Cube Root Calculator

Q: How do I use this cube root calculator?

Type your number into the Number (Radicand) field. Make sure the Degree of Root is set to 3. The calculator will instantly show the cube root in the Result field. You can also use the Quick Cube Root section for even faster answers.

Q: Can this calculator find roots other than cube roots?

Yes. Change the Degree of Root field to any number. Use 2 for square roots, 4 for fourth roots, 5 for fifth roots, and so on. You can also use the General Nth Root section at the bottom of the calculator.

Q: Can I work backward from the result to find the original number?

Yes. Enter the Result and the Degree of Root , and leave the Number field empty. The calculator will compute the original number for you. For example, entering a result of 5 with degree 3 gives you 125.

Introduction

A cube root is the number that, when multiplied by itself three times, gives you the original number. For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27. In algebra, finding cube roots is a key skill you need for solving equations, simplifying expressions, and working with volume formulas. Unlike square roots, cube roots can handle negative numbers too — the cube root of −8 is −2 because (−2) × (−2) × (−2) = −8.

This cube root calculator lets you find the cube root of any number instantly. Just type in a value and the tool does the math for you, showing the result along with a step-by-step verification. You can also use it to calculate square roots, fourth roots, or any nth root you need. A built-in reference table of common cube roots and perfect cubes makes it easy to check your homework or study for a test. Whether you are learning about radicals for the first time or solving advanced algebra problems, this calculator gives you fast, accurate answers every time.

How to Use Our Cube Root Calculator

Enter a number and a root degree to find the root value, or input any two of the three fields to solve for the missing one. The calculator gives you the result, checks if it is a perfect root, and verifies the answer.

Number (Radicand): Type the number you want to find the root of. This is the value that sits under the root symbol. You can use the ± button to switch between positive and negative numbers.

Degree of Root (Index): Enter the root degree. Use 3 for a cube root, 2 for a square root, or any whole number for a higher root. The default is set to 3 for cube roots.

Result (Root): This field shows the answer, or you can type a result here and the calculator will work backward to find the number or degree. Use the ± button to toggle the sign.

Quick Square Root (√): Enter any non-negative number in this section to instantly find its square root. This is a shortcut when you only need a simple square root without changing the degree.

Quick Cube Root (∛): Type any number, including negative values, to get its cube root right away. This section is ideal when you want a fast cube root answer without extra steps.

General Nth Root: Enter a root degree and a number to calculate any nth root. Set the degree to 4 for a fourth root, 5 for a fifth root, and so on. Negative numbers only work with odd root degrees.

Common Cube Roots Reference Table: Scroll through this table to see cube roots for a wide range of numbers, from negative values up to one million. Perfect cubes are highlighted so you can spot them easily.

Cube Root Function Visualization: View the chart to see how the cube root function behaves across positive and negative numbers. You can zoom in and hover over points to read exact values.

A cube root is a number that, when multiplied by itself three times, gives you the original number. For example, the cube root of 27 is 3, because 3 × 3 × 3 = 27. We write this using the radical symbol with a small 3: ∛27 = 3. Cube roots are a key part of algebra and show up whenever you need to reverse the process of cubing a number.

How Cube Roots Work

Every real number has exactly one real cube root. This is different from square roots, which only work with zero and positive numbers. Cube roots can handle negative numbers too. For instance, ∛(−8) = −2, because (−2) × (−2) × (−2) = −8. This works because multiplying three negative numbers together gives a negative result.

Perfect Cubes vs. Non-Perfect Cubes

A perfect cube is a number whose cube root is a whole number. The most common perfect cubes are:

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

These come from cubing the integers 1 through 10. Most numbers are not perfect cubes, so their cube roots are irrational numbers — decimals that go on forever without repeating. For example, ∛2 ≈ 1.2599 and ∛10 ≈ 2.1544.

The General Concept: Nth Roots

Cube roots are one type of nth root. The nth root of a number asks: "What number, raised to the power of n, equals this value?" A square root uses n = 2, a cube root uses n = 3, a fourth root uses n = 4, and so on. The general formula is:

ⁿ√x = x^1/n

So the cube root of a number can also be written as that number raised to the power of 1/3. For example, 27^1/3 = 3. This exponent form is especially useful in algebra when you need to simplify expressions or solve equations. You can explore exponent operations further with our Exponent Calculator.

