Power & Root Calculator
Calculate powers, square roots, cube roots and any exponentiation with our free online power and root calculator.
How to Use This Calculator
- Enter a base number in the first field.
- Enter an exponent (power) in the second field.
- Use the quick buttons for common operations: squaring (x²), cubing (x³), square root (√x), cube root (∛x), and reciprocal (x⁻¹).
- Click Calculate to see the result, mathematical notation, and expanded form.
Formula
Exponentiation raises a base number to a power. Special cases:
- Square root: a1/2 = √a
- Cube root: a1/3 = ∛a
- Negative exponent: a−n = 1 / an
- Zero exponent: a0 = 1 (for a ≠ 0)
Examples
Compound Interest
(1 + 0.05)10 = 1.6289 — $1 grows to approximately $1.63 at 5% annual interest over 10 years.
Physics (Gravity)
d = ½gt² where t = 3s gives d = ½ × 9.8 × 9 = 44.1 meters.
Root Finding
√144 = 12 — the side length of a square with area 144 square units.
Frequently Asked Questions
What is a power?
A power (or exponent) tells you how many times to multiply a number by itself. In 5², 5 is the base and 2 is the exponent, meaning 5 × 5 = 25.
What is a root?
A root is the inverse of a power. The square root of a number asks: what value multiplied by itself gives this number? For example, √25 = 5 because 5 × 5 = 25.
What does a negative exponent mean?
A negative exponent means taking the reciprocal. For example, 2−3 = 1/23 = 1/8 = 0.125.
Can I raise a negative number to a fractional power?
Raising a negative number to a fractional power can produce complex (imaginary) results. For real results, the base should be non-negative when the exponent is fractional.