Octal Calculator

What the octal calculator does

This adds, subtracts, multiplies, and divides octal numbers, giving the answer back in octal. Enter two octal numbers, choose an operation, and read off the result without converting to decimal yourself.

When your numbers are already in octal, working in octal the whole way through saves a couple of conversions and keeps the answer in the form you started with.

How to use it

1. Enter the first number. Type it in octal, using only the digits 0 to 7.
2. Pick an operation and enter the second number. Choose add, subtract, multiply, or divide, then type the second octal number.
3. Press Calculate. The answer appears in octal.

Press Reset to clear everything.

Arithmetic that carries at eight

Octal arithmetic is the same column method you already use, with one adjustment: a column carries when it reaches 8 rather than 10. That follows from octal being base 8, where each column is worth eight times the one to its right. When a column adds up to 8 or more, you subtract 8, write what is left, and carry 1 onward. The right-to-left order and the carrying itself are unchanged.

A worked example with real numbers

Let us add 27 and 16 in octal, carrying whenever a column reaches 8. Work right to left.

• Rightmost column: 7 + 6 = 13. That is 8 or more, so subtract 8 to get 5, write 5, and carry 1.
• Next column: 2 + 1, plus the carried 1, is 4. Write 4.

The answer is 45 in octal. To check it, 27 in octal is 23 and 16 in octal is 14, and 23 + 14 is 37, while 45 in octal is 4 eights and 5, which is 32 + 5, also 37. The only change from familiar addition was carrying at 8 instead of 10.

Only the digits 0 to 7

Octal counts with eight digits, 0 through 7, and that is the whole set. There is no 8 and no 9, since reaching 8 is exactly what triggers a carry into the next column. So both the numbers you enter and the answers you get stay within 0 to 7 in every column. If a number contains an 8 or a 9, it is not really octal, which is a quick way to catch a mistake.

Where octal arithmetic comes up

Octal's main home today is file permissions on Unix and Linux systems, where a setting like 755 is an octal number. If you are working out or adjusting permission values, you are doing octal arithmetic, and being able to compute with them directly is handy. Octal also turns up in some older systems and file formats that grew up in the era when it was the common base, so anywhere those appear, calculating in octal keeps you in step with them.

Questions people ask

How does octal arithmetic work?

The same as ordinary arithmetic, except a column carries when it reaches 8 instead of 10, because octal is base 8. You add right to left, carrying 1 whenever a column hits 8 or more.

What is 27 plus 16 in octal?

45. The rightmost column, 7 plus 6, is 13, which is 8 or more, so you write 5 and carry 1; the next column gives 4. As a check, both sides equal 37 in decimal.

Why are there no 8s or 9s?

Because octal only has eight digits, 0 to 7. Reaching 8 is what causes a carry, so 8 and 9 never appear in a single column. An 8 or 9 means the number is not octal.

Do I need to convert to decimal first?

No. The calculator works in octal throughout, so you enter octal and get octal back, with no manual conversion.

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