Convert hexadecimal whole numbers to octal exactly, or switch directions to convert octal values back to hexadecimal.
Last updated: August 2026 | By Workshelve Team
Hexadecimal uses sixteen digit values, while octal uses eight. Conversion changes the notation, not the integer itself.
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.
Validated values are converted with BigInt, so long whole-number inputs do not pass through floating-point Number precision.
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.
For example, 2AF₁₆ becomes 0010 1010 1111₂. Regrouping from the right gives 001 010 101 111, which maps to 1 2 5 7. Therefore 2AF₁₆ = 1257₈.
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 digits align with four binary bits and octal digits align with three. Binary therefore provides an exact regrouping method without first doing decimal arithmetic.
A, B, C, D, E, and F are hexadecimal digits with values 10 through 15.
Yes. In Hex → Octal mode, one optional leading 0x or 0X is accepted after an optional minus sign.
Each hex digit carries four bits while each octal digit carries three. The same integer can therefore require more octal digits than hexadecimal digits.
No. Only the base and written representation change. For example, FF₁₆ and 377₈ are the same integer.
Yes, within practical browser limits. After validation, BigInt is used so conversion is not restricted to JavaScript Number safe-integer precision.
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.
No. They are rejected so malformed input cannot be silently changed into a different number.
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