Antilog Calculator

Introduction

An antilog is the reverse of a logarithm. If a logarithm tells you the power needed to reach a number, the antilog takes that power and gives you the number back. For example, the log of 100 in base 10 is 2. So the antilog of 2 in base 10 is 100. The formula is simple: antilog(y) = base^y.

This antilog calculator finds the antilog for you. Enter your log value, pick a base, and get your answer right away. It works with base 10 (common logs), base e (natural logs), or any custom base you choose. The tool also shows a step-by-step solution so you can learn how the answer was found, a summary table of your inputs and results, and a chart that plots the antilog curve. You can copy the result or download it as a PDF.

Use this calculator for homework, test prep, science problems, or any time you need to convert a log value back into a regular number. It handles positive numbers, negative numbers, and decimals with ease.

How to Use Our Antilog Calculator

Enter a base and a log value, and this calculator will instantly find the antilogarithm with a full step-by-step solution.

Pick a base mode. Click Base 10 for common antilogs, Base e for natural antilogs, or Custom Base to type in any base you need.

Enter the log value (y). Type the exponent into the Log Value field. This is the number whose antilog you want to find. You can use decimals and negative numbers. Use the plus and minus buttons to adjust the value by small steps.

Set a custom base if needed. If you chose Custom Base mode, type your base into the Antilog Base field. The base must be a positive number and cannot equal 1. In Base 10 or Base e mode, this field is locked for you.

Click Calculate. Press the Calculate button to get your result. The calculator will show the antilog value, a summary table, a step-by-step solution, and an interactive chart of the antilog curve.

Change the decimal precision. Use the Decimal Precision dropdown below the result to show anywhere from 2 to 10 decimal places, or choose Full Precision for the most exact answer.

Copy or save your result. Click Copy Result to copy the answer to your clipboard, or click Download PDF to save or print your full solution.

What Is an Antilog?

An antilog, short for antilogarithm, is the reverse of a logarithm. A logarithm asks, "What power do I raise the base to in order to get a number?" An antilog flips that question and gives you the number itself.

The formula is simple: antilog(y) = a^y, where a is the base and y is the exponent (the log value). For example, if the base is 10 and y is 3, the antilog is 10³ = 1,000.

Common Antilog Bases

There are two bases you will see most often:

• Base 10 (Common Antilog): This is used in everyday math and science. It reverses the common logarithm (log). If log(1000) = 3, then antilog(3) = 1,000.
• Base e (Natural Antilog): The number e is about 2.71828. This base is used in advanced math, biology, and finance. The natural antilog reverses the natural logarithm (ln). It is also called the exponential function, written as e^y.

You can also use any positive base that is not equal to 1. This is called a custom base antilog. For example, base 2 is common in computer science.

How to Calculate an Antilog

Follow these steps to find an antilog by hand:

1. Find your base (a). Common choices are 10 or e.
2. Find your exponent (y). This is the log value you want to reverse.
3. Raise the base to the power of y. The answer is a^y.

For example, to find the antilog of 2 in base 10: raise 10 to the power of 2. That gives you 10 × 10 = 100.

Negative and Decimal Exponents

Antilogs work with negative numbers and decimals too. A negative exponent gives a small result. For instance, 10⁻² = 0.01. A decimal exponent like 10^0.5 gives the square root of 10, which is about 3.1623. The exponent does not need to be a whole number.

Where Are Antilogs Used?

Antilogs show up in many real-world areas:

• Science: pH levels in chemistry use base-10 antilogs to convert pH back to hydrogen ion concentration.
• Sound: Decibel scales measure loudness using logarithms, and antilogs convert those values back to actual sound intensity.
• Finance: Compound interest formulas often use the natural antilog (e^y) to calculate growth over time.
• Earthquakes: The Richter scale is logarithmic. An antilog tells you the true difference in energy between two earthquake readings.