Octal to Decimal Converter

Powers of 8 and positional notation

Like any positional number system, octal assigns a place value to each digit position based on a power of the base. In octal, the rightmost digit is 8⁰ (equals 1), the next position left is 8¹ (equals 8), the next is 8² (equals 64), then 8³ (equals 512), and so on.

To convert an octal number to decimal, multiply each digit by its place value and sum the results. For the octal number 755: the 5 in the rightmost position is 5 x 1 = 5, the 5 in the middle position is 5 x 8 = 40, and the 7 in the left position is 7 x 64 = 448. The sum is 448 + 40 + 5 = 493.

The tool above applies this multiplication and summing for any octal input. You do not need to remember the powers of 8; paste in the octal value and get the decimal result immediately.

Decoding chmod permission values

Unix file permissions are expressed as three-digit octal numbers (sometimes four digits when including the setuid, setgid, and sticky bits). Understanding what a chmod value means numerically is useful when comparing permissions returned by a stat() system call - which gives a decimal integer - to the octal form used by chmod.

For example, a stat() call might return mode 33188 for a regular file. That decimal number converted to octal gives 100644. The leading digits 10 indicate a regular file type; the trailing 644 is the permission: owner has read and write (6 = 4+2), group has read only (4), and others have read only (4). Converting back and forth between decimal and octal makes this breakdown possible.

Paste any decimal mode value here to get the octal representation, or enter an octal chmod value to get the decimal integer the kernel stores internally.

Positional notation in practice

Working through the math once or twice helps build intuition. The octal digits 0 through 7 cover every possible 3-bit combination. So when you see a two-digit octal number, the left digit is worth 8 times the right digit. A two-digit octal number ranges from 00 (decimal 0) to 77 (decimal 63). A three-digit octal number ranges from 000 (decimal 0) to 777 (decimal 511).

That upper limit of 777 (decimal 511) is significant for file permissions: the 9 permission bits can represent at most 2⁹ - 1 = 511 distinct combinations, which matches exactly.

Frequently asked questions