A cube root tells you what number must be multiplied by itself three times to produce a given number.
For example:
3 × 3 × 3 = 27
Therefore:
∛27 = 3
Cube roots are useful in mathematics, geometry, engineering, construction, science, and whenever you need to work backward from the volume of a cube.
A Cube Root Calculator makes this calculation quick and easy, especially when the number is not a perfect cube.
What Is a Cube Root?
The cube root of a number is the value that, when multiplied by itself three times, equals the original number.
For more information about cube roots and mathematical roots, see the Cube Root reference from Wolfram MathWorld.
The symbol for cube root is:
∛
For example:
∛8 = 2
because:
2 × 2 × 2 = 8
Another example:
∛125 = 5
because:
5 × 5 × 5 = 125
Cube Root Formula
If:
x³ = n
then:
∛n = x
In other words:
Cube Root = Number^(1/3)
For example:
64^(1/3) = 4
because:
4³ = 64
Example 1 — Cube Root of 27
Find:
∛27
We know:
3 × 3 × 3 = 27
Therefore:
∛27 = 3
Example 2 — Cube Root of 64
Find:
∛64
Since:
4 × 4 × 4 = 64
the answer is:
∛64 = 4
Example 3 — Cube Root of 1,000
Find:
∛1000
Since:
10 × 10 × 10 = 1,000
therefore:
∛1000 = 10
Perfect Cubes
Some numbers have whole-number cube roots. These are called perfect cubes.
| Number | Cube Root |
|---|---|
| 1 | ∛1 = 1 |
| 8 | ∛8 = 2 |
| 27 | ∛27 = 3 |
| 64 | ∛64 = 4 |
| 125 | ∛125 = 5 |
| 216 | ∛216 = 6 |
| 343 | ∛343 = 7 |
| 512 | ∛512 = 8 |
| 729 | ∛729 = 9 |
| 1,000 | ∛1000 = 10 |
A number does not have to be a perfect cube to have a cube root.
For example:
∛50 ≈ 3.684
A calculator is particularly useful for results like this.
Cube Roots of Negative Numbers
Cube roots can also be calculated for negative numbers.
For example:
∛−8 = −2
because:
(−2) × (−2) × (−2) = −8
Similarly:
∛−125 = −5
This differs from square roots in the real-number system: every real number, including a negative number, has a real cube root.
Cube Root and Volume
Cube roots are especially useful when working with cubes.
The volume of a cube is:
Volume = Side³
If you already know the volume, you can find the side length using:
Side Length = ∛Volume
For example, suppose a cube has a volume of:
216 cm³
Then:
Side = ∛216
Side = 6 cm
because:
6 × 6 × 6 = 216 cm³
Cube vs Cube Root
These two operations reverse each other.
Cube:
4³ = 64
Cube Root:
∛64 = 4
Think of it as:
Number → Cube → Cube Root → Original Number
Where Are Cube Roots Used?
Cube roots can be useful in:
📐 Geometry — finding cube dimensions from volume.
🏗️ Construction — working with three-dimensional measurements.
🔬 Science — solving formulas involving cubic quantities.
⚙️ Engineering — analyzing dimensions and mathematical relationships.
📚 Education — learning powers, exponents and roots.
🧮 Everyday calculations — quickly solving unfamiliar cube roots.
How to Use the Cube Root Calculator
Using your LivingToolsGuide calculator should be simple:
1️⃣ Enter the number
2️⃣ Click Calculate
3️⃣ See the cube root
For example:
Input: 125
↓
Cube Root: 5
The calculator is especially helpful for numbers whose cube roots are decimals.
Cube Root Calculator: Quick and Easy Results
Enter a positive or negative number into the calculator to find its cube root instantly.
The Cube Root Calculator makes it easy to find cube roots quickly and check your calculations accurately.
👉 Use the Cube Root Calculator
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