Octal to Decimal Converter
Enter an octal number below to convert it to decimal.
Steps to Convert to Decimal
On this page:
How to Convert Octal to Decimal
The octal number system is a base 8 number system that uses eight digits, from 0 to 7. The decimal number system, on the other hand, is a base 10 number system that uses ten digits, 0 to 9.
When working with octal numbers, you’ll often need to convert the number to its decimal value, considering the decimal system is most commonly used.
The base 8 system is often used in legacy computing applications because a single octal digit can represent three binary bits, which are cleanly divisible in 6, 12, 24, and 36-bit computer systems. Most modern computer systems, however, are 16, 32, or 64-bit systems, which are cleanly divisible into base 16 numbers.
Therefore, the hexadecimal system is more commonly used today.
To convert an octal number to a decimal number, you can use the positional notation method. To use this method, multiply each octal digit number starting from the rightmost number, moving to the left by 8 to the power of n, where n is the distance from the right.
So, reading the octal number from right to left, the furthest digit to the right is equal to the digit times 80. The digit that is one position from the right is equal to the digit times 81.
Octal to Decimal Formula
The octal to decimal formula can be expressed as:
decimal number10 = (d0 × 80) + (d1 × 81) + … + (dn – 1 × 8n – 1)
When using the formula, d0 is the octal digit furthest to the right, d1 is the digit one position from the right, and dn – 1 is the digit furthest to the left.
For example, let’s convert the octal number 730 to decimal.
decimal number10 = (7 × 82) + (3 × 81) + (0 × 80)
decimal number10 = 448 + 24 + 0
decimal number10 = 472
Octal to Decimal Conversion Table
The table below shows octal numbers and the equivalent decimal number values.
|Octal Number||Decimal Number|
Frequently Asked Questions
When would you convert from octal to decimal?
You would convert from octal to decimal when you are working in legacy computing applications and need to convert a base 8 number to one that is more easily readable.
Why is there no 9 in octal?
There is no 9 in octal because each digit represents a power of 8, and so the “ones” digit only contains numbers 0-7.
How do you know if a number is octal or decimal?
By just looking at a number, one cannot tell if it is octal or decimal unless it has a prefix. The prefix for an octal number is “0o” and is most often used when working with octal numbers in computing applications.