Free Octal to Decimal Converter – Convert Base-8 to Base-10 Online
Convert octal (base-8) numbers to decimal (base-10) instantly. See step-by-step conversion breakdown. Common values reference. Unix permissions explained. 100% free.
What Is Octal to Decimal Conversion?
Octal to decimal conversion transforms base-8 numbers (using digits 0-7) into base-10 numbers (our standard counting system). Octal was historically important in computing and remains crucial for Unix/Linux file permissions.
How to Use This Tool
Step 1: Enter Octal Number
Type digits 0-7 (no 8s or 9s).
Step 2: View Decimal Result
See the converted value instantly.
Step 3: Study Breakdown
Understand each digit's contribution.
Step 4: Copy Result
Copy for use elsewhere.
Conversion Method
Each octal digit represents a power of 8.
Example: Convert 754 to Decimal
7 × 8² = 7 × 64 = 448
5 × 8¹ = 5 × 8 = 40
4 × 8⁰ = 4 × 1 = 4
-----
Total: 492
So 754₈ = 492₁₀
Octal to Decimal Reference Table
| Octal | Decimal | Power of 8 |
|---|---|---|
| 1 | 1 | 8⁰ |
| 10 | 8 | 8¹ |
| 100 | 64 | 8² |
| 1000 | 512 | 8³ |
| 10000 | 4096 | 8⁴ |
| 77 | 63 | Max 2-digit |
| 777 | 511 | Max 3-digit |
| 7777 | 4095 | Max 4-digit |
Unix File Permissions
Octal is famously used for Unix/Linux file permissions:
| Octal | Binary | Permission | Meaning |
|---|---|---|---|
| 0 | 000 | --- | No permission |
| 1 | 001 | --x | Execute only |
| 2 | 010 | -w- | Write only |
| 3 | 011 | -wx | Write + Execute |
| 4 | 100 | r-- | Read only |
| 5 | 101 | r-x | Read + Execute |
| 6 | 110 | rw- | Read + Write |
| 7 | 111 | rwx | Full permissions |
Common Permission Examples
| Octal | Meaning |
|---|---|
| 755 | Owner: rwx, Group: r-x, Others: r-x |
| 644 | Owner: rw-, Group: r--, Others: r-- |
| 777 | Full permissions for everyone |
| 600 | Owner only: rw- |
| 400 | Owner only: r-- |
Why Octal Was Used Historically
Early computers used 12-bit, 24-bit, or 36-bit words, which divide evenly by 3. Since 3 bits = 1 octal digit, octal was a natural fit:
| Bits | Octal Digits |
|---|---|
| 3 | 1 |
| 6 | 2 |
| 12 | 4 |
| 24 | 8 |
| 36 | 12 |
Octal vs Hexadecimal
| Feature | Octal | Hexadecimal |
|---|---|---|
| Base | 8 | 16 |
| Digits | 0-7 | 0-9, A-F |
| Bits per digit | 3 | 4 |
| Common use | Unix permissions | Memory, colors |
| Prefix (C) | 0 (e.g., 0755) | 0x (e.g., 0xFF) |
Common Use Cases
System Administration
- Setting file permissions with chmod
- Understanding permission masks (umask)
Legacy Systems
- Working with older codebases
- Reading historical documentation
Education
- Learning number systems
- Understanding base conversion
Programming
- Writing octal literals (0755)
- Parsing configuration files
Position Value Chart
| Position | 5 | 4 | 3 | 2 | 1 | 0 |
|---|---|---|---|---|---|---|
| Power | 8⁵ | 8⁴ | 8³ | 8² | 8¹ | 8⁰ |
| Value | 32768 | 4096 | 512 | 64 | 8 | 1 |
Frequently Asked Questions
What digits are valid in octal?
Only 0, 1, 2, 3, 4, 5, 6, 7. No 8s or 9s.
Why is 10 in octal equal to 8?
10₈ means 1×8¹ + 0×8⁰ = 8 in decimal.
Where is octal used today?
Primarily in Unix/Linux file permissions (chmod 755).
Is there a length limit?
No practical limit for this tool.