Binary to Octal Converter
Convert binary to octal — three bits to each octal digit.
Octal groups bits in threes, because eight is two cubed.
How the binary to octal converter works
Octal groups bits in threes, because eight is two cubed. 111 is 7, 101 is 5, 000 is 0.
Octal was common when word sizes were multiples of three bits, and it survives in one place everyone meets: Unix file permissions. chmod 755 is three octal digits, each expanding to the read, write and execute bits for one class of user — 7 is 111, all three permissions; 5 is 101, read and execute.
Formula: value = Σ digitₖ × bᵏ
Worked examples
| Inputs | Converted | Note |
|---|---|---|
| 111101101 | 755 | 755 — the classic chmod |
| 11111111 | 377 | 377 |
| 1000 | 10 | 10 |
FAQFrequently asked questions
How do I convert binary to octal?
Group the bits in threes from the right and translate each group: 111 is 7.
Why three bits per octal digit?
Because 8 is 2³.
What is chmod 755 in binary?
111 101 101 — read, write and execute for the owner, read and execute for everyone else.
Is octal still used?
Mainly for Unix file permissions. Hex has replaced it almost everywhere else.
What is 11111111 in octal?
377, which is 255 in decimal.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.