Exponent & Root Calculator

What powers and roots actually do

Raising a number to a power means multiplying it by itself. In 5³, the base is 5 and the exponent is 3, so you get 5 × 5 × 5 = 125. A root runs that backward: the cube root of 125 asks "what number, multiplied by itself three times, gives 125?" — and the answer is 5. This tool handles both directions so you don't have to reach for a scientific calculator or remember which key does what.

When you'd reach for this

It's handy for homework and quick checks: squares and cubes, square roots for the Pythagorean theorem, or compound-growth figures like 1.05¹⁰ to see what a 5% yearly increase does over ten years. It also covers the awkward cases a basic calculator fumbles — a negative exponent such as 2^-3 (which equals 1/8 = 0.125), a fractional exponent, or a fourth or fifth root that most phone calculators simply don't offer a button for.

A worked example

Say you want the 5th root of 32. Enter 32 as the number and 5 as the root index, and you'll get 2, because 2⁵ = 32. Flip it around: base 2, exponent 5, and you're back to 32. Seeing both directions side by side is a quick way to sanity-check your own arithmetic.

How to use it

1. Pick the mode: power (base to an exponent) or root (the nth root of a number).
2. Type the base or number in the first field.
3. Enter the exponent, or the root index (2 for square root, 3 for cube root, and so on).
4. Read the result instantly. Change either field and it recalculates as you type — no submit button needed.

FAQ

Can it handle negative or decimal exponents?

Yes. Negative exponents give a fraction (2^-2 = 0.25), and decimals work too — 9^0.5 is the same as the square root of 9, which is 3.

Why does an even root of a negative number fail?

There's no real answer. No real number squared gives a negative result, so the square, fourth, or sixth root of a negative number isn't a real value. Odd roots, like the cube root of -27 (which is -3), work fine.

Are very large results exact?

Small whole-number powers are exact. Very large or many-decimal results are shown to standard browser precision and may round slightly at the far end, which is normal for any calculator.

Is it free, and does anything leave my device?

It's completely free, supported by the ads on the page, and every calculation runs inside your browser — nothing you type is uploaded or stored.