Antilog Calculator
The antilogarithm is the inverse of the logarithm — antilog_b(x) = b^x. Enter an exponent x and a base; the calculator returns b^x plus 10^x, e^x and 2^x for reference.
antilog base 10 (common antilog) of x
100
- 10^x
- 100
- e^x = exp(x)
- 7.39
- 2^x
- 4
antilog_b(x) is the inverse of log_b(x): it returns the number whose logarithm equals x. By definition antilog_b(x) = b^x. Any real exponent is valid; the base must be > 0 and ≠ 1 so the inverse is well-defined.
How to use this calculator
Enter the exponent x (any real number — positive, negative or fractional), then choose a base: 10 (common antilog), e (natural antilog, exp), 2 (binary antilog) or a custom positive base. The result is b^x, and 10^x, e^x and 2^x are always shown in the breakdown.
How the calculation works
Antilog "undoes" a logarithm. If log_b(N) = x, then antilog_b(x) = N — and N is just b^x. So the antilog operation is the same as raising the base to the exponent. The calculator computes it as exp(x · ln b) internally, which works for every positive base in one code path and matches your scientific-calculator key labelled "10^x" or "INV log".
Worked example
Default inputs — exponent 2, base 10. antilog₁₀(2) = 10² = 100, which matches the result panel. Switch the exponent to 3.5 and you get 10^3.5 ≈ 3162.278, the kind of number that comes out of pH or decibel inversions. Switch to base e with exponent 1 to recover Euler's number e ≈ 2.71828, and base 2 with exponent 8 gives 2⁸ = 256.
Frequently asked questions
What does "antilog" actually mean?
Antilog is shorthand for antilogarithm — the inverse function of a logarithm. If you know log_b(N) = x, the antilog tells you what N was: N = antilog_b(x) = b^x. Old log tables had two halves, "log" and "antilog", because slide rules and paper tables only stored one direction. On a modern calculator the antilog of 10 is the "10^x" key (often labelled INV log or SHIFT log).
Is antilog the same as raising to a power?
Yes — antilog_b(x) is just b^x. The two names exist because they come from different problem framings: 'raise b to the x' starts with a base and exponent, while 'antilog x base b' starts with a logarithm you want to invert. The arithmetic is identical, and that's what this calculator does — it pipes your inputs through Math.pow(base, exponent) internally.
Why can the exponent be negative or fractional, but the base must be positive?
For any positive base b, the function b^x is defined and continuous for every real x — including negatives (b^-1 = 1/b) and fractions (b^0.5 = √b). But if b were negative, b^0.5 would be imaginary, and if b were zero, 0^0 is contested. Excluding b = 1 keeps the inverse log unambiguous, since 1^x = 1 for every x.
How is antilog related to e^x and 10^x on my calculator?
e^x (often labelled "exp" or above the ln key) is the natural antilog — antilog_e(x). 10^x (above the log key) is the common antilog — antilog_10(x). Both are special cases of b^x. The calculator surfaces 10^x, e^x and 2^x in every result so you can sanity-check your inputs against the keys you already know.
When do I actually need an antilog in real life?
Anywhere you measure something on a log scale and want the underlying linear value. pH 3 → hydrogen-ion concentration 10⁻³ mol/L (antilog base 10). Magnitude 6.2 earthquake → energy ratio 10^6.2 vs reference (antilog base 10). Bel/decibel calculations, sound pressure, signal-to-noise — all of these store the data as logs and read it back via antilogs. In finance, continuously-compounded log returns convert to simple returns via e^r — that's antilog base e.
How accurate are the results?
Double-precision floating-point — about 15–16 significant decimal digits. For everyday science, engineering and finance that is effectively exact. Very large exponents (like 10^308 or beyond) overflow to Infinity, and very negative ones underflow to 0; the calculator returns those values honestly rather than rounding.