On This Page
- Cube volume formula
- How to calculate volume of a cube
- Find side length from cube volume
- Worked examples
- How to calculate the volume of a cuboid
- Box and solid figure problems
- Cube volume units, liters, and gallons
- Frequently asked questions
Cube Volume Formula
- V = volume
- s = side length (any edge, all edges are equal)
- s³ = side × side × side
A cube has equal length, width, and height, so one measurement gives the full three-dimensional volume. Note that s² gives the area of one square face, always cube (s³) for volume. For capacity problems, use the inside side length, not the outside.
The space diagonal, the longest straight line from corner to corner through the interior, is:
For packaging, the space diagonal is the maximum length of an item that fits diagonally inside a cube-shaped box.
How to Calculate Volume of a Cube
Identify the side length and multiply it by itself three times. Make sure the side length is in one consistent unit before calculating, mixing centimeters and inches gives a meaningless result.
- Find the side length: s
- Square it: s²
- Multiply once more: s³
- Write the answer in cubic units, cm³, m³, in³, ft³
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. For non-perfect-cube volumes, bracket estimation, and prime factoring methods, see How to Find the Side Length of a Cube from Its Volume. When the cube-shaped volume is a construction pour rather than a maths problem, the Concrete Calculator converts the same cubic measurement into cubic yards and bags of concrete needed.
Worked 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.
How to Calculate the Volume of a Cuboid
A cuboid (also called a rectangular prism) has three sides that are not all equal. To calculate the volume of a cuboid, multiply length by width by height, you cannot use the cube formula unless all three are the same.
- Cube: V = s³, use when length = width = height
- Cuboid: V = l × w × h, use when any two sides differ
For example, a box that is 5 cm × 5 cm × 5 cm is a cube: V = 5³ = 125 cm³. A box that is 5 cm × 4 cm × 3 cm is a cuboid: V = 5 × 4 × 3 = 60 cm³.
A common homework question asks you to calculate the volume of a cuboid where one or more dimensions include a variable. For example, a box with length 2x, width x, and height 3 has volume V = 2x × x × 3 = 6x². Treat it the same way, multiply all three dimensions together.
Box and Solid Figure Problems
Some problems say "box," "storage cube," or "solid figure" even when the shape is not a true cube. The first thing to check is whether all three dimensions are equal. If they are not, use the cuboid formula l × w × h rather than s³. The Tank Volume Calculator handles rectangular boxes with a filled-depth field if you also need partial-fill capacity.
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 |
Frequently Asked Questions
How do you calculate the volume of a cube?
Use V = s³. Multiply the side length by itself three times. A cube with side 5 cm has volume 5 × 5 × 5 = 125 cm³. If the problem gives volume and asks for the side length, use the cube root: s = ∛V.
What if my three dimensions aren't equal, cube or cuboid?
If length, width, and height are not all equal, the shape is a cuboid (rectangular prism), not a cube. Use V = length × width × height. The cube formula V = s³ only applies when all three sides are identical.
What is the difference between cube volume and surface area?
Volume measures how much the cube can hold, cubic centimeters of material, liters of liquid. Surface area measures the outside covering, how much paint or cardboard is needed. A 10 cm cube has 1,000 cm³ of volume and 600 cm² of surface area; they measure different things in different units.
How do you find the side length from cube volume?
Take the cube root: s = ∛V. If V = 512 cm³, then s = ∛512 = 8 cm. In Excel: =A1^(1/3).
Why does cubing a decimal like 0.5 give a much smaller result?
Decimals between 0 and 1 get smaller when multiplied by themselves: 0.5 × 0.5 × 0.5 = 0.125. Volume scales as the cube of side length, halving the side gives one-eighth the volume, not half. This is why small measurement errors in side length have an outsized effect on volume.
References
- Cube, Wolfram MathWorld: formal definition, all derived measurements including space diagonal, surface area, and inscribed sphere radius.
- Cuboid, Wolfram MathWorld: rectangular prism volume formula and distinction from the cube.
- Cuboids and Rectangular Prisms, Math is Fun: practical explanation of the cube vs. cuboid distinction with examples.