Octal to Hex Converter

What the octal to hex converter does

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

As with its mirror image, hex to octal, these two bases do not convert to each other directly. They each line up with binary but not with one another, so the conversion leans on binary in the middle.

How to use it

1. Enter your octal number. Use only the digits 0 to 7, for example 755.
2. Press Convert. The hex 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 the two do not line up

An octal digit is exactly three bits, and a hex digit is exactly four. Three and four do not divide into each other, so a single octal digit is not a whole number of hex digits, and the other way round too. That means there is no neat digit-for-digit lookup between octal and hex, unlike the clean groupings each of them shares with binary.

The method: through binary

So binary does the connecting. You expand the octal into bits, three bits per octal digit, which gives one plain binary number. Then you regroup that same string of bits into fours from the right and read it back as hex. Expand by threes, regroup by fours, with binary as the shared step in between. That is the path this tool follows.

A worked example with real numbers

Convert the octal number 755.

• Expand each octal digit to three bits: 7 is 111, 5 is 101, 5 is 101, so the binary is 111101101.
• Now regroup those same bits into fours from the right, padding the left: 0001, 1110, 1101.
• Read each group as a hex digit: 1, E, D, which is 1ED.

So 755 in octal is 1ED in hex. The underlying bits stayed the same throughout, grouped into threes to read the octal and into fours to read the hex. Both come to 493 in decimal.

Questions people ask

How do I convert octal to hex by hand?

Expand the octal to binary, three bits per octal digit, then regroup the bits into fours from the right and read them as hex. Binary is the bridge between the two.

Why can I not convert octal straight to hex?

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

Could I go through decimal instead?

Yes. Converting the octal to decimal and then to hex gives the same result. Going through binary is usually faster by hand, since both steps are just regrouping bits.

What is 755 in hex?

1ED. Expanding 755 to the bits 111101101 and regrouping into fours gives 0001 1110 1101, which reads as 1ED.

References

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