Antilog Calculator
Undo a logarithm. Enter the log value x and pick base 10, e, 2, or any custom base — the calculator raises the base to the power x and returns the antilog in plain and scientific notation.
Example: with Log value x (the exponent) 2 · Base of the logarithm Base 10 (common log) · Custom base (used only if selected) 5 → Antilog = base^x: 100.
- Scientific notation1 × 10^2
- Checklog base 10 of the result gives back x = 2
Computed by the calculator below using its default values. Change any input to see your own numbers.
Antilog is the inverse of the logarithm: antilog_b(x) = b^x. The antilog base 10 of 2 is 10² = 100, because log₁₀(100) = 2.
What an antilog actually is
A logarithm answers the question "what exponent gets me from the base to this number?" — log₁₀(100) = 2. The antilogarithm reverses it: start with the exponent, recover the number. Antilog base 10 of 2 is 10² = 100. That is the whole operation: antilog_b(x) = b^x, a plain exponentiation. The word survives mostly in chemistry (pH back to hydrogen-ion concentration), old statistics texts, and log-table arithmetic from the slide-rule era.
The base has to match the log you are undoing. Data that came from a natural log (ln) needs base e = 2.71828; common logs need base 10; information theory and computing use base 2. Feeding a natural-log value into a base-10 antilog is the classic way to get an answer that is wrong by a weird factor.
How it’s calculated
Antilog: y = b^x, computed as Math.pow(b, x). Bases: 10, e = 2.718281828459045, 2, or any custom base b > 0, b ≠ 1. Scientific notation splits y into m × 10^k with 1 ≤ m < 10. Results beyond ±1.8 × 10^308 overflow double-precision floats and are reported as such.
Double-precision arithmetic: results carry about 15-16 significant digits, so antilogs of very large x are exact in magnitude but not in every trailing digit.
Antilog base 10 at a glance
| Log value x | Antilog 10^x |
|---|---|
| −2 | 0.01 |
| −1 | 0.1 |
| 0 | 1 |
| 1 | 10 |
| 2 | 100 |
| 3 | 1,000 |
| 6 | 1,000,000 |
Computed with y = 10^x; every step of +1 in the log multiplies the result by 10.
Common mistakes
- Using base 10 to undo a natural log — ln values need base e, and the mismatch inflates or shrinks the answer by a factor of about 2.3 in the exponent.
- Entering the original number instead of the log value: antilog wants the exponent, not the number you took the log of.
- Expecting antilog of a negative x to be negative — 10^(−2) = 0.01, a small positive number. Antilogs are always positive.
- Trying base 1 or a negative base: b must be positive and not equal to 1, or the logarithm it inverts does not exist.
Frequently asked questions
What is the antilog formula?
antilog_b(x) = b^x. Raise the base of the logarithm to the power of the log value. Antilog base 10 of 3 is 10³ = 1,000.
Is antilog the same as inverse log?
Yes. Antilog, inverse log, and exponentiation with the log's base are the same operation. On most calculators it is the 10^x key (or e^x for natural logs).
How do I take the antilog of a natural log (ln)?
Use base e: antilog of x is e^x. For example, if ln(y) = 1.5, then y = e^1.5 ≈ 4.4817. Pick 'Base e' in the base menu.
Why is my antilog result smaller than 1?
A negative log value means the original number was between 0 and 1. Antilog of −2 in base 10 is 10^(−2) = 0.01. Negative exponents make reciprocals, not negative numbers.
What is antilog used for in chemistry?
Converting pH back to concentration: [H⁺] = 10^(−pH). A pH of 4.5 means an antilog of −4.5, or about 3.16 × 10^(−5) mol/L.