Hex to Octal Converter

Convert hexadecimal whole numbers to octal exactly, or switch directions to convert octal values back to hexadecimal.

Base 16 to base 8

Hexadecimal uses sixteen digit values, while octal uses eight. Conversion changes the notation, not the integer itself.

Binary is the useful bridge

One hex digit corresponds to four binary bits; one octal digit corresponds to three. Grouping the same bit pattern in fours or threes gives the two representations.

Exact integer conversion

Whole numbers retain their exact value during conversion, including long inputs.

How to Convert Hex to Octal

Hexadecimal is base 16 and uses 0–9 plus A–F. Octal is base 8 and uses only 0–7. A direct way to understand the conversion is through binary because 16 is 2⁴ and 8 is 2³.

Replace each hexadecimal digit with its four-bit binary value, join the bits, then regroup them into sets of three starting from the right. Pad the leftmost group with zeros when necessary. Each three-bit group maps to one octal digit.

When the input has several digits, keep the binary bits together before regrouping. Converting each hex digit separately to octal and joining the results would give the wrong number.

This calculator accepts an optional leading minus sign. That sign represents a negative integer directly; it does not interpret the input as a fixed-width two's-complement bit pattern.

Hex to Octal Examples

F₁₆ → 17
2A₁₆ → 52
7F₁₆ → 177
1A3₁₆ → 643
BEEF₁₆ → 137357
FFFF₁₆ → 177777

Worked Example: 2AF HEX to Octal

2 → 0010
A → 1010
F → 1111
0010 1010 1111 → 001 010 101 111
001 → 1, 010 → 2, 101 → 5, 111 → 7
2AF₁₆ = 1257₈

Hex to Octal FAQs

Why must binary groups start from the right?

The rightmost bit represents ones in both bases. Grouping from that end keeps every bit in its correct place; any padding belongs on the left.

What does A–F mean in a hexadecimal input?

A, B, C, D, E, and F are hexadecimal digits with values 10 through 15.

Can I enter 0x before the hexadecimal number?

Yes. In Hex → Octal mode, one optional leading 0x or 0X is accepted after an optional minus sign.

Why can the octal result have more digits than the hex input?

Each hex digit carries four bits while each octal digit carries three. The same integer can therefore require more octal digits than hexadecimal digits.

Does converting HEX to octal change the numeric value?

No. Only the base and written representation change. For example, FF₁₆ and 377₈ are the same integer.

Can this converter handle very long hexadecimal integers?

Yes. Long hexadecimal integers retain their exact value, within practical browser limits.

Does this tool interpret negative HEX as two’s complement?

No. A leading minus sign means an ordinary negative integer. Two’s-complement interpretation requires a specified bit width, which this converter does not assume.

Are spaces or punctuation allowed inside the hexadecimal value?

No. They are rejected so malformed input cannot be silently changed into a different number.

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