Octal to Decimal Converter
Octal (base 8) uses the digits 0 to 7 and maps cleanly to binary because 8 is 2 to the third power: every octal digit is exactly three bits. It survives today mainly in Unix file permission modes like 755. Enter an octal value and this converter returns the decimal equivalent, the binary equivalent, the hexadecimal equivalent, and the digit count. The decimal conversion is a positional sum: each digit is multiplied by a power of eight set by its place, then the products are added.
Octal to decimal formula
Decimal = sum of (digit * 8 ^ position)
Position counts from 0 at the rightmost digit
Each octal digit = three binary bits (8 = 2 ^ 3)
Example: 17 = (1*8) + (7*1) = 15
Example: 755 = (7*64) + (5*8) + (5*1) = 493
To get binary, replace each octal digit with its three-bit pattern; to get hex, convert the decimal value to base 16.
Octal number context
- Unix file permissions use octal: 755 means owner read/write/execute, group and others read/execute.
- Each octal digit covers three permission bits in that scheme.
- Octal was widely used on early computers with 12, 24, or 36-bit word sizes.
- Hexadecimal has largely replaced octal because modern byte-oriented hardware favors 4-bit grouping.
- The digits 8 and 9 never appear in a valid octal number.
Octal to decimal converter: frequently asked questions
How do you convert octal to decimal?
Multiply each octal digit by 8 raised to the power of its position, counting from zero at the rightmost digit, then sum. The octal value 17 equals 1 times 8 plus 7 times 1, which is 8 plus 7, equal to 15 in decimal.
Why does each octal digit map to three bits?
Because 8 equals 2 to the power of 3, every octal digit corresponds to exactly three binary bits. The octal digit 5 is 101 in binary, and 7 is 111. This made octal a convenient shorthand on older computers with word sizes that were multiples of three.
What digits are valid in an octal number?
Octal uses only the digits 0 through 7. The digits 8 and 9 are not valid in base 8, so a value containing them is rejected by this converter.
Where is octal still used today?
Octal is most commonly seen in Unix and Linux file permissions, where a mode like 755 expresses read, write, and execute bits for owner, group, and others. Each octal digit there represents three permission bits.
How does this converter handle a leading zero?
A leading zero does not change an octal value, so 017 and 17 both equal 15 in decimal. Note that in some programming languages a leading zero marks an octal literal; this tool treats the input as octal regardless of the prefix.
Official sources
- NIST: National Institute of Standards and Technology, positional number systems reference.
- IEEE and The Open Group: POSIX file mode (octal permission) specification.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.