When You Need Cube Roots

Cube roots appear in many real-world and math problems:

Volume problems: If you know a cube has a volume of 125 cubic inches, you find the side length by computing ∛125 = 5 inches. For related volume calculations, try our Sphere Volume Calculator or Cylinder Volume Calculator.
Solving cubic equations: Equations like x³ = 64 are solved by taking the cube root of both sides. For quadratic equations, our Quadratic Formula Calculator can help.
Science and engineering: Cube roots show up in formulas for density, scaling, and fluid dynamics.

Important Rules for Cube Roots

Product rule: ∛(a × b) = ∛a × ∛b
Quotient rule: ∛(a ÷ b) = ∛a ÷ ∛b
Cube root of zero: ∛0 = 0
Cube root of 1: ∛1 = 1
Negative inputs are allowed: Unlike even roots, odd roots (like cube roots) accept negative numbers.

Understanding cube roots builds a strong foundation for working with exponents, radicals, and higher-level algebra. Whether you are solving for a missing side length, simplifying an expression, or checking your homework, knowing how cube roots behave makes the math much easier to follow. For related math tools, explore our Log Calculator, Scientific Notation Calculator, or Fraction Calculator to tackle other common algebra tasks.

Frequently Asked Questions

What is a cube root?

A cube root is a number that, when multiplied by itself three times, gives you the original number. For example, the cube root of 64 is 4 because 4 × 4 × 4 = 64. We write it as ∛64 = 4.

How do I use this cube root calculator?

Type your number into the Number (Radicand) field. Make sure the Degree of Root is set to 3. The calculator will instantly show the cube root in the Result field. You can also use the Quick Cube Root section for even faster answers.

Can I find the cube root of a negative number?

Yes. Cube roots work with negative numbers. For example, ∛(−27) = −3 because (−3) × (−3) × (−3) = −27. Use the ± button next to the input field to switch your number to negative.

What is the difference between a cube root and a square root?

A square root asks what number times itself equals the original (2 factors). A cube root asks what number times itself three times equals the original (3 factors). Square roots cannot be taken of negative numbers in real math, but cube roots can.

What does the ± button do?

The ± button flips the sign of the number in the input field. If you have 8, pressing ± changes it to −8. If you have −8, it changes back to 8. This is a quick way to switch between positive and negative values.

How does the calculator verify my answer?

The calculator takes the result and raises it to the power of the root degree. If the answer matches the original number, a checkmark appears. For example, if ∛27 = 3, it checks that 3³ = 27 ✓.

What does 'perfect root' mean in the results?

A perfect root means the answer is a whole number with no decimals. For cube roots, numbers like 8, 27, 64, and 125 are perfect cubes because their cube roots are exactly 2, 3, 4, and 5. The calculator tells you Yes ✓ or No ✗.

Can this calculator find roots other than cube roots?

Yes. Change the Degree of Root field to any number. Use 2 for square roots, 4 for fourth roots, 5 for fifth roots, and so on. You can also use the General Nth Root section at the bottom of the calculator.

What happens if I enter a negative number with an even root degree?

The calculator will show an error. Even roots (like square roots or fourth roots) of negative numbers do not produce real number answers. Only odd roots (like cube roots or fifth roots) work with negative numbers.

Can I work backward from the result to find the original number?

Yes. Enter the Result and the Degree of Root, and leave the Number field empty. The calculator will compute the original number for you. For example, entering a result of 5 with degree 3 gives you 125.

How accurate are the results?

The calculator shows up to 10 decimal places for exact values and provides a rounded version at 4 decimal places. For perfect cubes, the answer is exact with no rounding needed.

What is a radicand?

The radicand is the number under the root symbol. In ∛27, the radicand is 27. It is the number you want to find the root of.

What is the index of a root?

The index is the small number in front of the root symbol that tells you which type of root to take. In ∛27, the index is 3 (cube root). In ⁴√16, the index is 4 (fourth root). If no index is shown, it is assumed to be 2 (square root).

Why does the cube root of 0 equal 0?

Because 0 × 0 × 0 = 0. There is no other number that, when cubed, gives you 0. So ∛0 = 0.

What are the highlighted rows in the reference table?

The highlighted rows are perfect cubes — numbers whose cube roots are whole numbers. These are useful to memorize because they come up often in math problems and exams.