Decimal to Octal Converter
to Convert Base 10 to Base 8

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The Decimal to Octal Converter on this page will convert base 10 numbers to base 8 numbers, plus show its work.

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.

What is an Octal Number?

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:

Place Values of Decimal Vs. Octal Systems

Power of 10: 103 102 101 100 . 10-1 10-2 10-3
Base 10 Place value: 1000 100 10 1 . 1/10 1/100 1/1000
Power of 8: 83 82 81 80 . 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 0-9 base 10 place values into 0-7 base 8 place values.

How to Convert Decimal to Octal

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 80 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:

First Base 8 Value Greater than 12510

Power of 8: 83 82 81 80
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:

Decimal to Octal Conversion Chart

A Power of 8: 83 82 81 80
B Remainder of Division: 125      
C Place value (A result): 512 64 8 1
D Octal digit  (B ÷ C):        


Notice that the decimal you want to convert is placed in left-most cell of Row B, just above the base 8 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. Here is how the completed conversion chart would look:

Conversion Chart for Converting 12510 to Octal

A Power of 8: 83 82 81 80
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


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 octal converter will show its work.

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.

Decimal to Octal Converter
Calcy sign introducing Decimal to Octal Converter


Instructions: Enter the decimal number you would like to convert into an octal number, and then click the "Convert Decimal to Octal" 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 Octal Converter.

Help Decimal number (base 10):
Help Octal (base 8) equivalent: 8

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Decimal to Octal Converter Glossary of Terms

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Octal number system: Number system that uses the base 8 system of expressing values, which consists of the digits 0,1,2,3,4,5,6, and 7. Base 8 numbers are usually written with a subscripted 8 behind them (1758).

Decimal number (base 10): Enter the decimal (base 10) number you would like to convert into an octal 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 octal converter will only convert out to the last digit entered and will not round the result.

Octal (base 8) equivalent: This is the octal equivalent to the entered decimal number. Note that after clicking the Convert Decimal to Octal button the Decimal to Octal 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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