What this calculator does
An antilog calculator does the opposite of a normal log calculation. Where a logarithm takes a number and tells you the power needed to produce it, an antilog starts from that power and reconstructs the original number: if log(x) = value, then antilog(value) = x.
This calculator handles the two bases people run into most often: base 10, the common log used in science and engineering, and base e, the natural log (ln) used throughout calculus and growth modelling. Enter a value and a base, and it returns 10 raised to that value, or e raised to that value.
The formula
Antilog is simply the base raised to the power of the value entered. For base 10, antilog(value) = 10^value; for base e, antilog(value) = e^value, where e is approximately 2.71828. The calculator also runs the result back through the matching logarithm as a check, since log₁₀(10^value) and ln(e^value) should return the original value entered.
| Term | Meaning |
|---|---|
| Antilogarithm | The inverse of a logarithm: given a log value, the number that produces it when the log is taken. |
| Common log (base 10) | The logarithm using base 10, written log or log₁₀, where the antilog is 10 raised to the given power. |
| Natural log (base e, ln) | The logarithm using base e ≈ 2.71828, written ln, where the antilog is e raised to the given power. |
The inputs explained
| Field | What to enter |
|---|---|
| Log value | The log value you want to reverse, sometimes called the mantissa and characteristic combined in older log-table workflows. |
| Log base | Choose base 10 for a common log value, or base e if the value came from a natural log (ln). |
When to use it
Reversing a pH, decibel or Richter-scale figure
Several real-world scales are defined as logarithms of an underlying quantity. Given the scale reading, antilog recovers the underlying concentration, intensity or amplitude that produced it.
Checking working on a log-based homework problem
If a worked answer states log(x) = 2.35, taking the antilog of 2.35 confirms what x actually is, which is a quick way to sanity-check an equation solved using logarithms.
Undoing a natural log in a growth or decay equation
Continuous growth and decay problems often reduce to ln(value) = something. Antilog with base e reverses that step directly, without rearranging the original equation by hand.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Antilog base 10 for a range of values
Common log values and the number each one represents.
Antilog base e (natural log) for a range of values
Natural log values and the number each one represents.
Questions
What is antilog on a calculator?
On a scientific calculator, antilog is usually the second function above the log or ln key, often labelled 10ˣ or eˣ. Pressing shift (or 2nd) then log raises 10 to the displayed value; shift then ln raises e to the displayed value.
How is antilog different from just typing the exponent?
It is not different mathematically, antilog base 10 of a value is exactly 10 raised to that value, and antilog base e is exactly e raised to that value. "Antilog" is simply the traditional name for that operation when it is being used to reverse a logarithm.
Can the log value be negative?
Yes. A negative log value produces an antilog between 0 and 1, since a negative exponent gives a fraction rather than a whole number, for example antilog base 10 of -1 equals 0.1.
Why does the calculator show a check that inverts the answer?
Taking the log of the antilog should return the original value entered, within rounding. Showing that check confirms the two operations are genuine inverses of each other and catches any base mix-up.
To work in the other direction, from a base and an exponent to the resulting value, see the exponential function calculator. For growth expressed as a percentage rate rather than a raw base, see the exponential growth calculator.