Octal to Hex Converter

Going the other way? Convert hex back to octal →

How do you convert octal to hex?

Octal to hex conversion passes through binary: each octal digit becomes its bit group, the bits are regrouped, and each new group becomes one hexadecimal digit.

1. Write each octal digit as three binary digits.
2. Join the bits into one run: 57 is 101111.
3. Regroup that run into fours from the right, padding the left group.
4. Replace each group with its hexadecimal digit: 57 = 2F.

Octal to Hexadecimal Conversion Table

One hexadecimal digit equals exactly 4 bits (16 = 2⁴); one octal digit equals exactly 3 bits (8 = 2³). Hex and octal are therefore converted by grouping bits, and hex ↔ octal passes through binary. That is the whole method, so the table below is the only thing you need: every group of 4 bits has exactly one hex digit, and the mapping never changes. Binary writes values on the digit set 0, 1 with each place worth 2ⁿ, and a value marked 0b is binary; hex values are marked 0x.

Each base is defined by three things: which digits it uses, how a value is marked, and what each position is worth.

Worked Example: 57 to Hexadecimal

One value, converted the long way so the working is visible. This is the same grid the converter shows when you turn on "show steps".

Both bases here are powers of two, so no division is needed. One hexadecimal digit is worth exactly 4 bits, which means the conversion is a regrouping of the same bits rather than a change of value.

Written out, 57 is 101111 in binary. Regrouping those bits into 4s from the right, and padding the leftmost group with zeros if it is short, gives 2F. Counting the groups from the left instead is where this goes wrong: the padding then lands on the wrong end and every digit shifts.

Check it in reverse

The value returns unchanged. Convert 2F back and you get 57, because a base change rewrites the digits without touching the quantity they stand for. That is the whole test: if the round trip differs, a digit was misread. To check it by hand, convert the octal result back to hex and compare it with the number you started from.

Worked examples: octal to hex

Each example gives the value first, then the working. Click a value to load it in the converter.

Every example above reverses exactly — regroup the same bits from four to three at a time.

What About Padding, Fractions and Width?

Leading zeros and width

A number carries no leading zeros unless a width is fixed. 2F and 02F are the same value, so the converter writes the short form. Fixed widths belong to bytes and registers, not to arithmetic. repeated division and positional expansion covers where width does matter.

Fractions and the point

Digits after a point convert by the same rule with negative powers, so the first place after the point is worth 1/16. Many fractions that end neatly in decimal repeat forever in binary, which is where rounding creeps in.

Negative values

A minus sign is kept in front of the digits. Fixed-width binary encodes sign differently, using two's complement, and that is a separate rule from the base change itself.

How large a value can be

The method has no ceiling; each extra octal digit multiplies the range by 8. Practical limits come from the width a machine stores the value in, not from the conversion.

Octal to Hex in Code

The same rule in one line. Both route through binary and return the hexadecimal digits.

Python: format(int('57', 8), 'X')

JavaScript: parseInt('57', 8).toString(16).toUpperCase()

Common Mistakes

• Reading the remainders top to bottom. They come out in reverse, so the digits land backwards.
• Using a digit the base does not have — an 8 in octal, or a 2 in binary. The value cannot be read at all.
• Grouping bits from the left. Groups are counted from the right, and the leftmost group is the one that gets padded.
• Treating the result as a character code. 101 is a number here, not the letter A.

Frequently Asked Questions

Related Conversions

• Octal also converts to binary by the same route — expand each octal digit to three bits.
• Octal also converts to decimal by the same route — work out an octal number's decimal value.
• Octal also converts to text by the same route — oct escape to character lookup.
• If your input is decimal rather than octal, decimal to hex by dividing by 16 instead.
• If your input is binary rather than octal, convert binary to hexadecimal instead.
• If your input is hex rather than octal, hex to decimal by positional expansion instead.

The rest of the family sits on back to the binary converter.