All Tools VerseOctal is the base-8 number system, using only the digits 0 to 7, and it maps to binary in clean groups of three bits. Converting octal to binary, decimal, or hex is mostly a matter of regrouping those bits, so octal 17 is binary 001 111 and decimal 15. This guide shows how to convert base 8 in every direction, the three-bit rule that makes it easy, and free converters for the work.
In this guide
What octal is
Octal counts in base 8, so after 7 it rolls over to 10, which means eight. Each position is worth a power of 8: ones, eights, sixty-fours, and so on. Its value comes from the link to binary: because 8 is two to the third power, one octal digit always equals exactly three binary bits. That made octal popular in early computing, when machine word sizes were multiples of three. For the full picture of how octal sits alongside binary, decimal, and hex, see our guide to number systems.
Octal to binary
To convert octal to binary, replace each octal digit with its three-bit pattern and join them. Octal 5 is 101, octal 2 is 010, so octal 52 is 101010. The reverse works by grouping bits into threes from the right. This direct mapping is why you never need to pass through decimal first.
For longer numbers the lookups pile up, so the octal to binary converter expands the whole value at once and pads the groups correctly.
Octal to decimal
Octal to decimal uses place value. Multiply each digit by its power of 8 and add the results. Octal 17 is 1 times 8 plus 7, which is 15 in decimal. Octal 100 is 64, because the leading 1 sits in the sixty-fours column. The arithmetic is simple but easy to slip on for long values, and you can always check a result by expanding to binary first and then using the binary to decimal converter.
Octal to hex
There is no direct digit-to-digit shortcut between octal and hex, because 8 and 16 do not group bits the same way. The reliable route is to expand the octal to binary, regroup the bits into fours, and read them as hex. The octal to hex converter does both steps for you, so octal 52 becomes binary 101010 and then hex 2A.
Where octal is still used
The most common place you will meet octal today is Unix and Linux file permissions. A setting such as 755 is an octal number, where each digit packs the read, write, and execute bits for one group of users into a single value from 0 to 7. Older systems and some hardware manuals also use octal, but permissions are why most people still see it. If you work with permissions often, our chmod numbers guide explains how those octal digits map to access rights.
Free converters used in this guide
Frequently asked questions
How do I convert octal to binary?
Replace each octal digit with its three-bit pattern and join them in order. Octal 5 is 101, so octal 52 is 101010. An octal to binary converter does this instantly.
What is octal 17 in decimal?
Octal 17 is 1 times 8 plus 7, which is 15 in decimal.
Why does one octal digit equal three bits?
Because 8 is two to the third power, so the eight octal digits 0 to 7 map exactly to the eight three-bit patterns from 000 to 111.
How do I convert octal to hex?
Expand the octal to binary, regroup the bits into fours from the right, then read each group as a hex digit. A converter handles both steps at once.
Why are Linux permissions in octal?
Because read, write, and execute are three bits, and three bits fit perfectly in one octal digit, so a permission such as 755 stores three groups cleanly.