Free Decimal to Octal Converter – Convert Base-10 to Base-8 Online
Convert decimal (base-10) numbers to octal (base-8) instantly. See step-by-step division method. Unix permission reference. Interactive examples. 100% free.
What Is Decimal to Octal Conversion?
Decimal to octal conversion transforms standard base-10 numbers into base-8 numbers using only digits 0-7. This is essential for Unix/Linux file permissions and certain computing applications.
How to Use This Tool
Step 1: Enter Decimal
Type any positive whole number.
Step 2: View Octal Result
See the converted base-8 value.
Step 3: Study the Steps
Understand the division method.
Step 4: Copy Result
Copy for use in chmod commands, etc.
Division Method Explained
To convert decimal to octal, repeatedly divide by 8 and collect remainders.
Example: Convert 492 to Octal
| Step | Dividend | ÷ 8 | Quotient | Remainder |
|---|---|---|---|---|
| 1 | 492 | ÷ 8 | 61 | 4 |
| 2 | 61 | ÷ 8 | 7 | 5 |
| 3 | 7 | ÷ 8 | 0 | 7 |
Reading remainders bottom to top: 754₈
Common Decimal to Octal Values
| Decimal | Octal | Use Case |
|---|---|---|
| 1 | 1 | Execute |
| 2 | 2 | Write |
| 4 | 4 | Read |
| 7 | 7 | Full single permission |
| 8 | 10 | 8¹ |
| 64 | 100 | 8² |
| 100 | 144 | Common round number |
| 255 | 377 | Max byte |
| 511 | 777 | chmod 777 |
| 512 | 1000 | 8³ |
Unix/Linux File Permissions
Octal is the standard for representing Unix permissions:
Permission Values
| Octal | Permission | Meaning |
|---|---|---|
| 0 | --- | No access |
| 1 | --x | Execute |
| 2 | -w- | Write |
| 3 | -wx | Write + Execute |
| 4 | r-- | Read |
| 5 | r-x | Read + Execute |
| 6 | rw- | Read + Write |
| 7 | rwx | Full access |
Common Permission Sets
| Decimal | Octal | chmod | Meaning |
|---|---|---|---|
| 493 | 755 | rwxr-xr-x | Executable |
| 420 | 644 | rw-r--r-- | Standard file |
| 384 | 600 | rw------- | Private file |
| 511 | 777 | rwxrwxrwx | Full access |
| 256 | 400 | r-------- | Read-only |
Why Octal for Permissions?
3 bits represent one permission set:
- Bit 2 (4): Read
- Bit 1 (2): Write
- Bit 0 (1): Execute
3 bits = 8 combinations = 1 octal digit
Three permission sets (owner, group, others) = 3 octal digits
Example: rwxr-xr-- = 111 101 100 = 754
Power of 8 Reference
| Power | Calculation | Value |
|---|---|---|
| 8⁰ | 1 | 1 |
| 8¹ | 8 | 8 |
| 8² | 8×8 | 64 |
| 8³ | 8×8×8 | 512 |
| 8⁴ | 8×8×8×8 | 4,096 |
| 8⁵ | 8⁵ | 32,768 |
Use Cases
System Administration
- Setting file permissions (chmod)
- Configuring umask values
- Scripting permission changes
Programming
- Writing octal literals
- Parsing permission values
- Working with legacy code
Education
- Learning number systems
- Understanding base conversion
- Computer science courses
Octal in Programming Languages
| Language | Octal Prefix | Example |
|---|---|---|
| C/C++ | 0 | 0755 |
| Python | 0o | 0o755 |
| JavaScript | 0o | 0o755 |
| Bash | Leading 0 | chmod 0755 |
| Perl | 0 | 0755 |
Frequently Asked Questions
What's the maximum value?
No practical limit in this tool.
Can I convert negative numbers?
This tool only converts positive integers.
Why 8 for the base?
8 symbols (0-7) = 3 bits, which maps cleanly to Unix permission triplets.
How do I use the result with chmod?
Copy the octal and use: chmod 755 filename