Hex to Octal Converter

What the hex to octal converter does

This converts a hexadecimal number into octal. Type the hex in, press the button, and copy out the octal.

Hex and octal are the odd couple of the number bases. Both get on beautifully with binary, but not with each other, so this conversion works a little differently from the others, and it is worth understanding why.

How to use it

1. Enter your hex number. Use digits 0 to 9 and letters A to F, entered as capitals.
2. Press Convert. The octal version 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.

Why there is no direct shortcut

Hex and binary group cleanly because one hex digit is exactly four bits. Octal and binary group cleanly because one octal digit is exactly three bits. The trouble is that four and three do not divide into each other. One hex digit is not a whole number of octal digits, and one octal digit is not a whole number of hex digits, so there is no tidy digit-to-digit map between them the way there is with binary. You cannot just look up each hex digit and read off octal.

The method: go through binary

The fix is to use binary as a common ground, since both bases line up with it. You expand the hex into bits, four bits per hex digit, which gives you one plain binary number. Then you regroup that same string of bits into threes from the right and read it back as octal. Two easy grouping steps, with binary as the bridge in the middle. That is exactly the route this tool takes for you.

A worked example with real numbers

Convert the hex number 2F.

• Expand each hex digit to four bits: 2 is 0010 and F is 1111, so the binary is 00101111.
• Now regroup those same bits into threes from the right, padding the left: 000, 101, 111.
• Read each group as an octal digit: 0, 5, 7, which is 57.

So 2F in hex is 57 in octal. The bits never changed, only the way they were grouped, first into fours to read the hex, then into threes to read the octal. Both, as a check, are 47 in decimal.

Questions people ask

How do I convert hex to octal by hand?

Expand the hex to binary, four bits per hex digit, then regroup the bits into threes from the right and read them as octal. Binary sits in the middle as the bridge.

Why can I not convert hex straight to octal?

Because one hex digit is four bits and one octal digit is three bits, and four and three do not divide into each other. There is no whole-digit map between them, so you go through binary.

Could I go through decimal instead?

Yes. Converting the hex to decimal and then the decimal to octal reaches the same answer. Going through binary is usually quicker by hand because both steps are simple regrouping.

Should I type the letters as capitals?

Yes, enter A to F as capitals, the usual way hex digits are written.

References

1. Weisstein, Eric W. "Octal." From MathWorld, A Wolfram Resource. https://mathworld.wolfram.com/Octal.html