Octal to decimal converter

Type a number in either field and the other converts as you type — octal to decimal or decimal to octal. The breakdown below shows the actual math for your number, not a canned example. Prefixes like 0o, spaces and underscores are fine.

How octal to decimal conversion works

Octal is base 8: each digit position is worth a power of 8, and only the digits 0–7 are used. To convert to decimal, multiply each digit by its positional value and add everything up:

755₈ = 7×8² + 5×8¹ + 5×8⁰ = 448 + 40 + 5 = 493₁₀

Going the other way — decimal to octal — divide repeatedly by 8 and read the remainders from bottom to top. The converter above shows both directions on whatever number you give it.

Octal and binary: one digit is three bits

Just like a hex digit maps to four bits, an octal digit maps to exactly three: 7₈ = 111₂, 5₈ = 101₂. That makes octal a compact way to write binary values whose fields split naturally in threes — which is exactly why Unix file permissions use it.

Where you'll meet octal numbers

The classic one is Unix/Linux file permissions: chmod 755 means rwxr-xr-x — each octal digit encodes the read/write/execute bits for owner, group and others. Octal also shows up in umask values, some escape sequences (\033 for ESC) and older computing literature.

Related tools and guides

• Binary ↔ decimal converter — octal is shorthand for binary, three bits per digit.
• Hex ↔ decimal converter — the same positional method in base 16.
• Hex calculator — add, subtract, multiply, divide and bitwise-operate in hex.