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Exponent and Root Calculator: Powers and Nth Roots

This free calculator raises a number to a power and finds square roots, cube roots and any nth root. Whole-number powers are shown exactly, however many digits they have.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

An exponent is repeated multiplication, and a root is its reverse. Squares and cubes appear in areas and volumes, powers of 2 in computing, and growth rates in finance and biology. Calculators often switch to scientific notation and hide the exact digits.

This tool keeps whole-number powers exact and also gives the result in scientific form for very large values.

How to Use This Tool

  1. Enter the base or the number in the first box.
  2. Enter the exponent, or the root degree, in the second box.
  3. Choose power or root.
  4. Press Calculate.

How the Calculation Works

Power: x^y is x multiplied by itself y times for whole y, and exp(y × ln x) in general. Root: the y-th root of x is x^(1/y). Whole-number powers up to 5,000 digits are worked out with big integers; other cases use floating-point maths with about 15 digits.

Worked Example

2^100 = 1,267,650,600,228,229,401,496,703,205,376. The 5th root of 32 is 2. 9^0.5 = 3. 10^−2 = 0.01. The cube root of −64 is −4.

Common Uses

  • Area and volume formulas.
  • Powers of 2 and 10 in computing.
  • Compound growth calculations.
  • Checking algebra answers.

Tips and Common Mistakes

  • 0^0 is left undefined in many books and is shown as 1 by most calculators.
  • Fractional exponents are roots: x^(1/2) is the square root.
  • Use the logarithm calculator to solve for the exponent.

Next, you may need the logarithm calculator, scientific notation converter, quadratic equation solver, area calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

An exponent says how many times to multiply a number by itself. 2^5 means 2 × 2 × 2 × 2 × 2 = 32.
It means one divided by the positive power: 2^−3 = 1 ÷ 2³ = 0.125.
Choose the root mode and enter 2 for a square root or 3 for a cube root. For example, the cube root of 27 is 3.
Odd roots of negative numbers work, for example the cube root of −8 is −2. Even roots of negative numbers are not real numbers.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.