Decimal to Octal Converter
Enter a whole decimal number and get the octal (base 8) equivalent — plus hex and binary with 3-bit triplet groups that show the direct relationship between binary and octal.
How does this calculator work?
Divide the decimal by 8 repeatedly, collecting remainders (0–7) in reverse order. Example: 255 → remainders 7, 7, 3 → read bottom-up: 377 → 0o377. Or convert to binary, zero-pad to a multiple of 3 bits, then group into triplets and replace each with its octal digit. Uses BigInt for arbitrary precision.
Formula
How this is calculated
To convert a decimal integer to octal, divide by 8 repeatedly and record each remainder (which will be 0–7). Write the remainders in reverse order to get the octal representation. For example, 255 ÷ 8 = 31 r 7, 31 ÷ 8 = 3 r 7, 3 ÷ 8 = 0 r 3. Remainders bottom-up: 3, 7, 7 → 0o377. You can verify: 3×64 + 7×8 + 7×1 = 192 + 56 + 7 = 255.
The equivalent shortcut via binary is elegant because 2³ = 8: convert to binary, then group bits into triplets from the right and swap each triplet for the octal digit it represents (000 → 0, …, 111 → 7). For 255 = 11111111 binary: two triplets 111 and 111 → both equal 7 → octal 77. But 255 has 8 bits; zero-pad to the nearest multiple of 3 gives 011 111 111 → 3, 7, 7 → octal 377. The calculator shows the triplet grouping so you can read off each octal digit directly.
Octal is rarely used in general computing today, but survives in Unix/Linux file permissions (e.g. chmod 755 = 111 101 101 binary = owner rwx, group r-x, other r-x) and some legacy assembly languages.
Frequently asked questions
64 ÷ 8 = 8 r 0, then 8 ÷ 8 = 1 r 0, then 1 ÷ 8 = 0 r 1. Remainders reversed: 1, 0, 0 → 0o100. Check: 1×64 + 0×8 + 0 = 64.
The most common use is Unix file permissions: chmod 755 means owner=7 (rwx), group=5 (r-x), other=5 (r-x), each digit being 3 binary permission bits. Octal also appears in some C/C++ literals prefixed with 0 (e.g. int x = 0377 sets x to 255).
The largest octal digit is 7 (binary 111). Octal has no digits 8 or 9, which is why a string like "08" is not valid octal — it would be a syntax error in C.
Also known as
TG we-Calculate Editorial Team. (2026). Decimal to Octal Converter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/decimal-to-octal-calculator
TG we-Calculate Editorial Team. "Decimal to Octal Converter." TG we-Calculate. 2026. https://we-calculate.com/calculator/decimal-to-octal-calculator.
TG we-Calculate Editorial Team, "Decimal to Octal Converter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/decimal-to-octal-calculator
@misc{wecalculate_decimal_to_octal_calculator, title = {Decimal to Octal Converter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/decimal-to-octal-calculator}}, year = {2026}, note = {TG we-Calculate} }
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