Antilog Calculator

If you have a logarithm value and want to find the number it came from, you want the antilog. This one handles any base you throw at it: common (10), natural (e), binary, or something custom. It also runs in either direction. Give it any two of the three numbers (log value, base, antilog) and it solves for the third.

What is an antilog?

An antilog reverses a logarithm. If $\log_b(y) = x \implies \text{antilog}_b(x) = y$. Put another way, $\text{antilog}_b(x)$ is just b raised to the power x. That is the whole definition.

Quick example: $\log_{10}(100) = 2 \implies \text{antilog}_{10}(2) = 100$. The antilog walks you back to the number you started with. That matters whenever a logarithm sits in the way of what you actually want to know, like pH in chemistry, decibel readings on a sound meter, or magnitudes on the Richter scale.

How to use this calculator

Type any two of the three values, and the third fills in.

• Log value (x): the exponent. Any real number works, positive or negative.

• Base (b): defaults to 10. Set it to e (about 2.718) for natural logs, 2 for binary, or any other positive number that isn't 1.

• Antilog: b raised to x. If you already know the antilog, leave x or the base blank and the calculator solves the other way.

Where antilogs show up

Antilogs come up wherever something is reported on a log scale and you need the underlying number.

• In chemistry, pH is defined as -log[H⁺], so hydrogen ion concentration is antilog(-pH). A solution at pH 4 has [H⁺] = 10⁻⁴ mol/L.

• Decibel readings in acoustics and electronics convert back to actual intensity ratios through an antilog.

• The Richter scale is logarithmic. A magnitude-7 quake releases roughly ten times the energy of a magnitude-6 one, and that ratio is antilog of the difference.

• When you linearize an exponential growth equation with logs (compound interest, population models), antilog reverses the step to give you the actual rate or final value.

• Algorithm analysis uses log₂ for time complexity. The antilog tells you how many operations a given depth corresponds to.

Tips and edge cases

• The base has to be positive, and it can't be 1. $\log_1(x)$ has no answer, since 1 raised to any power is still 1.

• For natural logs, use 2.718281828 (or just call the base e).

• A negative log value gives an antilog between 0 and 1. $\text{antilog}_{10}(-2)$ is 0.01.

• Large log values grow quickly. $\text{antilog}_{10}(20)$ is $10^{20}$, so don't be surprised when the result switches to scientific notation.

Frequently asked questions

What's the difference between antilog and exponent?

Same operation, different framing. $\text{antilog}_b(x)$ is just $b^x$. The word "antilog" highlights that you're undoing a log; "exponent" is the general term for raising a number to a power.

Can I compute antilog without a calculator?

For clean inputs, sure. $\text{antilog}_{10}(3)$ is 1,000, $\text{antilog}_{2}(8)$ is 256, no calculator needed. For anything messier, you'd reach for a log table (the old-school way) or a scientific calculator. This one just gives you the number directly.

Can an antilog be negative?

Not when the base is positive and you're sticking to real numbers. A positive base raised to any real power stays positive. The log value going in can be negative, though, in which case the antilog lands between 0 and 1.