 5y inches
- Volume = (5y)³
- (5y)³ = 5³y³ = 125y³
Answer: The volume is 125y³ cubic inches.
Example: Volume 0.001 Cubic Units, Find the Edge
Problem: The volume of a cube is 0.001 cubic units. Find the length of one edge.
- Use s = ∛V
- s = ∛0.001
- 0.1 × 0.1 × 0.1 = 0.001
Answer: The edge length is 0.1 units.
If your shape has different length, width, and height, the closest current tool is the Tank Volume & Liquid Capacity Calculator, which uses the rectangular prism formula.
Cube Volume Units, Liters, and Gallons
Cube volume is written in cubic units. If the side length is in centimeters, the result is cubic centimeters. If the side length is in inches, the result is cubic inches.
| Input Unit | Volume Unit | Useful Conversion |
|---|---|---|
| Centimeters | cm³ | 1,000 cm³ = 1 liter |
| Meters | m³ | 1 m³ = 1,000 liters |
| Inches | in³ | 231 in³ = 1 US gallon |
| Feet | ft³ | 1 ft³ ≈ 7.48052 US gallons |
Cube Volume Mistakes to Avoid
- Squaring instead of cubing: s² gives face area. s³ gives volume.
- Using different units: Convert the side length before calculating if measurements are mixed.
- Using outside measurements for capacity: Use inside side length for containers.
- Using the cube formula for a cuboid: If length, width, and height are not equal, use l × w × h.
Frequently Asked Questions
How do you calculate the volume of a cube?
Use V = s³. Multiply the side length by itself three times.
What is the formula for cube volume?
The formula is V = s³, where s is the side length of the cube.
How do you calculate cube volume from side length?
Substitute the side length into V = s³. For example, if s = 6 cm, then V = 6³ = 216 cm³.
How do you find the side length from cube volume?
Take the cube root of the volume: s = ∛V.
What is the difference between cube volume and surface area?
Volume measures the space inside the cube and uses s³. Surface area measures the outside covering and uses 6s².