Octal to Decimal Converter

The powers-of-8 method

Each octal position is worth a power of eight: 1, 8, 64, 512 reading right to left. Multiply every digit by its column weight and add the totals. Take 247:

2 4 7
2×64 + 4×8 + 7×1
= 128 + 32 + 7 = 167

So octal 247 equals decimal 167. Because octal only ever uses 0–7, any digit of 8 or 9 means the value is not valid octal — a quick error check.

Unix permissions explained

The reason octal still matters is that file permissions group three bits per user class: read (4), write (2) and execute (1). Adding those gives a digit from 0 to 7, and three classes — owner, group, others — give the familiar three-digit code. chmod 755 means owner 7 = read+write+execute, group 5 = read+execute, others 5 = read+execute. Converting 755 to decimal (493) is rarely needed in practice, but understanding the per-digit bit sum is essential for anyone managing servers.

7 = 111 = rwx
5 = 101 = r-x
5 = 101 = r-x
755 → rwxr-xr-x

Reference table

Note that 777 — full permissions for everyone — is decimal 511, one less than 512 (8³). Just like in binary, an all-max run is one below the next power.

Where octal appears

• Unix/Linux chmod, umask and file mode bits.
• Legacy systems and older programming languages where 0 prefixes an octal literal.
• Some escape sequences and byte representations in C and shell scripts.
• Digital systems where bits are naturally grouped in threes.