Root CalculatorFree online math calculator — instant results, no sign-up
Square, cube and nth roots.
About the Root Calculator
The Root Calculator computes the principal square root, cube root, and arbitrary nth root of a given number. It serves students, engineers, and scientists solving radical equations, evaluating geometric scaling, or working through algebraic powers.
- Number
- The radicand (x) from which roots are extracted; typically a positive real number.
- Root (n)
- The degree or index (n) of the custom root; any non-zero real number.
Formula and method
√x = x^(1/2) ∛x = x^(1/3) nth root = x^(1/n)
- xThe radicand (input number)
- nThe root index (degree of the nth root)
The tool computes the square root via Math.sqrt, the cube root via Math.cbrt, and the nth root by raising x to the exponent (1 / n). All outputs are rounded to a maximum of 10 decimal places.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Number64
- Root (n)3
Results
- √x8
- ∛x4
- nth root4
How to use the Root Calculator
- 1Enter the base value into the Number field.
- 2Enter the desired degree into the Root (n) field.
- 3Evaluate the standard square root and cube root of the base number.
- 4Evaluate the nth root by raising the base number to the power of 1 divided by n, formatted up to 10 decimal places.
Reading your result
The results display three values simultaneously: the square root (√x), the cube root (∛x), and the specific nth root chosen. When the input is a perfect square, cube, or nth power, the output yields an exact integer; otherwise, it provides a high-precision decimal approximation.
Limitations
The calculator does not evaluate complex or imaginary numbers; negative bases will return NaN for the square root and the general nth root. It also outputs decimal approximations rather than simplified radical expressions or surds.
Common questions
Why does the nth root return NaN for negative numbers?+
In JavaScript, fractional exponentiation of negative bases (x ** (1/n)) is not supported for real numbers and returns NaN, even when n is an odd integer.
What happens if the Root (n) is set to 0?+
A root index of zero requires evaluating an exponent of 1/0, which is undefined in mathematics and causes the calculation to fail.
Can n be a decimal or a negative number?+
Yes. A decimal root represents a non-integer power, and a negative root index computes the reciprocal root, equivalent to 1 / (x^(1/|n|)).
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.