Enter a logarithm value and pick a base to get its antilog, the number that has that logarithm. You get the result in plain and scientific notation, the characteristic and mantissa split used with log tables, and a check that takes the log back.
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The number whose antilog you want. Negative values and decimals are fine, e.g. −1.3010.
Any positive number except 1.
Enter your values to see the result.
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How to use the Antilog Calculator
Enter the log value y, the number whose antilog you need.
Choose the base: 10 for common logs, e for natural logs, 2 for binary logs, or enter any other base.
Set the significant figures you want in the answer.
Read the antilog at the top, with scientific notation and the exact value when there is one.
Follow the steps to see the characteristic and mantissa, then copy the results or download a table.
Antilog formula
The antilog undoes a logarithm. If logb(x) = y, then x = antilogb(y) = by. Any base can be rewritten in base 10 with by = 10y × log₁₀ b, which is how the calculator handles very large and very small answers.
Log type
Written as
Antilog
Calculator key
Common log
log(x) = y
x = 10y
10x (Shift + log)
Natural log
ln(x) = y
x = ey
ex (Shift + ln)
Binary log
log₂(x) = y
x = 2y
2, xy, y
Any base b
logb(x) = y
x = by
b, xy, y
Characteristic and mantissa
Before calculators, antilogs were found with printed tables. The log value is split into a whole-number characteristic and a decimal mantissa between 0 and 1. The table gives the digits for the mantissa and the characteristic tells you where the decimal point goes.
Log value
Characteristic + mantissa
10mantissa
Antilog
2.4771
2 + 0.4771
3.000
3.000 × 10² = 300
0.6990
0 + 0.6990
5.000
5.000
−1.3010
−2 + 0.6990 (written 2̄.6990)
5.000
5.000 × 10⁻² = 0.05
−3.5229
−4 + 0.4771 (written 4̄.4771)
3.000
3.000 × 10⁻⁴ = 0.0003
Notice that for a negative log value the mantissa is kept positive, so −1.3010 becomes −2 + 0.6990, not −1 − 0.3010. The bar over the characteristic in 2̄.6990 marks that only the integer part is negative.
Where antilogs are used
Chemistry: hydrogen ion concentration from pH, [H⁺] = 10−pH. A pH of 7.4 gives about 3.98 × 10⁻⁸ mol/L.
Sound: converting decibels back to a power ratio, ratio = 10dB ÷ 10.
Earthquakes: each step of 1 on a base-10 magnitude scale means 10 times the measured wave amplitude.
Statistics: back-transforming the mean of log-transformed data gives the geometric mean.
Frequently asked questions
What is an antilog?
The antilogarithm is the inverse of the logarithm. If log_b(x) = y, then the antilog of y is x = b^y. For common logs the base is 10, so antilog(2) = 10² = 100 and antilog(0.5) = 10^0.5 ≈ 3.1623.
How do I find the antilog of a negative number?
Use the same rule: raise the base to the negative power. antilog(−2) = 10^−2 = 0.01, and antilog(−1.3010) = 10^−1.3010 ≈ 0.05. The answer is always positive and lies between 0 and 1 for negative log values.
What is the inverse of the natural log (ln)?
The inverse of ln is the exponential function e^y, sometimes written antiln or exp(y). For example, if ln(x) = 1, then x = e ≈ 2.71828, and if ln(x) = 2.3026, then x ≈ 10.
How do you calculate antilog with a log table?
Split the log value into its characteristic (the integer part) and mantissa (the decimal part, made positive). Look up the mantissa in an antilog table to get the digits, then place the decimal point using the characteristic. For 2.4771 the mantissa 0.4771 gives 3.000 and the characteristic 2 moves the point, giving 300.
How do I calculate antilog on a calculator?
On a scientific calculator press the 10^x key (often Shift + log) for base 10 or e^x (Shift + ln) for base e. For another base b, use b^y with the power key, or compute 10^(y × log b).
What is the antilog of 0 and 1?
In any valid base, the antilog of 0 is 1, because b^0 = 1. The antilog of 1 is the base itself, so it is 10 in base 10, about 2.71828 in base e and 2 in base 2.
Why can the base not be 1, 0 or negative?
Logarithms are only defined for positive bases other than 1. With base 1 every power equals 1, so no unique logarithm exists. Negative bases raised to fractional powers are not real numbers.
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