Volume of a Cube Calculator
Calculate the volume, surface area, face diagonal, and space diagonal of a cube from its side length. See also Volume of Rectangular Prism Calculator and Volume of Cylinder Calculator.
How to Calculate the Volume of a Cube
To find the volume of a cube, measure the length of any edge — all edges of a cube are equal. Cube that length (multiply it by itself three times) to get the volume. The surface area is six times the square of the side length, since a cube has six identical square faces. This calculator also computes the face diagonal and space diagonal.
Cube Volume Formula
V = s³
SA = 6 × s²
Face Diagonal = s × √2
Space Diagonal = s × √3
Example
Find the volume of a cube with side length 5:
V = s³
V = 5³
V = 125 cubic units
SA = 6 × 5² = 6 × 25 = 150 square units
Cube Volume Reference Table
| Side | Volume | Surface Area | Space Diagonal |
|---|---|---|---|
| 1 | 1 | 6 | 1.7321 |
| 2 | 8 | 24 | 3.4641 |
| 3 | 27 | 54 | 5.1962 |
| 4 | 64 | 96 | 6.9282 |
| 5 | 125 | 150 | 8.6603 |
| 6 | 216 | 216 | 10.3923 |
| 7 | 343 | 294 | 12.1244 |
| 8 | 512 | 384 | 13.8564 |
| 9 | 729 | 486 | 15.5885 |
| 10 | 1000 | 600 | 17.3205 |
| 12 | 1728 | 864 | 20.7846 |
| 15 | 3375 | 1350 | 25.9808 |
| 20 | 8000 | 2400 | 34.6410 |
| 25 | 15625 | 3750 | 43.3013 |
| 50 | 125000 | 15000 | 86.6025 |
Solved Examples
Example 1: Ice Cube Melting
An ice cube has a side length of 3 cm. What volume of water does it produce when it melts? (Ice and water have nearly the same volume for this approximation.)
V = s³ = 3³
V = 27 cm³ = 27 mL of water
Example 2: Rubik's Cube Volume
A standard Rubik's Cube has a side length of 5.7 cm. Find its total volume.
V = s³ = 5.7³
V = 5.7 × 5.7 × 5.7
V ≈ 185.19 cm³
Example 3: Dice Volume
A standard die (singular of dice) has sides of 1.6 cm. What is its volume?
V = s³ = 1.6³
V = 4.096 cm³
Example 4: Cubic Storage Container
A cubic storage box has an internal side length of 0.5 m. How many liters can it hold?
V = 0.5³ = 0.125 m³
1 m³ = 1000 L
V = 0.125 × 1000 = 125 liters
Practice Questions
Q1: Find the volume of a cube with side length 8 cm.
Answer: V = 8³ = 512 cm³
Q2: A cube has a volume of 343 cm³. What is its side length?
Answer: s = ∛343 = 7 cm
Q3: If the side of a cube is tripled, how does the volume change?
Answer: V₂ = (3s)³ = 27s³ = 27V₁. The volume increases by a factor of 27.
Q4: What is the surface area of a cube with volume 64 cm³?
Answer: s = ∛64 = 4 cm; SA = 6 × 4² = 6 × 16 = 96 cm²
Q5: A cube has a space diagonal of 10√3 cm. Find its volume.
Answer: Space diagonal = s√3; s√3 = 10√3; s = 10 cm; V = 10³ = 1000 cm³
Q6: How many 2 cm cubes fit inside a 10 cm cube?
Answer: Along each edge: 10/2 = 5 cubes; Total = 5 × 5 × 5 = 125 small cubes
Common Mistakes
Confusing s² with s³: Surface area uses s² (squared), but volume uses s³ (cubed). A cube with side 5 has SA = 150 but V = 125.
Multiplying by 6 for volume: The factor 6 is for surface area (6 faces), not volume. Volume is simply s × s × s.
Using edge length as diagonal: The space diagonal (s√3) and face diagonal (s√2) are longer than the side. Don't substitute them for s in the volume formula.
Incorrect cube root: When finding side from volume, use cube root (∛), not square root (√). ∛27 = 3, not √27 ≈ 5.2.
Key Takeaways
- Cube volume is simply V = s³ — the side length multiplied by itself three times.
- A cube is the simplest volume calculation — only one measurement needed.
- To find the side from volume, take the cube root: s = ∛V.
- Surface area = 6s² (six identical square faces).
- The space diagonal of a cube = s√3; the face diagonal = s√2.
- Doubling the side increases volume by 8×, and tripling by 27×.
Frequently Asked Questions
What is the volume of a cube?
The volume of a cube is the total three-dimensional space enclosed within its six square faces. Since all edges are equal, the volume is simply the side length cubed: V = s³.
What is the difference between a cube and a rectangular prism?
A cube is a special case of a rectangular prism where all three dimensions (length, width, height) are equal. A rectangular prism can have different values for each dimension.
What is the space diagonal of a cube?
The space diagonal connects two opposite corners of the cube, passing through its interior. It equals s√3, where s is the side length. For a cube with side 5, the space diagonal is 5√3 ≈ 8.6603.
How do I find the side length from the volume?
Take the cube root of the volume: s = ∛V. For example, if V = 125, then s = ∛125 = 5.