THE NUMORIX GUIDE
How to use the Square Root Calculator
Last reviewed September 14, 2026
What this calculator does
Use Newton's iteration x_(n+1) = (x_n + value/x_n)/2, starting at value/2 and taking at most ten iterations.
Formula and method
Use Newton's iteration x_(n+1) = (x_n + value/x_n)/2, starting at value/2 and taking at most ten iterations. The displayed result is rounded to four decimals.
Variables and inputs
Value defaults to 2 and the UI allows nonnegative values. The result is the principal nonnegative square root.
Worked example
For value 2, start x0=1; x1=(1+2/1)/2=1.5; x2=(1.5+2/1.5)/2=1.4166667; later iterations approach 1.41421356, displayed as 1.4142.
How to interpret the result
The principal square root is the nonnegative number whose square equals the input. Negative numbers have no real square root.
Common mistakes to avoid
Do not report both plus and minus roots for this calculator's square-root operation; those are solutions of x^2=value, while sqrt(value) is the principal root.
Assumptions and limitations
The engine can produce NaN for value 0 because its initial guess is zero and the iteration divides by x. Complex roots and exact radical simplification are not supported.
Practical use and checks
The Square Root Calculator returns the principal nonnegative number whose square equals the input. Enter 2 as a check; the result should be about 1.4142, and squaring that displayed value gives approximately 1.99996 because of rounding. Entering 25 should return exactly 5, which is an easier check for a distance, diagonal, or scale calculation. Do not report both 5 and -5 for the square-root operation; those are the two solutions to x^2 = 25, while the principal square root is 5. Use a square root only after confirming the input represents a nonnegative real quantity. A negative radicand needs a complex-number treatment, not a silently invented real distance. The implementation uses an iterative method and rounds the visible result, so retain the full internal value when a later calculation is sensitive to precision. Zero is handled directly and returns zero. Units also change: the square root of square meters is meters, but the square root of an arbitrary number has no useful unit until the original formula is understood.