Root Calculator
Calculate the nth root of any number, from square roots to higher degrees.
- 1
Exponent (1/n)
1 ÷ 2 = 0.5 - 2
ⁿ√x
144 ^ 0.5 = 12
Formula
How this is calculated
This tool takes two inputs: the value x (the radicand, the number you want the root of) and the root degree n (the index, where 2 means square root and 3 means cube root). The nth root is the inverse of raising to the nth power, so it asks: what number, multiplied by itself n times, equals x?
For any non-negative x the calculator evaluates x^(1/n) directly, since raising to the reciprocal power undoes exponentiation. When x is negative, a real root exists only if n is an odd integer; in that case it computes −(−x)^(1/n) so the sign is preserved. Even roots of a negative number have no real value, so those inputs are flagged instead of returning a number.
Results are real-valued only (no complex roots) and n must be non-zero. Because floating-point powers are used, the output is shown rounded, and the "Check" row raises the result back to the nth power so you can confirm it returns approximately x. Tiny rounding differences in that check are expected and not errors.
About this calculator
The nth root of a number x is the value that, raised to the power n, gives back x. The square root (n = 2) and cube root (n = 3) are the most common cases. Roots are the inverse operation of exponentiation.
For non-negative values the nth root is x^(1/n). Negative values have a real root only when n is an odd integer, in which case the result is negative. Even roots of negative numbers are not real, so the calculator flags those inputs.
Frequently asked questions
Not within the real numbers. The square root of a negative number is imaginary, so this real-valued calculator does not return a result for it.
It is negative. For example, the cube root of −27 is −3, because (−3)³ = −27. Any odd root of a negative number is defined and negative.
Taking the nth root is the same as raising to the power 1/n, so the cube root of 8 equals 8^(1/3) = 2.
Also known as
TG we-Calculate Editorial Team. (2026). Root Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/root-calculator
TG we-Calculate Editorial Team. "Root Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/root-calculator.
TG we-Calculate Editorial Team, "Root Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/root-calculator
@misc{wecalculate_root_calculator, title = {Root Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/root-calculator}}, year = {2026}, note = {TG we-Calculate} }
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