# Decimal to Hex Converterto Convert Base 10 to Base 16

The Decimal to Hex Converter on this page will convert base 10 numbers to base 2 numbers, and show its work.

This free online decimal to hexadecimal calculator will convert decimal numbers into hexadecimal numbers and display a conversion chart to show how it came up with the result.

Be sure to check out my other base conversion calculators for converting Base 2 to Base 10 and Base 10 to Base 2.

### What is a Hexadecimal Number?

The easiest way to understand what a hexadecimal number is, is to compare it to something you already know -- a decimal number. As you know, a decimal number uses the base 10 system for counting and expressing value. It's called "base 10" because it uses ten digits (0,1,2,3,4,5,6,7,8,9) to count and express values.

The hexadecimal system, on the other hand, uses the base 16 method for counting and expressing value. It's called "base 16" because it uses 16 digits to count and express value. However, since we only have 10 numeric characters to work with, the hexadecimal system uses letters to express values that are greater than 9.

Here is how the base 16 (hexadecimal) numbering system compares to the base 10 numbering system you are accustomed to:

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

Now, since we are looking to convert a base 10 number into a base 16 number, let's compare the base 10 place values to the place values in a base 16 system:

Place Values of Decimal and Hex Systems

 Power of 10: 103 102 101 100 . 10-1 10-2 10-3 Place value : 1000 100 10 1 . 1/10 1/100 1/1000 Power of 16: 163 162 161 160 . 16-1 16-2 16-3 Place value : 4096 256 16 1 . 1/16 1/256 1/4096

So you see, since each place value in a base 10 number is different than the corresponding place value in a base 16 system, we need a method for converting 0-9 base 10 place values into 0-F base 16 place values.

### How to Convert Decimal to Hexadecimal

In order to convert a base 10 number into a base 16 number, the first step is to find the first base 16 place value that is greater than or equal to the decimal number you are converting -- starting at the 160 place and working your way to the left. For example, suppose you want to convert the decimal number 125 into a hexadecimal number. In that case you would find the first base 16 place value that is greater than or equal to 125, which would be 256:

First Base 16 Value Greater than 12510

 Power of 16: 162 161 160 Place value : 256 16 1

Once you have located your base 16 place value starting point, the next step is to create a conversion chart, like this:

Conversion Chart

 A Power of 16: 162 161 160 B Remainder of Division: 125 C Place value (A result): 256 16 1 D Quotient of  B ÷ C: E Hex (D > 9 to letter):

Notice that the decimal you want to convert is placed in left-most cell of Row B, just above the base 16 place value row (C).

Next, attempt to divide the amount in row B into the amount in row C. If the amount in row C is greater than the amount in row B, enter a "0" in row D and move the amount in row B one cell to the right. Otherwise, if the amount in row C is less than the amount in row B, enter the number of times row C goes into row B in row D and enter the remainder in the next open cell in row B. Then simply repeat this process for each subsequent column. Finally, change all numbers in row D that are greater than 9 to their letter equivalent (10=A, 11=B, 12=C, 13=D, 14=E, and 15=F). Here is how the completed conversion chart would look:

Conversion Chart for Converting 12510 to Hexadecimal

 A Power of 16: 162 161 160 B Remainder of Division: 125 125 13 C Place value (A result): 256 16 1 D Quotient of  B ÷ C: 0 7 13 E Hex (D > 9 to letter): 0 7 D

Divide each cell in row C into the corresponding cell in row B and move the remainder of each division to the next cell in row B. Repeat for all columns. Note that the above is how the decimal to hex converter will show its work.

From the above we can see that the base 10 number 125 converts to the base 16 number 7D (7*16 + 13*1 = 125). Note that the leading zeros are dropped since they represent no value (just like the base 10 system).

As you can see, converting a decimal number to a hexadecimal number is a simple process of identifying the first base 16 place value greater than or equal to the base 10 number you are converting, and then dividing each place value into the remainder of previous division.

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

Decimal to Hex Converter

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

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Decimal number (base 10):
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### Decimal to Hex Converter Glossary of Terms

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). The hexadecimal system is often used for interpreting colors from a color spectrum for displaying on electronic video screens.

Decimal number (base 10): Enter the decimal (base 10) number you would like to convert into a hexadecimal number. Note that the entered number may only consist of digits 0-9, a single decimal point, and the leading number must not be a zero. For numbers containing a decimal point, the decimal to hex converter will only convert out to the last digit entered and will not round the result.

Hexadecimal (base 16) equivalent: This is the hexadecimal equivalent to the entered decimal number. Note that after clicking the Convert Decimal to Hexadecimal button the Decimal to Hex converter will display a detailed explanation of how it arrived at the result immediately below the line this field appears on.

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