Decimal to Octal Converter
Convert decimal (base-10) numbers to octal (base-8). Octal uses digits 0-7 and appears frequently in Unix/Linux file permissions and legacy computing systems.
Common Values
| Input | Octal |
|---|---|
| 0 | 0 |
| 7 | 7 |
| 8 | 10 |
| 15 | 17 |
| 16 | 20 |
| 63 | 77 |
| 64 | 100 |
| 100 | 144 |
| 127 | 177 |
| 128 | 200 |
| 255 | 377 |
| 256 | 400 |
| 512 | 1000 |
| 1000 | 1750 |
| 1024 | 2000 |
| 4096 | 10000 |
How It Works
To convert decimal to octal, repeatedly divide by 8 and record the remainders. For example, 255: 255÷8=31 R7, 31÷8=3 R7, 3÷8=0 R3 — reading upward gives 377. Octal groups naturally align with 3-bit binary patterns, making it historically convenient for programmers.
Worked Examples
| Decimal | Octal |
|---|---|
| 0 | 0 |
| 7 | 7 |
| 8 | 10 |
| 15 | 17 |
| 16 | 20 |
| 63 | 77 |
| 64 | 100 |
| 255 | 377 |
| 256 | 400 |
| 512 | 1000 |
Related Conversions
Frequently Asked Questions
- How do I convert decimal to octal?
Repeatedly divide by 8 and note each remainder (0-7). Read the remainders from bottom to top to get the octal number.
- What is 255 in octal?
255 in octal is 377. You can verify: 3×64 + 7×8 + 7×1 = 192 + 56 + 7 = 255.
- Where is octal used?
Octal is most commonly seen in Unix/Linux file permission codes (chmod 755), in C language octal literals (leading 0), and in some legacy systems and protocols.
- How does octal relate to binary?
Each octal digit maps exactly to 3 binary bits: 0=000, 1=001, 2=010, 3=011, 4=100, 5=101, 6=110, 7=111. This makes converting between binary and octal straightforward.