Square root and nth-root calculations
What is a Square Root Calculator? It finds the square root or another positive whole-number root of a number and shows the formula, calculation steps, and result.
How to Use the Square Root Calculator
- Enter a decimal value in Number (x).
- Enter a whole-number root from
1through1000in Root index (n). It starts at2for a square root. - Optionally enter text in Number unit. The label is attached unchanged; it is not converted or reduced.
- Select Calculate to show the result and formula steps.
- Use Copy result or Download result (.txt) to save the plain-text output.
How the calculator handles values and roots
For x and n, the calculator uses x^(1/n), or the value r where r^n = x. It includes the formula steps in the result.
- Zero returns zero for any supported positive root index.
- Positive values return a real, non-negative root.
- Negative values work with odd root indexes, such as the cube root of
-8. - Negative values with even root indexes are rejected because this calculator does not return complex results.
Input rules and validation
Number (x) must use the calculator's supported decimal format. Scientific notation and a leading plus sign are not accepted, and the absolute value cannot exceed 1e15. Root index (n) must be a whole number from 1 through 1000.
Required fields, invalid number text, an oversized root index, a negative value with an even root index, or a non-finite calculated result show an error instead of a result.
Reset the calculator
Select Reset to clear Number (x) and Number unit, restore Root index (n) to 2, and hide the current result.
Privacy and calculation limits
The calculation is performed locally by the calculator code, and the calculator script does not upload the entered calculation values. The tool only handles the number, root index, and optional label described above; it does not convert or validate unit labels.
Frequently Asked Questions
What is the square root formula?
The square root of a number x is the value r such that r * r = x, written as sqrt(x) or x^(1/2). This calculator generalizes to the nth root: the value r such that r^n = x, written as x^(1/n).
Can I calculate a root other than the square root?
Yes. Enter a root index n, for example 3 for a cube root or 4 for a fourth root. Leaving the root index at 2 gives the standard square root.
What happens with a negative number?
A negative number has no real square root. It does have a real odd-index root (for example the cube root of -8 is -2). This calculator returns the real odd-index root when possible and shows an error for even-index roots of negative numbers instead of returning a complex number.
What is the root index?
The root index n specifies which root to take: n = 2 is the square root, n = 3 is the cube root, and so on. It must be a positive whole number for this calculator.
What units does this calculator support?
You can leave Number unit blank or type a label such as m^2, cm^2, or another text value. The result keeps the label as entered; the calculator does not convert or reduce unit exponents.