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Root Calculator

Math

Calculate the square root, cube root, or any nth root of a number instantly. Enter a value and degree to get a precise result with step-by-step working.

Reviewed by the thecalcu.com team · Last updated June 30, 2026

64

Result

8

This calculator computes your Result from the values you enter.

Inputs
ValueRoot Degree
Outputs
Result

What is a Root?

A Root Calculator finds the square root, cube root, or any nth root of a number, the value that, when raised to the chosen power, returns the original number. While square roots are the most commonly needed, many maths, science, and engineering problems call for cube roots, fourth roots, or other degrees, and calculating these by hand for non-perfect values requires either a lookup table or iterative approximation.

This calculator computes any root degree from 2 to 6 instantly and precisely, including for numbers that aren't perfect squares or cubes. It pairs well with the Quadratic Formula Calculator, which uses square roots internally as part of solving quadratic equations.

Why Use a Root Calculator?

Calculating roots by hand is straightforward only for perfect squares and cubes, finding the square root of 10 or the cube root of 50 without a calculator means either estimating or working through a slow approximation method. Getting an accurate answer quickly matters whenever a root calculation feeds into a larger problem, like finding a side length from a known area or volume.

This calculator handles any root degree precisely in one step. A student checking homework, an engineer working through a calculation involving a non-perfect root, or anyone curious about a specific root value gets an instant, accurate decimal result rather than an estimate.

Who Should Use This Calculator?

  • Students and teachers working through algebra or geometry problems involving square roots, cube roots, or higher-degree roots.
  • Engineering and science students needing precise root calculations as part of a larger formula or equation.
  • Anyone reversing a power calculation, for example, finding the side length of a cube from its known volume.
  • Finance students calculating compound annual growth rates, which involve taking an nth root of a growth ratio.
  • Puzzle and maths enthusiasts exploring properties of roots and exponents.

What Insights Does the Root Calculator Give You?

The calculator returns a single, precise result along with a verification step:

  • Result, the calculated root, shown to six decimal places for non-perfect roots.
  • Verification, in the step-by-step breakdown, the calculator shows the result raised back to the chosen degree, confirming it returns close to your original input.

This verification step is particularly useful for double-checking that the root degree you selected matches what you intended, since selecting the wrong degree (square root instead of cube root, for example) gives a very different result.

How to use this Root calculator

  1. Enter the Value you want to find the root of.
  2. Select the Root Degree, Square Root, Cube Root, Fourth Root, Fifth Root, or Sixth Root.
  3. Read the Result card for the calculated root.
  4. Open the step-by-step breakdown to see the equivalent exponent form and a verification check.
  5. Change the Root Degree at any time to recalculate the same value at a different root.
Show formula & methodology ↓Show less ↑

Formula & Methodology

Taking the nth root of a number is equivalent to raising it to the power of 1/n:

Result = Value^(1/n), where n is the selected root degree

Worked example: for a value of 64 with Cube Root (n = 3) selected:
- Result = 64^(1/3) = 4
- Verification: 4³ = 4 × 4 × 4 = 64 ✓

Worked example (non-perfect root): for a value of 10 with Square Root (n = 2) selected:
- Result = 10^(1/2) ≈ 3.162278
- Verification: 3.162278² ≈ 10.0000 ✓

Frequently Asked Questions

What is a root in mathematics?
A root is the inverse of raising a number to a power, the nth root of a number x is the value that, when multiplied by itself n times, equals x. The square root (n=2) is the most common, but cube roots, fourth roots, and higher-degree roots follow the same underlying idea.
How do I calculate a square root?
Select 'Square Root' as the Root Degree and enter the number, for example, entering 64 gives a result of 8, since 8 × 8 = 64. This calculator handles square roots that aren't perfect squares too, giving a precise decimal result.
What is the cube root of a number?
The cube root of a number x is the value that, when multiplied by itself three times, equals x. For example, the cube root of 27 is 3, since 3 × 3 × 3 = 27.
What is the relationship between roots and exponents?
Taking the nth root of a number is mathematically the same as raising it to the power of 1/n, for example, the square root of x equals x^(1/2). This calculator uses that exponent form internally to compute any root degree precisely.
Can I calculate roots of numbers that aren't perfect squares or cubes?
Yes, this calculator handles any non-negative number, giving a precise decimal result even when the answer isn't a whole number. For example, the square root of 10 is approximately 3.162278, not a clean integer.
Why does this calculator only accept non-negative values?
Even-degree roots (square root, fourth root, etc.) of a negative number aren't real numbers, they require imaginary numbers, which this calculator doesn't compute. Restricting input to non-negative values keeps results meaningful for all root degrees without needing separate handling for odd-degree roots of negative numbers.
What is the difference between a root and a radical?
'Root' and 'radical' refer to the same mathematical concept, radical specifically refers to the √ symbol used to denote a root, while 'root' refers to the value itself. The terms are often used interchangeably in everyday usage.
How accurate is the result for non-perfect roots?
The calculator returns results rounded to six decimal places, which is precise enough for academic, engineering, and most practical calculations. The verification step shown alongside the result lets you confirm the answer raised back to the chosen degree returns close to the original value.
What's a real-world use for calculating roots?
Roots come up in geometry (finding a side length from an area or volume), finance (calculating compound growth rates), and statistics (standard deviation calculations use square roots). Many of these calculations require working backwards from a power to find the original base value.
What is the difference between this and the Quadratic Formula Calculator?
The [Quadratic Formula Calculator](/quadratic-formula-calculator/) solves a full quadratic equation, which internally uses a square root as part of a larger formula. This Root Calculator isolates just the root operation itself, useful whenever you need a root calculation on its own rather than as part of solving an equation.
Also known as
square root calculatorcube root calculatornth root calculatorradical calculatorfourth root calculator