How unix permissions calculator works
Every Unix file carries nine permission bits in three triples: what the owner can do, what the group can do, and what everyone else can do. Each triple is read (r), write (w) and execute (x), and each one is worth 4, 2 and 1. rwx is 4+2+1 = 7, r-x is 5, rw- is 6 — which is why the octal shorthand 755, 644 and 600 is everywhere: each digit is one role’s triple added up.
This tool converts in both directions. Type an octal mode like 755 and it produces the symbolic string rwxr-xr-x, the numeric value, and a per-role breakdown; paste a symbolic string like rw-r--r-- (an ls -l fragment with or without the leading file-type character also works) and it produces the octal digits. Special bits work too: a leading fourth digit (4755) or the letters s, S, t and T inside the triples encode setuid, setgid and sticky, and the tool reports which are active with a plain-English explanation.
Use it to decode a chmod command from a tutorial before you run it, to figure out why your web server refuses to read a file (it usually wanted 644 on files and 755 on directories), or to check a private key is properly locked down to 600. The conversion is pure arithmetic with no file system access, and it runs entirely in your browser.