Octal Converter — Free Decimal, Binary, Hex to Octal
Convert numbers between octal (base 8), decimal (base 10), binary (base 2), and hexadecimal (base 16). Free, instant.
About Octal Converter
An octal converter translates between octal (base 8) and other bases — decimal (base 10), binary (base 2), hex (base 16). Octal was historically used in early computing (PDP-11, Unix file permissions) and remains the standard format for Unix/Linux file mode notation (e.g. `chmod 755`). The ZTools Octal Converter handles bidirectional conversion across all four common bases with bit-grouping display (binary in groups of 3 for octal alignment) and Unix-permission breakdown (octal 755 = rwxr-xr-x). Useful for sysadmins, embedded developers, and CS students.
Use cases
- Unix / Linux file permissions. `chmod 755 file.sh` — what does 755 mean? Calculator decodes: owner=rwx, group=r-x, other=r-x. Daily sysadmin task.
- Embedded systems / older hardware. PDP-11, classic minicomputers, some embedded MCUs use octal for register bits. Conversion bridges modern hex docs to octal hardware specs.
- CS coursework. Number-systems homework. Calculator confirms manual conversions during practice.
- Number representation in language source. C/C++ allow octal literals with leading 0 (e.g. 0755 = decimal 493). Pitfall when accidentally writing 0755 expecting decimal.
How it works
- Enter value. Pick base (octal / decimal / binary / hex). Numeric input.
- Validate digits. Octal allows only 0–7; binary 0–1; hex 0–9 + a–f. Tool rejects out-of-range digits.
- Convert to all bases. Output shown in decimal, octal, binary (grouped 3-bits for octal alignment), hex.
- Unix permission breakdown (when 3-digit octal). e.g. 755 → owner rwx (7=4+2+1), group r-x (5=4+0+1), other r-x (5).
Examples
Input: 755 (octal, Unix permission)
Output: decimal 493, binary 111 101 101, hex 1ED. rwxr-xr-x.
Input: 0o644 (chmod default)
Output: decimal 420, binary 110 100 100. rw-r--r--.
Input: 255 (decimal) → octal
Output: 377. (Each octal digit = 3 binary bits; 255 = 11111111 = 011 111 111 = 377.)
Frequently asked questions
Why is octal still used?
Mainly Unix file permissions (because each digit cleanly maps to 3 permission bits — rwx). Outside that, octal has been mostly replaced by hex in modern computing.
Why not use binary directly for permissions?
111101101 (9 binary bits) is hard to read; 755 (3 octal digits) is faster. 3-digit octal is the right tradeoff for 9-bit permissions.
What does each Unix permission digit mean?
Each octal digit = sum of: 4 (read) + 2 (write) + 1 (execute). 7 = all (4+2+1). 6 = read + write. 5 = read + execute. 4 = read only.
C-language octal pitfall?
In C, leading 0 means octal: `int x = 0755;` is 493 in decimal, not 755. Easy to write accidentally — most modern languages dropped this convention (Python, JavaScript use 0o755 prefix instead).
Why no leading zeros in normal numbers?
Most modern languages and conventions don't use leading-0 octal anymore — too easy to confuse with decimal. Use 0o (Python, ES2015+) or 0O prefix.
Larger than 32 bits?
Yes — JavaScript BigInt handles arbitrarily large integers. Tool supports up to 64-bit values comfortably.
Pro tips
- Memorise: 7=rwx, 6=rw-, 5=r-x, 4=r--, 0=---. Covers 95% of chmod uses.
- Common file mode: 644 (rw-r--r--) for documents, 755 (rwxr-xr-x) for scripts/dirs, 600 (rw-------) for SSH keys.
- In code, prefer 0o755 over 0755 — clarity beats compactness.
- For new development, hex (base 16) is more common than octal — better fits 8-bit byte boundaries.
- For permission planning, draw the 9-bit grid: owner rwx | group rwx | other rwx — fill in 4/2/1 sums.
Reviewed by Ahsan Mahmood · Last updated 2026-05-06 · Part of ZTools.
For the full,
formatted version of this page, please enable JavaScript and reload
https://ztools.zaions.com/octal-converter.