About the exponent calculator
The exponent calculator raises a base to a power, including negative, decimal and fractional exponents, and shows the result in plain and scientific notation. It can also work backwards to find the missing base or the missing exponent.
For whole-number results it gives the exact value, even when it has dozens of digits.
Who should use the exponent calculator
- Students learning indices and powers.
- People working with growth, decay or scientific notation.
- Anyone who needs a quick power without a full scientific calculator.
How to use the exponent calculator: what each input means
- Solve for
- The result, the base or the exponent.
- Base and exponent
- Any real numbers, with the restrictions explained below. Type e for Euler's number.
- Result
- Used when solving for the base or the exponent.
How the exponent calculator works: method and formula
A positive whole exponent means repeated multiplication. A negative exponent means the reciprocal: 2^-3 = 1 ÷ 2^3. A fractional exponent is a root: x^(1/2) is the square root of x. When solving for the base, the calculator takes the result to the power 1 ÷ exponent; when solving for the exponent, it uses logarithms.
- Negative exponent
- x^−n = 1 ÷ x^n
- Fractional exponent
- x^(m/n) = (n-th root of x)^m
- Missing exponent
- n = ln(result) ÷ ln(base)
How to read your exponent calculator result
A base between 0 and 1 shrinks as the exponent grows; a base above 1 grows. Zero to the power zero is conventionally 1 in many contexts, though it is mathematically undefined in some. A negative base with a fractional exponent has no real result and is reported as such.
Exponent Calculator worked example
Calculate 2 raised to the power −3.
- 2^−3 = 1 ÷ 2^3.
- 2^3 = 8, so 2^−3 = 1 ÷ 8.
- Check by solving the other way: the exponent that turns 2 into 8 is 3.
2^−3 = 0.125 = 1/8.
Practical uses of the exponent calculator
- Evaluating compound growth or decay factors.
- Converting between roots and fractional powers.
- Finding how many doublings it takes to reach a target.
Assumptions and limitations of this calculator
- Results use double-precision numbers; very large powers overflow and are reported as too large. Exact digits are shown for whole-number results within a safe size.
- Real numbers only: negative bases with non-integer exponents are not supported.