Exponent Calculator

Calculate powers and exponents instantly. Enter a base and exponent to get the result, with support for negative and fractional exponents in this free online power calculator.

How to Use

  1. Enter the base

    Input the base number for the exponentiation.

  2. Enter the exponent

    Input the exponent value. Negative numbers and decimals are supported.

  3. View result

    Click Calculate to see the result of the power calculation instantly.

What is an exponent (power)?

An exponent, or power, is the operation of multiplying the same number by itself several times. It is written as aⁿ, where the base a on the bottom is multiplied by itself n times (the exponent). For example, 2³ = 2 × 2 × 2 = 8, read as 'two to the power of three'.

Why use exponents?

  • Compact notation for large numbers: 1,000,000 can be written more concisely as 10⁶.
  • Compound growth: compound interest, population growth, and cell division that grow by a fixed rate each period are modeled in the form (1+r)ⁿ.
  • Area and volume: a cube with a side of 5 has a volume of 5³ = 125.

This calculator handles not only integers but also negative exponents (reciprocals) and fractional or decimal exponents (roots) all at once, instantly computing large powers that are tedious to work out by hand.

Formula

The basic formula for a power is as follows.

result = base^exponent = aⁿ

  • a (base): the number to multiply repeatedly
  • n (exponent): the number of times to multiply

Example 1 — integer exponent: 3⁴ = 3 × 3 × 3 × 3 = 81

Example 2 — negative exponent: 2⁻³ = 1 / 2³ = 1 / 8 = 0.125

Example 3 — fractional exponent: 8^(1/3) = ³√8 = 2 (cube root)

This calculator rounds the result to up to 10 decimal places, and if the result grows too large to represent, it is shown as ∞.

Frequently Asked Questions

What is an exponent (power)?
An exponent (power) is the operation of multiplying the same number several times. For example, 2^3 = 2 × 2 × 2 = 8, where 2 is the base and 3 is the exponent.
How are negative exponents calculated?
A negative exponent a^(-n) means the reciprocal and is calculated as 1/(a^n). For example, 2^(-3) is 1/8 = 0.125, and 10^(-2) is 1/100 = 0.01.
Can I enter fractional exponents?
Yes, entering a fractional exponent as a decimal gives a root. Entering 8^(1/3) as about 0.3333 yields the cube root of 8, which is 2, and 9^0.5 gives the square root of 9, which is 3.
What about powers of zero?
Any nonzero number raised to the power of 0 is 1 (e.g., 5^0 = 1). A positive power of 0 is 0, while a negative power of 0 becomes 1/0 and is undefined (infinity).
What is zero to the power of zero?
0^0 is a mathematically debated indeterminate form, but in most practical contexts such as combinatorics and polynomials it is conventionally defined as 1. This calculator also treats it as 1.
How is a result shown when it becomes too large?
When a result like 10^400 exceeds the range a computer can represent, it is shown as infinity (∞). If it diverges in the negative direction it shows -∞, and undefined operations are reported as 'undefined'.
How does exponentiation differ from multiplication?
2 × 3 means adding 2 three times (2+2+2), whereas 2^3 means multiplying 2 three times (2×2×2). That is why values grow explosively faster than multiplication as the exponent increases.
To how many decimal places is it calculated?
If the result is an integer it is shown as is, and if a decimal appears it is rounded to up to 10 decimal places. This provides enough precision even when irrational numbers arise, as with fractional exponents.
Verified 2026 formulas

Related Calculators