Nth Root Calculator

Calculate the real-number nth root of any value. The tool validates that the degree is positive, handles negative bases correctly for odd roots, and returns precise decimals suitable for math homework, engineering, or data analysis.

Use the same unit that raised to the nth power produced this value. Negative numbers are allowed for odd integer roots.
Enter a positive integer. For square roots use 2, for cube roots use 3, and so on.

Mathematical tool for educational use. Validate critical engineering or scientific calculations independently.

Examples

  • Value 81 with n = 4 ⇒ 3, because 3⁴ = 81.
  • Value 0.008 with n = 3 ⇒ 0.2, matching 0.2³ = 0.008.
  • Value −125 with n = 3 ⇒ −5, the real cube root of −125.

FAQ

Can I enter fractional values for n?

Enter positive integers for real results. Fractional degrees often lead to complex numbers, which this calculator does not display.

Why do I get an error for negative numbers with even n?

Even-degree roots of negative numbers require complex arithmetic. The tool alerts you so you can switch to an odd root or handle the problem with complex numbers separately.

How precise are the results?

Outputs retain full double-precision (about 15 decimal digits). Round manually if you need a specific number of decimal places.

What if I need the principal complex root?

This calculator focuses on real numbers. For complex analysis, use a CAS or scientific calculator that supports complex outputs.

Additional Information

  • General formula: the nth root of a is a^(1/n), provided n ≠ 0.
  • Even-degree roots of negative numbers are not real; the calculator flags those cases instead of returning an incorrect value.
  • Results use JavaScript's double-precision floating point. Tiny rounding differences (on the order of 1e-12) may appear for very large exponents.
  • To convert roots into exponents, remember that a^(m/n) = (nth root of a)^m.

Related calculators