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Math & Statisticsalgebra

Antilog Calculator

The inverse of a logarithm: given the log, recover the number. Useful for reading log-scale data such as pH, decibels or seismic magnitudes back into ordinary units.

Also called: inverse log, antilogarithm.

Antilogarithm
1,000

10 raised to 3 is 1,000. Taking the log base 10 of that returns 3, which is what makes them inverses.

If the log had been natural
20.09
If the log had been base ten
1,000
In scientific notation
1 x 10^3
How this is calculated
Method and background

How this is calculated

An antilogarithm is just exponentiation, named from the days when logs came out of a table and you needed a second table to go back. It matters wherever a scale is logarithmic: a pH of 4 is ten times more acidic than a pH of 5, and a magnitude 7 earthquake releases about thirty-two times the energy of a magnitude 6.

antilog = base ^ logarithm
y
The logarithm
b
The base

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

antilog base ten of three

Logarithm
3
Base
10

Antilogarithm1,000

arithmetic identity

Open this example

a log of zero returns one

Logarithm
0
Base
10

Antilogarithm1

boundary: any base to the power zero

Open this example

Method and limits

What it assumes

  • A positive base other than one.

What it deliberately does not model

  • Results beyond what a double can hold are reported as not finite.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

What is an antilog used for?
Reading a logarithmic scale back into ordinary units. Sound levels, acidity and earthquake magnitude are all recorded as logs precisely because the raw range is too wide to work with.