# Convert Hexadecimal Number (Base 16) to Decimal Number (Base 10)

This 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 (on the full site).

Convert hexadecimal to decimal number (ase 16 to base 10).

#### Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None

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:Decimal:Decimal (base 10) equivalent:Decimal (base 10) equivalent:

#### 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.

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

## Learn

### What hexadecimals are, why they are used, and how to convert them to decimals.

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.

Using the base 16 system of counting 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 that 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

← swipe left and right →← swipe left and right →
 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, 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. Let's 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

← swipe left and right →← swipe left and right →
 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)

← swipe left and right →← swipe left and right →
 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.

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".