Symbolic chmod Notation: u, g, o, a With Plus, Minus and Equals

Octal sets all nine bits at once, which is precise and destructive: you have to know and restate every permission even if you only wanted to change one. Symbolic notation changes a class at a time, so chmod g+w adds group write and leaves everything else exactly as it was. For an incremental change on a file whose current mode you have not checked, that is the safer instrument.

The operators are not interchangeable. Plus and minus are relative, so the result depends on what was already set, which makes them unpredictable in a script run against files in unknown states. Equals is absolute for the class it names: chmod g=rx sets group to read and execute and clears group write whatever was there before. Scripts should prefer equals or octal for that reason.

Capital X is the piece most people never learn and the one that solves the recursive chmod problem. It sets the execute bit only on directories and on files that already have execute set for at least one class, so chmod -R a+rX makes a whole tree readable and traversable without marking every text file as a program.

Omitting the class has a subtlety: chmod +x is equivalent to a+x with the umask applied, so under a umask of 077 it adds execute for the owner only. Writing chmod a+x or chmod u+x says exactly what you mean and removes the dependency on an ambiguous environment value.

The calculator works in both directions and it is worth knowing which form each box takes. Its symbolic input accepts the nine character rendering you would copy out of an ls -l line, with or without the leading type character, and its output includes the clause form you would paste into a terminal. Octal accepts three or four digits and converts either way.