Decimal to Octal Converter

You must be well familiar with the decimal number system. After all, we have been using it since we first started learning to count. But have you noticed that each position in a decimal number system can be expressed as a power of ? For example, we can write as:

Hence, we can also say that the base of the decimal number system is and it contains ten unique symbols from to .

The octal number system has as its base. We can express each place as a power of . The digits of an octal number can be a number between and . Examples of numbers in the octal system are , , etc.

We can express these numbers as:

In the following sections, we will see how we can convert a number from decimal to the octal system and vice-versa.

🙋 If you want to learn how to convert decimal numbers to binary or hexadecimal numbers, we recommend checking out our binary converter and decimal to hexadecimal converter.

To convert a number from the decimal system to the octal system, we will use a very simple approach:

1. Divide the number by .

2. Take note of the remainder. It can be any number between to . This number will be the last digit of the octal number, i.e., the rightmost digit.

3. Use the quotient from step 1 as your new initial number.

4. Repeat steps 1-3, and keep adding the remainder to the left of the previously obtained digits.

Let us understand this using an example. We will convert the number to octal representation:

1. Divide by , i.e., , remainder is .
2. Now, we will use the quotient from step 1, i.e., as the new number, and repeat step 1.
3. We will continue repeating the above steps until we get as the quotient. The results are shown in the table below.

Reading upwards, i.e., from bottom to top, the number is in octal representation.

If you have understood how to convert decimal to octal, then you must have realized by now how we can go the other way, i.e., convert a number from the octal to decimal system. Just reverse the algorithm explained above:

1. Start with the last digit (i.e., the rightmost one) and count the positions of digits as 0, 1, 2, 3, .... We will denote the digit at position 0 as , position 1 as , ..., and so on.

2. Now use the following algorithm to get the number () in the decimal system:
   

For example, let us convert to decimal.

1. First, we will count the position of each digit starting from the last one.

2. Now using the algorithm,
   

   we will get:

Hence, the number corresponds to in the decimal representation.

You can also check our binary to octal converter to convert between binary and octal numbers.

Now let us see how we can use our decimal to octal converter to solve the same octal to decimal conversion examples:

1. Using the drop-down menu, choose the option decimal to octal.

2. Type the number you want to convert, i.e., 6521.

3. The tool will display the result in the octal number system, i.e., 14571.

4. You can also convert octal to decimal by choosing it as the option.