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Convert octal numbers (base-8) to decimal numbers (base-10) instantly. Essential for Unix permissions, legacy systems, and programming.
| Octal | Decimal | Unix Permissions |
|---|---|---|
| 0 | 0 | - |
| 1 | 1 | - |
| 7 | 7 | - |
| 10 | 8 | - |
| 20 | 16 | - |
| 77 | 63 | - |
| 100 | 64 | - |
| 144 | 100 | - |
| 200 | 128 | - |
| 377 | 255 | - |
| 400 | 256 | - |
| 777 | 511 | rwxrwxrwx |
| 1000 | 512 | - |
Octal (base-8) is a number system using eight digits: 0-7. Each octal digit represents exactly three binary digits (bits), since 2³ = 8. While less common than hexadecimal in modern computing, octal remains widely used in Unix/Linux file permissions and appears in some legacy systems and specialized applications.
To convert octal to decimal, multiply each digit by 8 raised to its position (counting from right to left, starting at 0), then sum all the results. This is similar to binary conversion but uses powers of 8 instead of powers of 2.
Example: Convert 755 (octal) to decimal
7 × 8² = 7 × 64 = 448
5 × 8¹ = 5 × 8 = 40
5 × 8⁰ = 5 × 1 = 5
Total: 448 + 40 + 5 = 493
In Unix, each octal digit represents permissions for owner, group, and others. Each digit is the sum of read (4), write (2), and execute (1) bits:
Unix permissions use 9 bits (3 groups of 3 bits each for owner, group, and others). Octal is perfect because each octal digit represents exactly 3 bits. This makes it easy to express all permission combinations with just 3 octal digits (e.g., 755, 644).
chmod 755 means: Owner has full permissions (7=rwx), Group has read and execute (5=r-x), Others have read and execute (5=r-x). This is common for executable files and directories where the owner can modify but others can only read and execute.
Octal is base-8, meaning it only uses 8 digits (0-7). Just as decimal stops at 9 before going to 10, octal stops at 7 before going to 10 (which equals 8 in decimal). The digits 8 and 9 don't exist in octal notation.
Most languages use a leading 0 for octal literals (e.g., 0755 in C/C++/JavaScript). Python uses 0o prefix (0o755). When you see a number starting with 0 in older code, it's likely octal. Modern best practice is to avoid implicit octal notation to prevent confusion.
Yes, octal remains essential for Unix/Linux system administration and file permissions. While hexadecimal is more common for general computing, octal's clean 3-bit mapping makes it ideal for permissions and certain legacy systems. Anyone working with Unix-based systems should understand octal.