Binary to Octal Converter
Enter any binary number and see the octal (base 8) equivalent in one step — plus decimal and hex for context, with the binary grouped into 3-bit triplets that map one-to-one to octal digits.
How does this calculator work?
Pad your binary string to a multiple of 3 bits, split into triplets, then replace each triplet with the matching octal digit (000 → 0, …, 111 → 7). Three binary bits = one octal digit. Enter any binary number and the octal result appears instantly alongside decimal and hex equivalents.
Formula
How this is calculated
Octal (base 8) uses digits 0–7. The shortcut between binary and octal comes from 2³ = 8: exactly three binary bits map to exactly one octal digit. To convert, left-pad the binary string with zeros until its length is a multiple of 3, then replace each 3-bit group with its octal equivalent — 000 → 0, 001 → 1, 010 → 2, 011 → 3, 100 → 4, 101 → 5, 110 → 6, 111 → 7. For binary 101 010, the triplets 101 and 010 give octal digits 5 and 2, producing 0o52 (decimal 42).
Octal was widely used in early computing (notably in Unix file-permission notation: chmod 755 means 111 101 101 in binary) because early computers used 6-bit or 12-bit word sizes, which divide evenly by 3. Today it is mostly encountered in Unix/Linux permissions and some assembly-language contexts.
This calculator uses BigInt arithmetic, handling binary numbers of any length without rounding. Spaces in the input are ignored, so you can paste nibble-grouped or byte-grouped binary and still get the correct octal result.
Frequently asked questions
Group the binary digits into triplets from the right (pad left with zeros if needed) and replace each triplet with the octal digit it represents: 000 → 0, 001 → 1, 010 → 2, 011 → 3, 100 → 4, 101 → 5, 110 → 6, 111 → 7. Three bits always give one octal digit, so the conversion is purely mechanical.
The most common modern use is Unix/Linux file permissions: the three octal digits of a permission code like 0o755 represent the owner (7 = rwx), group (5 = r-x) and other (5 = r-x) permission triplets, each of which is literally three bits. Some assembly languages also use octal for instruction encoding.
No — octal is base 8 (digits 0–7, 3 bits per digit) while hexadecimal is base 16 (digits 0–9 and A–F, 4 bits per digit). Both are compact representations of binary, but hex is far more common in modern computing because 8-bit bytes divide evenly into two hex digits, while an 8-bit byte requires two and two-thirds octal digits.
TG we-Calculate Editorial Team. (2026). Binary to Octal Converter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/binary-to-octal-calculator
TG we-Calculate Editorial Team. "Binary to Octal Converter." TG we-Calculate. 2026. https://we-calculate.com/calculator/binary-to-octal-calculator.
TG we-Calculate Editorial Team, "Binary to Octal Converter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/binary-to-octal-calculator
@misc{wecalculate_binary_to_octal_calculator, title = {Binary to Octal Converter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/binary-to-octal-calculator}}, year = {2026}, note = {TG we-Calculate} }
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