Online Octal to Decimal converter

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Octal to Decimal converter

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Octal to Decimal

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 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.

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.

1. Find out the number of digits in the number.

2. Let the number have n digits.

3. Think of the digits nth 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.

4. Multiply each digit with 8n-1, n being the position.

5. Add all the individual results from this multiplication process.

6. The result will be the decimal equivalent of the given octal number.


7014 in base 8 is equal to each digit multiplied with its corresponding power of 8:

70148 = 7×83+0×82+1×81+4×80= 3584+0+8+4 = 359610all


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