Decimal to Octal Converter - MathCalculators

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What is Decimal?

The decimal system is a base-10 numeral system that uses ten digits: 0 through 9. It is the most widely used system for representing numbers in everyday life, from counting to financial transactions and engineering calculations.

Example: 25 (decimal)

Each decimal digit is multiplied by powers of 10, starting from the rightmost position.

25₁₀ = 2 * 10¹ + 5 * 10⁰ = 20 + 5 = 25

What is Octal?

The octal system is a base-8 numeral system that uses eight digits: 0 through 7. Each position in an octal number represents a power of 8, with the rightmost position being (8^0), the next (8^1), and so on. Octal is a shorthand for binary because each octal digit represents exactly three binary digits (bits).

Example: 31 (octal)

Each octal digit represents a sum of powers of 8:

31₈ = 3 * 8¹ + 1 * 8⁰ = 24 + 1 = 25₁₀

Decimal to Octal Conversion

To convert a decimal number to octal, we use the repeated division by 8 method. In this method, the decimal number is repeatedly divided by 8, and the remainders are recorded. The octal equivalent is obtained by reading the remainders in reverse order, starting from the last remainder.

Steps to Convert Decimal to Octal

Divide the decimal number by 8.
Record the remainder.
Divide the quotient by 8 and record the remainder.
Repeat the process until the quotient becomes zero.
Read the octal number by writing the remainders in reverse order.

Example Conversions

Let’s go through a few examples to better understand how to convert decimal numbers to octal.

Example 1: Convert 25 (decimal) to octal.

Divide 25 by 8: quotient = 3, remainder = 1
Divide 3 by 8: quotient = 0, remainder = 3

Now, reading the remainders from bottom to top: 31

So, 25 (decimal) is equal to 31 (octal).

Example 2: Convert 100 (decimal) to octal.

Divide 100 by 8: quotient = 12, remainder = 4
Divide 12 by 8: quotient = 1, remainder = 4
Divide 1 by 8: quotient = 0, remainder = 1

Now, reading the remainders from bottom to top: 144

So, 100 (decimal) is equal to 144 (octal).

Example 3: Convert 78 (decimal) to octal.

Divide 78 by 8: quotient = 9, remainder = 6
Divide 9 by 8: quotient = 1, remainder = 1
Divide 1 by 8: quotient = 0, remainder = 1

Now, reading the remainders from bottom to top: 116

So, 78 (decimal) is equal to 116 (octal).

Decimal to Octal Conversion Table

Here’s a quick reference table showing common decimal numbers converted to their octal equivalents:

Decimal	Octal
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	10
9	11
10	12
20	24
30	36
50	62
100	144

Online Decimal to Octal Converter

Online tools provide a quick and efficient way to convert decimal numbers to octal, especially when dealing with large numbers. These tools are commonly used in computer science, programming, and digital electronics