Antilogarithm Calculator
The antilogarithm is the inverse operation of the logarithm. If log_b(y) = x, then the antilogarithm of x in base b equals b^x = y. In other words, computing the antilog of x in base b raises the base b to the power x. The most common cases are base 10 (where antilog(x) = 10^x, reversing the common logarithm) and base e (where the natural antilog is exp(x) = e^x). This calculator works for any positive base other than 1. Enter the value x and the base b to compute the antilogarithm.
Antilogarithm formula
antilog_b(x) = b^x
Common antilog (base 10): 10^x
Natural antilog (base e): e^x = exp(x)
The antilogarithm is simply exponentiation with the given base. It is the exact inverse of the logarithm: log_b(b^x) = x and b^(log_b(y)) = y for any positive y and valid base b.
Common antilogarithm uses
- pH: hydrogen ion concentration [H+] = 10^(-pH).
- Richter magnitude M: seismic amplitude = 10^M relative to reference.
- Decibels: sound intensity = 10^(dB/10) relative to reference intensity.
- Natural growth: population at time t = P0 * e^(r*t).
- Finance: future value = PV * e^(r*t) with continuous compounding.
Antilogarithm calculator: frequently asked questions
What is an antilogarithm?
The antilogarithm (antilog) is the inverse of the logarithm. If log_b(y) = x, then antilog_b(x) = b^x = y. Computing the antilog undoes what the logarithm did: if log(100) = 2 in base 10, then antilog(2) = 10^2 = 100.
What is antilog base 10?
Antilog base 10 of x equals 10^x. For example, antilog(3) = 10^3 = 1,000 and antilog(-2) = 10^(-2) = 0.01. This is used to reverse common (base-10) logarithms in pH calculations and the Richter scale.
What is antilog base e (natural antilog)?
The natural antilogarithm is exp(x) = e^x, where e is approximately 2.71828. It is the inverse of the natural logarithm ln(x). For example, antilog_e(1) = e approximately 2.71828 and antilog_e(0) = 1.
Where are antilogs used?
Antilogs appear in pH chemistry (pH = -log[H+], so [H+] = 10^(-pH)), earthquake magnitude (Richter scale uses base 10), decibel calculations (intensity ratio = 10^(dB/10)), and exponential growth and decay models.
What is the relationship between antilog and exponentiation?
Antilog_b(x) = b^x is exactly the same as raising b to the power x. The term antilogarithm is simply the traditional name for this operation, particularly in the context of reversing a logarithm computation.
Official sources
- NIST Digital Library of Mathematical Functions, Section 4 (Logarithms and Exponentials): dlmf.nist.gov/4.
- NIST, Mathematical topics: nist.gov/topics/mathematics.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.