Convert between decimal (base 10) and octal (base 8) number systems. Octal is commonly used in Unix file permissions and legacy computing systems.
Last updated: March 2026 | By Patchworkr Team
Octal is a base-8 number system that uses eight distinct symbols: 0, 1, 2, 3, 4, 5, 6, and 7. It was historically popular in computing because three binary digits (bits) can be represented by exactly one octal digit, making it a convenient shorthand for binary representations.
Octal is most commonly encountered in Unix and Linux file permissions (like 755 or 644), where each digit represents read, write, and execute permissions for owner, group, and others. It's also used in some legacy programming contexts and embedded systems.
While hexadecimal has largely replaced octal in modern computing (because 4 bits map to 1 hex digit), octal remains important for file permissions and understanding older codebases.
Repeatedly divide by 8 and take remainders:
Multiply each digit by 8 raised to its position:
Convert 100 (octal) to decimal:
Unix file permissions use 3 bits for read (4), write (2), and execute (1). One octal digit (0-7) perfectly represents these 3 bits, making permissions like 755 or 644 compact and easy to work with.
7 is the largest octal digit, representing decimal 7. Since octal is base-8, it only uses digits 0 through 7. If you see an 8 or 9, it's not a valid octal number.
Octal numbers are often prefixed with '0' (zero) in programming languages like C. For example, 0755 is octal. Without context, only numbers using digits 0-7 can be octal.
Hexadecimal (base-16) aligns better with modern computing where bytes (8 bits) are standard. Two hex digits represent one byte exactly, while octal requires different groupings.
Yes! Each octal digit converts to exactly 3 binary digits. For example, octal 5 = binary 101, and octal 7 = binary 111. This makes octal-binary conversion straightforward.
In Unix/Linux, 755 means: owner has full permissions (7=rwx), group can read and execute (5=rx), and others can read and execute (5=rx). Each digit is an octal representation of permission bits.
Octal is less common in modern programming but still appears in file permissions, some embedded systems, and when working with legacy code. Hexadecimal has largely replaced it for most purposes.
777 (octal) gives full permissions (read, write, execute) to everyone: owner, group, and others. It's generally considered insecure as it allows anyone to modify or execute the file.
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