Antilog
Calculate the antilogarithm (inverse log) of any number in any base. Free online tool supports base 10, base e (natural antilog), and custom bases with interactive exponential curve chart.
About This Calculator
Our free online Antilog Calculator computes the inverse logarithm (antilog) of any number in any base. An antilog answers the question: if log_b(x) = y, then what is x? The answer is x = b^y. This tool supports common antilog (base 10), natural antilog (base e), and custom bases, with results displayed to 6 decimal places and an interactive exponential curve chart showing how the function behaves across a range of y values.
The antilogarithm is essential in fields where log-transformed data needs to be converted back: pH to hydrogen ion concentration, decibels to sound intensity, Richter magnitude to seismic energy, and log-odds to probabilities in logistic regression. When you set base = 10, you get the common antilog (10^y); with base = e, you get the natural exponential (e^y or exp(y)).
Regional Notes
India (IN): Antilog tables were traditionally used in CBSE and state board examinations before the widespread adoption of scientific calculators. Understanding antilogarithms remains relevant for chemistry (pH, Nernst equation) and physics (sound, optics) curricula at the Class 11-12 level.
United States (US): Antilogs are taught as the inverse of logarithmic functions in Algebra II and Precalculus. They appear in AP Chemistry (pH calculations), AP Physics (decibels), and college-level statistics (logistic regression, log-normal distributions).
United Kingdom (UK): A-Level Mathematics covers antilogs as part of exponential and logarithmic function units. They are used in chemistry for pH and kinetics, in biology for bacterial growth, and in geography for earthquake magnitude analysis.
Frequently Asked Questions
What is an antilog?
An antilogarithm (antilog) is the inverse operation of a logarithm. If log_b(x) = y, then the antilog of y in base b is x = b^y. For example, if log10(100) = 2, then antilog10(2) = 10^2 = 100. The antilog undoes the logarithm, returning the original number.
How do you calculate antilog?
To calculate antilog_b(y), raise the base b to the power y: b^y. For base 10, antilog10(y) = 10^y. For natural antilog (base e), antilog_e(y) = e^y also written as exp(y). Simply enter the log value y and choose or enter the base b, then the calculator computes b^y instantly.
What is the difference between antilog and exp?
The exponential function exp(y) = e^y is specifically the antilog with base e (natural antilog). The general antilog can use any positive base: antilog_b(y) = b^y. When people say 'antilog' without specifying a base, they usually mean base 10. The term 'exp' always means base e.
Where is antilog used in real life?
Antilogs are used in pH calculations (pH = -log[H⁺], so [H⁺] = antilog(-pH)), decibel measurements (sound intensity = antilog(dB/10)), the Richter scale for earthquakes, exponential growth projections in finance and biology, and in reverse-engineering log-transformed data in statistics and machine learning.
How do I find antilog of a negative number?
The antilog of a negative number is simply b raised to that negative power. For example, antilog10(-2) = 10⁻^2 = 0.01. A negative log value means the original number is between 0 and 1. This calculator handles negative, zero, and positive log values correctly.
What is antilog table and how is it used?
Before digital calculators, antilog tables were used to find the antilog of a mantissa. The table listed values of 10^m for fractional mantissas m (0.000 to 0.999). To find antilog of a number, you'd split it into characteristic (integer part) and mantissa (decimal part), then look up the mantissa in the table and multiply by 10^characteristic. Modern calculators like ours provide instant results.
How is antilog used in Indian education?
Antilog tables were traditionally taught in Indian schools for pre-calculator logarithm computations. While digital tools have replaced physical tables, understanding antilogs remains important for CBSE and state board chemistry (pH calculations), physics (decibels, intensity), and mathematics (exponential functions) curricula.