Octal to Decimal Converter
Convert octal to decimal: multiply each digit by 8^position and sum. 777₈ = 511₁₀. Free tool for chmod and CS.
How to Convert Octal to Decimal
Multiply each octal digit by 8^position (rightmost = 8⁰) and add.
Decimal = Σ (digit × 8^position) from right (position 0).
777₈ = 7×64 + 7×8 + 7 = 511₁₀ (Unix rwx-rwx-rwx).
Octal is still used for chmod permissions and legacy systems.
Unix chmod permission values. The table and FAQ on this page walk through the factor if you need it.
Conversion Examples
Example: 777 octal to decimal
- 7×64 + 7×8 + 7 = 511
511 decimal
Full Unix permissions.
Example: 10 octal to decimal
- 1×8 + 0 = 8
8 decimal
Simple two-digit octal.
Common Use Cases
- Unix chmod permission values.
- CS and digital logic courses.
- Legacy mainframe data.
- Debugging octal dumps.
Frequently Asked Questions
How do you convert octal to decimal?
Multiply each digit by 8 raised to its position (from 0 on the right) and sum.
What is 755 octal in decimal?
7×64 + 5×8 + 5 = 493 decimal (common chmod).
Why is octal used in Unix?
Each octal digit maps cleanly to 3 binary bits—handy for rwx permission triplets.