Decimalto Octal Converter
Free Decimalto octal Converter for numeral systems units. Enter a value to see equivalent measurements across systems. Free to use with no signup required.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Octal = Repeated division by 8, read remainders bottom-to-top | Decimal = Sum of (digit x 8^position)
Decimal to octal conversion uses repeated division by 8. Each remainder becomes a digit in the octal result, read from bottom to top. Octal to decimal reverses this by multiplying each octal digit by 8 raised to its positional power and summing the results.
Worked Examples
Example 1: File Permission Conversion
Problem:Convert the decimal number 493 to octal to understand a Unix file permission.
Solution:493 / 8 = 61 remainder 5\n61 / 8 = 7 remainder 5\n7 / 8 = 0 remainder 7\nRead remainders bottom to top: 755
Result:493 in decimal = 755 in octal (rwxr-xr-x permission)
Example 2: Large Number Conversion
Problem:Convert 1000 in decimal to octal.
Solution:1000 / 8 = 125 remainder 0\n125 / 8 = 15 remainder 5\n15 / 8 = 1 remainder 7\n1 / 8 = 0 remainder 1\nRead remainders bottom to top: 1750
Result:1000 in decimal = 1750 in octal
Frequently Asked Questions
How do you convert a decimal number to octal?
To convert a decimal number to octal, repeatedly divide the number by 8 and record each remainder. Continue dividing the quotient by 8 until the quotient reaches zero. Then read the remainders from bottom to top to form the octal number. For example, converting 255 to octal: 255 divided by 8 gives 31 remainder 7, then 31 divided by 8 gives 3 remainder 7, then 3 divided by 8 gives 0 remainder 3, so 255 in decimal equals 377 in octal.
What is the octal number system used for?
The octal (base-8) number system is commonly used in computing and digital electronics. It provides a compact representation of binary numbers since each octal digit corresponds exactly to three binary digits. Unix and Linux file permissions use octal notation extensively, where values like 755 or 644 define read, write, and execute permissions for owner, group, and others.
What digits are valid in the octal system?
The octal number system uses only the digits 0 through 7. Any number containing the digits 8 or 9 is not a valid octal number. This is because octal is a base-8 system, so it only needs eight unique symbols to represent all values. If you encounter an 8 or 9 in what appears to be an octal number, it is likely a decimal or another base.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy