√ Square Root Calculator
Find the square root, cube root or any nth root of a number. Enter a value and a root degree to get an instant, precise result.
What is this tool?
A root is the inverse operation of raising a number to a power. The square root of a number x is the value that, when multiplied by itself, gives x back — for example, the square root of 25 is 5 because 5 × 5 = 25. The cube root is the value that, when used as a factor three times, gives x, so the cube root of 27 is 3. Roots show up in geometry (the Pythagorean theorem), in statistics (standard deviation), and in physics (root-mean-square values), so having a quick root calculator is genuinely handy. This tool computes three things at once: the square root, the cube root, and a custom nth root of your choosing. Just enter the number and, for the custom root, the degree n (so entering 4 gives the fourth root). It works with whole numbers, decimals, and — for odd roots — negative numbers, and it reports clearly when a root is not defined for real numbers (such as the square root of a negative value). Everything runs locally in your browser with no server and no stored history, so the values you enter are completely private. Results are shown to high precision and update instantly whenever you change an input.How it works
The square root is calculated as x raised to the power of one half, which the calculator evaluates with JavaScript’s Math.sqrt for maximum accuracy. The cube root uses Math.cbrt, which correctly handles negative inputs (the cube root of −8 is −2). The custom nth root is computed as x raised to the power of 1/n, again using the power function for precision. Validation is built in. The square root of a negative number is not a real value, so the tool warns you instead of showing an imaginary result. The same applies to even roots (fourth root, sixth root) of negative numbers, which are also not real. Odd roots of negative numbers, however, are perfectly valid and are returned as negative values. The custom root degree must be a positive integer greater than zero, and the tool will prompt you if it is missing or invalid.How to use
- Enter the number you want to take the root of.
- Optionally enter a custom root degree n (for example 4 for the fourth root).
- Press the Calculate button.
- Read the square root, cube root and custom nth root of your number.
- Adjust the value or root degree to recalculate.
Frequently Asked Questions
Frequently Asked Questions
Why can I not take the square root of a negative number?
Multiplying any real number by itself always gives a positive result (or zero), so no real number squared equals a negative value. The square root of a negative number is an imaginary number, which this real-number calculator does not display, so it shows a warning instead.
What is the difference between square root and cube root?
The square root finds a value that, multiplied by itself, gives the original number. The cube root finds a value that, used as a factor three times, gives the original number. Cube roots are special because they work for negative numbers too — the cube root of −8 is −2.
How do I calculate a fourth or higher root?
Enter the number in the main field, then type the root degree in the custom root field (4 for the fourth root, 5 for the fifth root, and so on). The result appears in the custom root line. Even roots of negative numbers are not real and will trigger a warning.
How precise are the results?
Very precise. The calculator uses JavaScript’s built-in square-root and power functions, which are accurate to about 15 significant figures. The displayed result is rounded to a readable number of decimals, but the underlying calculation is essentially exact for practical purposes.
Tips & Advice
Many square roots are irrational, which means the result is a long non-repeating decimal — √2 is roughly 1.41421 and never ends, so do not expect a tidy whole number unless your input is a perfect square like 16, 25 or 144. Cube roots are friendlier for negative numbers because the cube root of a negative is simply the negative of the cube root of the positive (the cube root of −27 is −3). For quick estimates, remember that √2 ≈ 1.41 and √3 ≈ 1.73 — two values that come up constantly in engineering and physics. If you need the root of a very large number, scientific notation keeps things readable. Roots and fractional exponents are interchangeable, so the fourth root of 16 is the same as 16 raised to the power 0.25, which is 2.
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