Octal ⇄ Decimal
Convert between octal (base 8) and decimal (base 10). Useful for Unix file permissions, legacy computing, and programming exercises involving number systems.
How to use the octal ⇄ decimal
Octal uses digits 0–7; common in legacy Unix permission notations.
Formula & explanation
Each octal digit represents 3 bits.
Examples
777 = 511. 644 = 420.
Frequently asked questions
- What is octal used for?
- Octal is most commonly seen in Unix/Linux file permissions. chmod 755 means owner can read/write/execute (7), group and others can read/execute (5).
- How do I convert octal to decimal?
- Multiply each octal digit by 8 raised to its position (starting at 8⁰ on the right) and sum them. For example, 777 = (7×64) + (7×8) + (7×1) = 511.
- Why does octal use digits 0–7 only?
- Octal is base-8, so valid digits are 0 through 7. Using 8 or 9 is invalid and will produce an error.
- What does chmod 644 mean?
- 644 in octal means owner has read+write (6), and group/others have read-only (4). In binary: 110 100 100.
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