How to Calculate N Root in Excel

The nth root of a number is a fundamental mathematical operation that finds a value which, when raised to the power of n, equals the original number. In Excel, you can calculate nth roots using built-in functions or custom formulas. This guide explains how to perform these calculations accurately in spreadsheets.

What is the Nth Root?

The nth root of a number x is a value y such that y^n = x. For example, the cube root of 27 is 3 because 3^3 = 27. The nth root is the inverse operation of exponentiation.

Common roots include:

Square root (2nd root)
Cube root (3rd root)
Fourth root (4th root)

For non-integer roots, Excel provides functions to handle these calculations precisely.

Excel Formula for Nth Root

Excel provides two main functions to calculate nth roots:

POWER Function

For positive real numbers, you can use the POWER function to calculate roots:

y = x^(1/n)

In Excel: =POWER(x, 1/n)

EXP and LN Functions

For more complex calculations, you can use logarithms:

y = EXP(LN(x)/n)

In Excel: =EXP(LN(x)/n)

Note

The POWER function is generally preferred for most root calculations as it's more straightforward and performs better with positive numbers. The logarithmic approach is useful when dealing with very large or very small numbers.

Step-by-Step Calculation

Determine the number (x) you want to find the root of.
Choose the root index (n).
Use the formula =POWER(x, 1/n) in Excel.
Press Enter to calculate the result.

For example, to find the cube root of 64:

=POWER(64, 1/3)

This will return 4 because 4^3 = 64.

Examples with Numbers

Number (x)	Root Index (n)	Formula	Result
16	2	=POWER(16, 1/2)	4
81	4	=POWER(81, 1/4)	3
1000	3	=POWER(1000, 1/3)	10

These examples demonstrate how to calculate different roots in Excel using the POWER function.

Common Mistakes

Using the wrong root index (n). Always ensure you're using the correct root for your calculation.
Attempting to find roots of negative numbers with even roots. Excel will return an error for these cases.
Forgetting to include the "1/" in the formula. The correct formula is =POWER(x, 1/n), not =POWER(x, n).

Frequently Asked Questions

Can I calculate fractional roots in Excel?

Yes, you can calculate fractional roots in Excel using the POWER function. For example, the 1/2 root is the same as the square root.

What happens if I try to calculate an even root of a negative number?

Excel will display a #NUM! error because even roots of negative numbers are not real numbers in the real number system.

Is there a difference between the POWER function and the EXP/LN approach?

The POWER function is generally preferred for most root calculations as it's more straightforward. The logarithmic approach is useful for very large or very small numbers where precision might be an issue.