Octal to Decimal Converter

What the octal to decimal converter does

Octal is the base-8 number system, and these days you meet it most often as a file permission on a Linux or Mac machine. This tool turns an octal number into its ordinary decimal value. Type the octal in, press the button, and copy out the plain number.

If you have ever seen something like 755 next to a file and wondered what number that really is, this is the tool that tells you.

How to use it

1. Enter your octal number. Use only the digits 0 to 7, for example 157.
2. Press Convert. The decimal value appears in the output box.
3. Click the result to copy it. Tap the output to copy it to your clipboard.

Press Reset to clear both boxes.

Eight digits, no 8 and no 9

Octal is base 8, so it counts with exactly eight digits, 0 through 7, and that is the whole alphabet. There is no 8 and no 9. After 7 it rolls over to 10, which in octal means one eight and no ones, the same way decimal rolls from 9 to 10. A quick sanity check follows from this: if a number you are looking at contains an 8 or a 9, it is not octal, so something has been mislabelled.

Place value: powers of eight

Like every positional system, octal reads by place value, and here the columns are powers of eight. The rightmost column is the ones. The next is the eights. The next is the sixty-fours, which is eight times eight, and so on. To read an octal number you multiply each digit by what its column is worth and add the results.

A worked example with real numbers

Take the octal number 157.

• The 1 is in the sixty-fours column, so it is worth 1 × 64 = 64
• The 5 is in the eights column, so it is worth 5 × 8 = 40
• The 7 is in the ones column, so it is worth 7 × 1 = 7
• Add them: 64 + 40 + 7 = 111

So 157 in octal is 111 in decimal. Same method every time, multiply each digit by its column value and add.

Octal and file permissions

This is where octal still earns its place. On Unix-style systems, a file's permissions come in three groups, what the owner can do, what the group can do, and what everyone else can do. Each group has three switches: read, write, and execute. Three on-or-off switches is three bits, and three bits is exactly one octal digit, which is why permissions are written as three octal digits.

The switches are worth read 4, write 2, execute 1, and you add up the ones that are on. So the familiar 755 reads as 7 for the owner, which is 4 plus 2 plus 1, meaning read, write, and execute, then 5 for the group and 5 for others, each being 4 plus 1, meaning read and execute but not write. Run 755 through this converter and you get 493, the same permission set expressed as a plain number. The neat part is that one octal digit captures a full group of three permission bits with nothing left over.

Questions people ask

Why are there no 8s or 9s in octal?

Because octal is base 8, so it only has eight digits, 0 to 7. After 7 it carries to 10. An 8 or a 9 in a number means it is not octal.

What does 755 mean as a permission?

It is read in three octal digits: 7 for the owner (read, write, and execute), then 5 and 5 for group and others (read and execute). As a plain number, 755 in octal is 493 in decimal.

Why is octal tied to three bits?

Because eight is two cubed, so one octal digit stands for exactly three binary bits. That clean fit is why a three-bit permission group maps onto a single octal digit.

Where is octal used today?

Mostly in Unix and Linux file permissions, the chmod values like 644 and 755. It also turns up in some older systems and in a few programming languages, where a leading zero on a number can mean it is octal.

References

1. Weisstein, Eric W. "Octal." From MathWorld, A Wolfram Resource. https://mathworld.wolfram.com/Octal.html
2. IEEE and The Open Group. chmod, change the file modes. The Open Group Base Specifications (POSIX.1-2017). https://pubs.opengroup.org/onlinepubs/9699919799/utilities/chmod.html