Square Root Calculator — √n with Curve
Enter any non-negative number to instantly find its square root (√n), plus the reciprocal (1/√n), cube root, and n². A y = √x curve plots where your value falls along the radical function.
The non-negative value that, when multiplied by itself, gives n
- 1
Radicand (input n)
16 - 2
Square root √n
√16 = 4 - 3
Verify: (√n)² = n
4² = 16Squaring the square root returns the original number.
How does this calculator work?
The square root √n is the non-negative number that, squared, returns n. Enter any non-negative number to get √n with up to 6 decimal places, plus the reciprocal (1/√n), cube root (∛n), n², and a y = √x plot. Perfect squares give exact integers; all others give irrational decimals.
Formula
How this is calculated
The square root of a non-negative number n is the non-negative value r such that r × r = n. Written as √n or n^(1/2), it is the inverse of squaring. For example √16 = 4 because 4² = 16, and √2 ≈ 1.41421356 because 1.41421356² ≈ 2.
For perfect squares (1, 4, 9, 16, 25, …) the result is an exact integer. For all other non-negative numbers, √n is irrational — a non-repeating, non-terminating decimal. The calculator uses IEEE 754 double-precision floating point, giving about 15–16 significant digits of accuracy.
Negative numbers have no real square root; their square roots are imaginary (written as √(−n) = i√n in complex notation). This calculator only handles the real case; enter non-negative values. The reciprocal 1/√n is undefined at n = 0.
Frequently asked questions
For a rough estimate, find the two nearest perfect squares (e.g. √20 is between √16 = 4 and √25 = 5). For more digits, use the digit-by-digit method or Newton's method: start with a guess g, then iterate g = (g + n/g)/2 until it converges. Most calculators and phones have a √ key for direct computation.
No — √2 is irrational, proved in ancient Greece. It cannot be expressed as a fraction p/q of integers. Its decimal expansion begins 1.41421356… and continues forever without repeating.
Square root (√n = n^½) finds the value that when squared gives n. Cube root (∛n = n^⅓) finds the value that when cubed gives n. For n = 8: √8 ≈ 2.828 but ∛8 = 2. The cube root of negative numbers is real (e.g. ∛(−8) = −2), unlike the square root.
Also known as
TG we-Calculate Editorial Team. (2026). Square Root Calculator — √n with Curve [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/square-root-calculator
TG we-Calculate Editorial Team. "Square Root Calculator — √n with Curve." TG we-Calculate. 2026. https://we-calculate.com/calculator/square-root-calculator.
TG we-Calculate Editorial Team, "Square Root Calculator — √n with Curve," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/square-root-calculator
@misc{wecalculate_square_root_calculator, title = {Square Root Calculator — √n with Curve}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/square-root-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?