Decimal to Octal Converter

Our decimal to octal converter is an easy to use tool for converting base-10 numbers to base-8 numbers quickly.

A decimal number is a main type of number system in which numbers are expressed in a base-10 numeral system. The decimal number contains 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 numeric digits. 

The combination of 0-9 numbers is said to be the decimal number system. Each digit of a decimal number counts a power of 10. Keep in mind that if any number is written without a base, then it would be a decimal number with a base 10.

An octal number, on the other hand, is a number expressed in a base-8 numeral system. It includes the digits 0-7, which are different from the decimal system. The octal number system is the combination of 0-7 numbers. Each digit of an octal number counts as a power of 8.

The decimal to octal conversion can be done easily by using our decimal to octal converter above. For manual conversion, follow the steps below.

1. Take a decimal number.
2. If the given base-10 number is less than equal to 7, then the octal number is the same.
3. If the given base-10 number is greater than 7, then we’ve to divide it by 8.
4. Write the quotient and remainder. 
5. Repeat the process with each quotient until the quotient is less than 8.
6. Write the obtained remainders from bottom to top to get the octal number.

Below are a few examples of decimal to octal conversion.

Example 1:

Convert 345₁₀ to an octal number.

Solution

Step 1: Divide 345 by 8.

345/8 = 43 r 1

Quotient = 43

Remainder = 1

Step 2: Divide the above obtained quotient by 8.

43/8 = 5 r 3

Quotient = 5

Remainder = 3

Step 3: Now divide the above obtained quotient by 8.

5/8 = 0 r 5

Quotient = 0

Remainder = 5

Step 4: Write the obtained remainders from bottom to top.

531

Step 5: Write the given decimal with its octal number.

345₁₀ = (531)₈

Example 2:

Convert 2456₁₀ to an octal number.

Solution

We’ll solve this by division method.

Divided by	Quotient	Remainder
8	2456
8	307	0
8	38	3
	4	6

The octal number will be formed by taking the last quotient and all the remainder from bottom to top.

Hence 

2456₁₀ = (4630)₈

Use our octal to decimal converter if you want to convert octal numbers to decimals.