A walkthrough, end to end.
- 1
Enter the number (radicand) and the root degree (n).
- 2
The calculator returns the n-th root.
- 3
Negative numbers work for odd-n roots; even-n roots of negatives are undefined in real numbers.
N-th root definition
ⁿ√x is the number that, raised to the n-th power, gives x. Equivalent to x^(1/n). For negative x, only odd n gives real result; even n gives complex.
What you can do with this.
Square root (n=2)
√25 = 5. Most common root operation. Used in geometry (Pythagoras), statistics (standard deviation), physics (kinetic energy).
Cube root (n=3)
∛27 = 3. Cubes work for negative inputs too: ∛(−8) = −2. The calculator handles signed cube roots correctly.
Higher-order roots
⁴√16 = 2. ⁵√32 = 2. Less common but appear in compound-growth math (n-period rate from total) and engineering.
CAGR back-calculation
If $1,000 grew to $1,500 over 5 years, CAGR = ⁵√(1.5) − 1 = 0.0845 = 8.45%. Use the calculator with radicand 1.5 and degree 5.
Geometric mean
Geometric mean of n numbers = n-th root of their product. The calculator's n-th root applied to the product gives geometric mean.
RMS (root mean square)
RMS = √(mean(x²)). Used in electrical engineering for AC voltage. Square the values, take mean, then square root — the calculator handles that final square root.
Negative numbers + even roots
√(−4) is undefined in reals (would be 2i). The calculator returns NaN. For complex roots, use a complex-number tool.
Root calculator 2026 — what's current
Built into every device. Useful for verification or when you don't have a sci-calc handy. AI tools handle reliably.
Frequently asked.
Undefined in real numbers. √(−1) is defined as the imaginary unit i in complex math. The calculator returns NaN for even-degree roots of negatives.
Cube roots of negatives are real (∛(−8) = −2). The calculator applies the negative sign correctly. JavaScript's Math.cbrt handles this; for higher odd n, the calculator uses sign manipulation.
Just a number with decimal places. ⁵√(1.5) ≈ 1.0845. Works the same way as integer radicands.
No. Calculations run entirely in your browser.