Octal to Decimal Converter

To use this octal (base-8) to decimal (base-10) conversion tool, you must type an octal value like 345 into the left field below and hit the Convert button. The converter will give you the decimal equivalent of the given octal.

Octal Value Convert

Decimal Value swap conversion: Decimal To Octal Converter

Octal to decimal conversion result in base numbers

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.

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)

How to Calculate Octal to Decimal

An octal number can be converted to a decimal number by following simple rules. Here are two ways to convert octal to decimal step by step. The first is a more conventional method whereas the second one applies the repeated division and remainder algorithm technique in reverse.

Method 1:

• Step 1: Find out the number of digits in the number.
• Step 2: Let the number have n digits.
• Step 3: Think of the digits n^th position from the right to the left as the position. This means you are showing the position of each digit as an increasing power of 8.
• Step 4: Multiply each digit with 8^n-1, n being the position.
• Step 5: Add all the individual results from this multiplication process.
• Step 6: The result will be the decimal equivalent of the given octal number.

Now, let’s apply these steps to, for example, the octal number (765)₈

Step 1: This octal number has 3 digits.
Step 2: n is 3. 
Step 3: 5 is in position 1, so n-1 will be equal to 0. This will lead to 80
6 is in position 2, so n-1 will be 1. This will lead to 81;
7 is in position 3, so n-1 will be 2. This will lead to 82.
Step 4: (5 * 80) + (6 * 81) + (7 * 82)
Step 5: 5 + 48 + 448 = 501
Step 6: (501)10 equals (765)8

Method 2:

• Step 1: Start with the result 0.
• Step 2: Remove the most significant digit in the octal number (the leftmost one) and add it to the result (0).
• Step 3: Multiply the result by 8.
• Step 4: Go to step 2 and remove the leftmost digit. Add it to the result you got in step 3.
• Step 5: Keep until all octal digits have been removed. When you are left with only one digit, add it to the previous result. Do NOT multiply by 8. The sum from the last addition is the decimal equivalent.

Let’s apply these steps to the same octal number above, (765)₈

Step 1: Write down 0.
Step 2: Remove 7 (the leftmost digit) and add it to 0, which is 0 + 7 = 7. 
Step 3: Multiply the result by 8, which is 7 * 8 = 56.
Step 4: In the octal number (765)8, the leftmost digit is now 6. Add 6 to 56 and multiply the result by 8, which follows as: (6 + 56) * 8 = 496.
Step 5: In the octal number (765)8, we are only left with the digit 5. Therefore; 496 + 5 = 501.
Step 6: (501)10 equals (765)8

Example 1: (345)₈ = (229)₁₀

Method 1: 
(5 * 80) + (4 * 81) + (3 * 82) = 5 + 32 + 192 = 229

Method 2: 
0 + 3 = 3
3 * 8 = 24
24 + 4 = 28
28 * 8 = 224
224 + 5 = 229 

Example 2: (2675)₈ = (1469)₁₀

Method 1: 
(5 * 80) + (7 * 81) + (6 * 82) + (2 * 83) = 5 + 56 + 384 + 1024 = 1469

Method 2: 
0 + 2 = 2
2 * 8 = 16
16 + 6 = 22
22 * 8 = 176
176 + 7 = 183
183 * 8 = 1464
1464 + 5 = 1469

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Decimal To Octal Converter

Octal Decimal Conversion Chart Table

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