Decimal to Octal Converter

To use this decimal to octal converter, you must type a decimal value like 245 into the left field below, and then hit the Convert button. The converter will give you the octal equivalent of the given decimal number.

Decimal Value (max: 9223372036854775807) Convert

Octal Value swap conversion: Octal To Decimal Converter

Decimal to octal conversion result in base numbers

Decimal System

The decimal numeral system is the most commonly used and the standard system in daily life. It uses the number 10 as its base (radix). Therefore, it has 10 symbols: The numbers from 0 to 9; namely 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

As one of the oldest known numeral systems, the decimal numeral system has been used by many ancient civilizations. The difficulty of representing very large numbers in the decimal system was overcome by the Hindu–Arabic numeral system. The Hindu-Arabic numeral system gives positions to the digits in a number and this method works by using powers of the base 10; digits are raised to the n^th power, in accordance with their position.

For instance, take the number 2345.67 in the decimal system:

• The digit 5 is in the position of ones (10⁰, which equals 1),
• 4 is in the position of tens (10¹)
• 3 is in the position of hundreds (10²)
• 2 is in the position of thousands (10³)
• Meanwhile, the digit 6 after the decimal point is in the tenths (1/10, which is 10^-1) and 7 is in the hundredths (1/100, which is 10^-2) position
• Thus, the number 2345.67 can also be represented as follows: (2 * 10³) + (3 * 10²) + (4 * 10¹) + (5 * 10⁰) + (6 * 10^-1) + (7 * 10^-2)

The Octal System

The octal number system (or shortly oct) uses the number 8 as its base (radix). As a base-8 numeral system, it uses eight symbols: The numbers from 0 to 7, namely 0, 1, 2, 3, 4, 5, 6 and 7. Although it was used by some native American tribes until the 20th century, the octal system has become popular in the early ages of computing as a language of computer programming. This is because the octal system shortens binary by simplifying long and complex chains of binary displays used by computers.

The octal system is mainly used for counting binary in groups of three: Each octal digit represents three binary digits. Since 8 is 2 to the third power (2³), the octal system became a perfect abbreviation of binary for machines that employ word sizes divisible by three - which were 6-bit, 12-bit, 24-bit or 36-bit. Nowadays, most modern systems use hexadecimal rather than octal. However, octal numbers are an important part of basic knowledge in electronics.

How to Calculate Decimal to Octal

Decimal to octal conversion can be achieved by applying the repeated division and remainder algorithm. Simply put, the decimal number is repeatedly divided by the radix 8. In between these divisions, the remainders give the octal equivalent in reverse order.

Here is how to convert decimal to octal step by step:

• Step 1: If the given decimal number is less than 8, the octal equivalent is the same. If the given number is greater than 7, divide the number by 8.
• Step 2: Write down the remainder.
• Step 3: Divide the part before the decimal point of your quotient by 8 again.
• Step 4: Write down the remainder.
• Step 5: Continue this process of dividing by 8 and noting the remainders until the last decimal digit you are left with is less than 8.
• Step 6: When the last decimal digit is less than 8, the quotient will be less than 0 and the remainder will be the digit itself.
• Step 7: The last remainder you get will be the most significant digit of your octal value while the first remainder from Step 3 is the least significant digit. Therefore, when you write the remainders in reverse order - starting at the bottom with the most significant digit and going to the top- you will reach the octal value of the given decimal number.

Now, let's apply these steps to, for example, the decimal number (501)₁₀

Step 1: As 501 is greater than 7, divide by 8. 
501 ÷ 8 = 62.625
Step 2: To calculate the remainder, you need to multiply the part after the decimal point by 8.
0.625 * 8 = 5
So the first remainder (and the least significant digit in the octal) is 5.
Step 3: Divide 62 (the part of the quotient that is before the decimal point) by 8.
62 ÷ 8 = 7.75
Step 4: Calculate the remainder.
0.75 * 8 = 6
Step 5: Divide the integer part of the last quotient by 8.
7 ÷ 8 = 0.875
Step 6: Calculate the remainder.
0.875 * 8 = 7 
(Note that when you reached a number less than the radix 8 in Step 3, the remainder 7 was already obvious. This is because if a decimal number is less than 8, the octal equivalent has the same value.)
Step 7: The remainders written from below to top give you the octal number (765)8
Therefore, (765)8 equals (501)10

Decimal to Octal Conversion Examples

Example 1: (1465)₁₀ = (2671)₈

1465 ÷ 8 = 183.125
0.125 * 8 = 1 (Remainder: 1)
183 ÷ 8 = 22.875
0.875 * 8 = 7 (Remainder 7)
22 ÷ 8 = 2.75 
0.75 * 8 = 6 (Remainder 6)
2 ÷ 8 = 0.25
0.25 *8 = 2 (Remainder 2)
Read the remainder from the most significant to the least - from bottom to top: 2671.
This is the octal equivalent of (1465)10

Example 2: (8)₁₀ = (10)₈

8 ÷ 8 = 1
Remainder 0
1 ÷ 8 = 0.125
0.125 * 8 = 1 (Remainder 1)
Read the remainder from the most significant to the least - from bottom to top: 10.

Example 3: (10)₁₀ = (12)₈

10 ÷ 8 = 1.25
0.25 * 8 = 2 (Remainder 2) 
1 ÷ 8 = 0.125 (Remainder 1)
Read the remainder from the most significant to the least - from bottom to top: 12.

Example 4: (1234)₁₀ = (2322)₈

1234 ÷ 8 = 154.25 (Remainder 2)
154 ÷ 8 = 19.25 (Remainder 2)
19 ÷ 8 = 2.375 (Remainder 3)
2 ÷ 8 = 0.25 (Remainder 2)
The octal number is 2322.

Decimal to Octal Conversion Chart Table

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