Exponent and Power Calculator

Calculate powers, exponents, and exponential expressions with support for any base and exponent.

Exponent and Power Calculator tool

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Example

Input: Base 2, exponent 10

Result: 1,024 (1.024000e+3)

2^10 means 2 multiplied by itself 10 times: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1,024.

Exponent Rules With Examples

RuleExampleResult
Same base, multiply2^3 x 2^4 = 2^7128
Same base, divide5^6 / 5^4 = 5^225
Power of a power(3^2)^3 = 3^6729
Zero exponent7^01
Negative exponent2^-3 = 1 / 2^30.125
Fraction exponent (root)16^0.54
Decimal exponent10^2.5316.2277660168

Results from this calculator, up to 10 decimal places.

  1. Enter the base number in the base input field.
  2. Enter the exponent (power) in the exponent field - supports positive, negative, and decimal exponents.
  3. View the calculated result displayed instantly with up to 10 decimal places.
  4. Review the scientific notation form and the full expression shown alongside the result.
  5. Click the copy button to copy the result.

How Exponents Work, Including Negative Powers

An exponent tells you how many times to multiply a number by itself: 2^10 means ten 2s multiplied together, which is 1,024. This calculator raises any base to any power, including negative and decimal exponents. It shows the result, the same value in scientific notation, and the expression written out.

A few rules explain the results that surprise people. A negative exponent means one over the positive power, so 2^-3 is 1/8, or 0.125. Any non-zero number to the power of 0 is 1. An exponent of 0.5 is a square root, so 16^0.5 is 4. Decimal exponents land between whole powers: 10^2.5 is about 316.23, between 100 and 1,000. The table on this page collects these rules with worked examples.

Powers are how growth is measured. Money that grows 5% a year for 10 years is multiplied by 1.05^10, about 1.629. For savings with deposits, the Compound Interest Calculator builds on the same idea. To solve for the exponent, such as how many years it takes to double, use the Logarithm Calculator.

Fraction exponents must be typed as decimals. That works well for halves and quarters, but 1/3 has no exact decimal. Typing 0.333333 gets close to a cube root, not exact. For exact cube roots, the Square Root and Nth Root Calculator is a better fit. The calculator also flags inputs with no real answer. A negative base with a decimal exponent, such as (-8)^0.5, gives an error. So does 0 raised to a negative power. Negative bases work with whole exponents, so (-2)^3 is -8. Results above about 1.8 x 10^308 are too large to show.

Formula / How It Works

a^n = a x a x ... x a (n times) | a^(-n) = 1/a^n | a^(m/n) = n-th root of a^m

Frequently Asked Questions

It means one divided by the same power with a positive exponent. So 2^-3 = 1 / 2^3 = 1/8 = 0.125, and 10^-2 = 0.01. A negative exponent never makes the answer negative. It makes it smaller than 1 when the base is bigger than 1.
Any non-zero number to the power of 0 is 1. You can see why by dividing: 5^3 / 5^3 is 1, and by the rules of exponents it is also 5^0. The case 0^0 is debated in math, but most calculators and programming languages, including this one, return 1.
Type it as a decimal. An exponent of 0.5 is a square root and 0.25 is a fourth root, and both are exact. Thirds have no exact decimal, so 8^0.6667 gives about 4.0003 rather than 4. For exact roots, find the root first with a root calculator and then raise it to the power.
Add the exponents: a^m x a^n = a^(m+n). So 2^3 x 2^4 = 2^7 = 128. To divide, subtract them: 5^6 / 5^4 = 5^2 = 25. To raise a power to a power, multiply them: (3^2)^3 = 3^6 = 729. These rules only work when the bases match.
A decimal exponent means taking a root, and even roots of negative numbers are not real numbers. For example, (-4)^0.5 is the square root of -4, which needs imaginary numbers. The calculator works with real numbers only, so it shows an error instead of a result.

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