Hex to Decimal Converter
to Convert Base 16 to Base 10

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The Hex to Decimal Converter on this page will convert base 16 numbers to base 10 numbers, and show its work.

This free online hexadecimal to decimal calculator will convert hexadecimal numbers into decimal numbers and display a conversion chart to show how it arrived at the answer.

If you're not sure what a hexadecimal number is, or you would like to convert a decimal number into a hexadecimal number, please visit the Decimal to Hex Conversion page.

What Are Hexadecimals and Why Are They Used?

Hexadecimals are numbers that use the base 16 system of counting and expressing value. Instead of using just the numeric characters 0-9 like we're accustomed to, hexadecimals also use the letters A-F to represent the values 10-15. This allows us to more succinctly express or communicate numeric values than other number systems that have fewer numeric characters to work with (decimal, octal, binary).

To illustrate, suppose you were a computer programmer and you needed to write or communicate a binary number like 1101101101102 (the numbering system recognized by computers). The decimal equivalent of that binary number would be "3510" whereas the hexadecimal equivalent would simply be "DB6". So as you can see, the primary reason we use hexadecimals instead of other number systems is simply because they are more compact and therefore more convenient to write and communicate.

How to Convert Hexadecimal to Decimal

If the hexadecimal number you are converting is less than 16, then you can simply use the following hex to decimal conversion chart:

Conversion Chart for Hexadecimals Less Than 16

Base 16 : 0 1 2 3 4 5 6 7 8 9 A B C D E F
Base 10: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

On the other hand, if the hexadecimal you are converting is greater than 15, then it helps to use a conversion method that identifies and sums place values -- a method you are already familiar with for identifying place values in the decimal number system.

So, in order to help you to understand how to convert hexadecimal to decimal, it may help to recall how we translate the value of a decimal number. Lets use the decimal number 1357 (135710, or one-thousand, three-hundred and fifty-seven) as an example:

Translating the Value of a Decimal (base 10) Number

A Power of 10: 103 102 101 100
B Place value (A result): 1000 100 10 1
C Entered decimal digit: 1 3 5 7
D Product of B * C: 1000 300 50 7
E Cumulative total of D: 1000 1300 1350 1357

Multiplying the values in row B by their corresponding values in row C gives us the equation: 1(1000) + 3(100) + 5(10) + 7 -- which calculates out to 1357.

With the above base 10 translation in mind, here is how you would convert the base 16 number 12CA (12CA16 or one-two-C-A) into a base 10 number:

Converting a Hexadecimal (base 16) to a Decimal (base 10)

A Power of 16: 163 162 161 160
B Place value (A result): 4096 256 16 1
C Entered hex digit: 1 2 C A
D Product of B * C: 4096 512 192 10
E Cumulative total of D: 4096 4608 4800 4810

Adding the values of line D we get the base 10 number of 4810. In other words, the number 12CA16 coverts to the number 481010. Note that the above is how the hex to decimal converter shows its work.

As you can see, converting a hexadecimal number to a decimal number is a simple process of identifying the hexadecimal place value of each digit, multiplying each digit by its place value, and then adding up all of the products.

With that, let's use the Hex to Decimal Converter to convert base 16 to base 10.

Hex to Decimal Converter
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Instructions: Enter the hexadecimal number you would like to convert into a decimal number, and then click the "Convert Hex to Decimal" button.

Mouse over the blue question marks for a further explanation of each entry field. More in-depth explanations can be found in the glossary of terms located beneath the Hex to Decimal Converter.

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Help Hexadecimal number (base 16): 16
Help Decimal (base 10) equivalent: 10
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Hex to Decimal Converter Glossary of Terms

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Hexadecimal system: Number system that uses the base 16 system of expressing values, which consists of the digits 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E and F. Base 16 numbers are usually written with a subscripted 16 behind them (7D16), a lowercase "h" behind them (7Dh), or a "0x" placed in front of them (0x7D). The hexadecimal system is often used in computer programming because it is more convenient to express values in base 16 mode than it is to express values in binary machine code.

Hexadecimal number (base 16): Enter the hexadecimal (base 16) number you would like to convert into a decimal (base 10) number. Note that the entered number may only consist of digits 0-9 and letters A-F, a single decimal point, and the leading digit must not be a zero (also remove all hex identifiers such as 0x, h, and/or a subscripted 16).

Decimal (base 10) equivalent: This is the decimal equivalent to the entered hexadecimal number. Note that after clicking the Convert Hex to Decimal button the hex to decimal converter will display a detailed explanation of how it arrived at the result immediately below this line.

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