Octal Converter
Octal (base-8) uses the digits 0–7. Because 8 = 2³, one octal digit represents exactly three binary bits — making octal a compact shorthand for binary. It was the dominant shorthand in 1960s–70s computing and is still used today for Unix/Linux file permissions.
Notes
Octal Digit Values and Powers of 8
Just like decimal uses powers of 10, octal uses powers of 8. The rightmost digit is 8⁰ = 1, the next is 8¹ = 8, then 8² = 64, 8³ = 512, and so on.
| Position | 3 | 2 | 1 | 0 |
|---|---|---|---|---|
| Power of 8 | 512 | 64 | 8 | 1 |
Octal → Decimal: Positional Notation
Multiply each octal digit by the corresponding power of 8 and sum the products.
Octal → Binary: One Digit at a Time
Each octal digit corresponds to exactly 3 binary bits. Replace each digit using the table below — no arithmetic required.
| Octal | Binary | Octal | Binary |
|---|---|---|---|
| 0 | 000 | 4 | 100 |
| 1 | 001 | 5 | 101 |
| 2 | 010 | 6 | 110 |
| 3 | 011 | 7 | 111 |
Octal → Hexadecimal: Via Binary
There is no direct octal-to-hex table, so convert via binary in two steps: expand each octal digit to 3 bits, concatenate the bits, then regroup into 4-bit chunks and convert each chunk to its hex digit.
Real-World Use: Unix File Permissions
Unix permissions are a perfect example of octal in practice. A permission value like 755 is three octal digits, each representing 3 binary flags (read, write, execute) for owner, group, and others.
| Octal | Binary (rwx) | Meaning |
|---|---|---|
| 7 | 111 | read + write + execute |
| 6 | 110 | read + write |
| 5 | 101 | read + execute |
| 4 | 100 | read only |
| 0 | 000 | no permissions |
- How Octal Conversion Works — Detailed Notes — Methods with full worked examples and the binary connection
- Octal Conversion Formula Reference — Positional notation formula, variables, and examples
Frequently Asked Questions
What digits are valid in an octal number?
Only 0 through 7. The digits 8 and 9 do not exist in octal. If you see an 8 or 9 in a supposed octal number, it is not a valid octal value.
Why is octal used for Unix file permissions?
Unix permissions are groups of 3 binary flags (read/write/execute), and 3 bits = one octal digit. This makes octal a natural compact representation: chmod 644 is immediately readable as owner=rw (6=110), group=r (4=100), others=r (4=100).
Is octal still used in modern computing?
Yes, though less commonly than hex. Octal appears in Unix/Linux file permissions, some older networking protocols, and in escape sequences in several programming languages (e.g., \077 in C/Python).