This free online decimal to octal calculator will convert decimal numbers into octal numbers and display a conversion chart to show how it arrived at the result.
Be sure to check out my other decimal conversion calculators for converting Base 10 to Binary and Base 10 to Hexadecimal.
The easiest way to understand what an octal 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 numeric characters (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to count and express values.
The octal number system, on the other hand, uses the base 8 method for counting and expressing value. It's called "base 8" because it uses 8 numeric characters to count and express value. The 8 octal numeric characters are 0, 1, 2, 3, 4, 5, 6, and 7.
Now, since we are looking to convert a base 10 number into a base 8 number, let's compare the base 10 place values to the place values in a base 8 number system:
Power of 10:  10^{3}  10^{2}  10^{1}  10^{0}  .  10^{1}  10^{2}  10^{3} 
Base 10 Place value:  1000  100  10  1  .  1/10  1/100  1/1000 
Power of 8:  8^{3}  8^{2}  8^{1}  8^{0}  .  8^{1}  8^{2}  8^{3} 
Base 8 Place value:  512  64  8  1  .  1/8  1/64  1/512 
As you can see, since each place value in a base 10 number is different than the corresponding place value in a base 8 system, we need a method for converting 09 base 10 place values into 07 base 8 place values.
In order to convert a base 10 number into a base 8 number, the first step is to find the first base 8 place value that is greater than or equal to the decimal number you are converting  starting at the 8^{0} place and working your way to the left. For example, suppose you want to convert the decimal number 125 into an octal number. In that case you would find the first base 8 place value that is greater than or equal to 125, which would be 512:
Power of 8:  8^{3}  8^{2}  8^{1}  8^{0} 
Place value :  512  64  8  1 
Once you have located your base 8 place value starting point, the next step is to create a conversion chart, like this:
A  Power of 8:  8^{3}  8^{2}  8^{1}  8^{0} 
B  Remainder of Division:  125  
C  Place value (A result):  512  64  8  1 
D  Octal digit (B ÷ 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. Here is how the completed conversion chart would look:
A  Power of 8:  8^{3}  8^{2}  8^{1}  8^{0} 
B  Remainder of Division:  125  125  61  5 
C  Place value (A result):  512  64  8  1 
D  Octal digit (B ÷ C):  0  1  7  5 
From the above we can see that the base 10 number 125 converts to the base 8 number 175 (1*64 + 7*8 + 5*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 an octal number is a simple process of identifying the first base 8 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 Octal Converter to convert base 10 to base 8.

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