## Summary

The Excel DECIMAL function converts a number in a given base into its decimal number equivalent. For example, the DECIMAL function can convert the binary number 1101 into the decimal number 13.

## Purpose

Convert a number in a different base to a decimal number

Decimal number

## Arguments

• number - A text string representing a number.
• radix - The base of the number to be converted, an integer between 2-36.

## How to use

The DECIMAL function converts a number in a known base into its decimal number equivalent. For example, the DECIMAL function can convert the binary number 1101 into the decimal number 13. The number provided to DECIMAL should be a text string.

The DECIMAL function takes two arguments: number and radix. Number should be the text representation of a number in a known base. Radix is the number of digits used to represent numbers (i.e. the base) and should be an integer between 2 and 36. The characters given in number need to conform to the numbering system specified with radix

### Examples

In the hexadecimal number system, the number 255 is represented as "FF". To convert the text string "FF" to the decimal number 255, you can use the DECIMAL function like this:

``````=DECIMAL("FF",16) // returns 255
``````

To convert the binary number 1101 to its decimal number equivalent, 13, use DECIMAL like this:

``````=DECIMAL("1101",2) // returns 13
``````

In the example shown, the numbers in column B are in different bases, and the base is given in column C. The formula in column D5 is:

``````=DECIMAL(B5,C5) // returns 3
``````

As the formula is copied down, the DECIMAL function converts each number in column B to its decimal equivalent using the base specified in column C for the radix argument. The decimal numbers in column D are the output from DECIMAL.

### BASE function

The BASE function performs the opposite conversion as the DECIMAL function:

``````=BASE(100,2) // returns "1100100"
=DECIMAL("1100100",2) // returns 100
``````

### Number system characters

Different bases use different alphanumeric characters to represent numbers. The table below shows the characters uses for binary, octal, decimal, and hexadecimal number systems.

Name Base Alphanumeric characters
binary 2 0 - 1
octal 8 0 - 7
decimal 10 0 - 9
hexadecimal 16 0 - 9 and A - F

### Notes

• The number argument should be provided as a text string.
• The result from DECIMAL is a numeric value.
• If number is negative, DECIMAL returns a #NUM! error.
• if number contains a decimal value,  DECIMAL returns a #NUM! error.
• If number is out-of-range for the given base, DECIMAL returns a #NUM! error.

Author

### Dave Bruns

Hi - I'm Dave Bruns, and I run Exceljet with my wife, Lisa. Our goal is to help you work faster in Excel. We create short videos, and clear examples of formulas, functions, pivot tables, conditional formatting, and charts.