Antilog Calculator

Antilogarithm: reversing the logarithm operation

The antilogarithm is the inverse of the logarithm. If log base b of x = y, then the antilog base b of y = x. In other words, the antilog raises the base to the power of the logarithm value to recover the original number. For base 10: antilog(3) = 10^3 = 1,000. For the natural base e: antilog(2) = e^2 = approximately 7.389. For base 2: antilog(8) = 2^8 = 256.

Antilogs are used whenever you need to convert from log space back to linear scale. In chemistry, pH = -log10([H+]), so the hydrogen ion concentration is [H+] = 10^(-pH), which is an antilog calculation. In acoustics, if you know a sound level in decibels and want to find the ratio of intensities, you compute the antilog of the dB value divided by 10. In finance and statistics, if a value was log-transformed for modelling purposes, the antilog recovers the original scale.

This calculator supports the four most useful bases. Base 10 is used for pH, decibels, and most logarithm table problems encountered in secondary and college mathematics. Base e (the natural base, approximately 2.71828) is used in calculus, differential equations, and exponential growth models. Base 2 is used in computer science for bit calculations and information entropy. A custom base option is also available for any other scenario.

The result includes a verification line: it takes the log of the computed antilog and checks that it matches the input value. This confirms the calculation ran correctly and helps spot any entry error. Minor floating-point rounding at the last decimal place is normal and does not indicate an error.

Antilogs in logarithm tables and historical use

Before electronic calculators existed, scientists and engineers used printed tables of logarithms and antilogarithms to perform multiplications, divisions, and root calculations. The standard four-figure log tables gave log10(x) for values of x from 1 to 10, and the corresponding antilog tables gave 10^y for values of y from 0 to 1. To multiply two numbers, you looked up their logs, added the logs, then looked up the antilog of the sum. This converted multiplication into addition, making complex computations tractable by hand.

Today the term antilog still appears in chemistry textbooks when working with pH and pKa values, in signal processing when converting back from decibels, and in any field where data was log-transformed before analysis. The concept is the same whether you use a printed table or an online calculator: raise the base to the given power to reverse the logarithm.

Negative and fractional logarithm values

The antilog accepts any real number as input, including negative values and fractions. A negative logarithm value produces a result between 0 and 1 for bases greater than 1. For example, antilog base 10 of -2 = 10^(-2) = 0.01. This is the correct result for the hydrogen ion concentration of a solution with pH 2. Fractional inputs like 2.5 give antilog base 10 of 2.5 = 10^2.5 = approximately 316.23. All values accepted by the calculator follow standard mathematical definitions without restriction.