Decimal to Octal Converter

About this calculator

Octal is a base-8 positional numbering system using only the digits 0–7, converted from decimal by repeated division by 8 and reading the remainders in reverse order — so decimal 83 becomes octal 123 (83 = 1×64 + 2×8 + 3). Each octal digit maps neatly onto exactly three binary bits, which made it a convenient shorthand for binary in the early computing era.

Octal's clearest surviving use today is Unix and Linux file permissions: the familiar chmod 755 or 644 notation is octal, with each digit's three bits representing read, write, and execute permissions for owner, group, and others — a convention that dates back to early Unix systems and remains standard in system administration and scripting today.