Exponent Calculator
Calculate b^n for any base and exponent, also shown in scientific notation.
Written by Golam Rabbani, Founder & Lead Engineer
How to use this exponent calculator
- Enter the base (b) in the first field.
- Enter the exponent (n) in the second field — positive, negative, or fractional.
- Press Calculate to see b^n and its scientific-notation form.
- Use Copy to put the result on your clipboard, or Reset to clear the inputs.
About this exponent calculator
The exponent calculator evaluates b^n for any real base and exponent. The result is displayed in both standard decimal notation and scientific notation, which is useful when the answer is very large or very small.
The formula is b^n = b × b × … × b (n times), with the conventions b^0 = 1 for any non-zero b and b^−n = 1 ÷ b^n. Fractional exponents express roots: b^(1/n) is the n-th root of b. For example, 10^3 = 10 × 10 × 10 = 1000 (also written 1.000000 × 10^3), and 2^−4 = 1 ÷ 16 = 0.0625. The tool uses IEEE-754 double-precision floating point, so results are accurate to about 15–16 significant digits. It blocks 0^(negative exponent) and (negative base)^(fractional exponent) because those have no real result.
Another handy example: radioactive decay. If a substance has a half-life of 3 days and you want the fraction remaining after 9 days, compute (0.5)^3 = 0.125, meaning only 12.5% of the original amount remains. The tool displays this as 1.250000 × 10^−1 in scientific notation, making the order of magnitude immediately clear. Common uses include scientific notation conversion, compound growth, decay calculations, and quickly evaluating expressions in maths homework or coursework.
FAQ
- What does the exponent calculator compute?
- It evaluates b^n for any real base and exponent and shows the result in both decimal and scientific notation. Negative and fractional exponents are supported.
- What formula is used for b^n?
- b^n = b × b × … × b (n times), with b^0 = 1 for any non-zero b and b^−n = 1 ÷ b^n. Fractional exponents express roots, so b^(1/n) is the n-th root of b.
- Why does the tool also show scientific notation?
- Powers can quickly become very large or very small. Scientific notation (mantissa × 10^k) keeps the result readable when standard notation would be unwieldy.
- Why does negative base with a fractional exponent return an error?
- A negative base raised to a non-integer exponent has no real result — it would be a complex number. The tool returns real numbers only.
- Does this tool store my numbers?
- No. The calculation runs entirely in your browser; nothing is sent to a server or saved between visits.
- Is the exponent calculator free?
- Yes. It is free to use with no signup, no account, and no usage limit.