Octal ↔ Decimal Converter
Convert between octal (base-8) and decimal (base-10) number systems effortlessly. Essential for Unix file permissions, computer science education, and legacy computing systems that still rely on octal notation.
Octal ↔ Decimal Converter
Convert between octal (base-8) and decimal (base-10) number systems
Use only digits 0-7. Three digits will show Unix file permissions.
Quick Examples
Octal Reference
Octal Digits
Note: 8 and 9 are not valid octal digits
Powers of 8
How to Use the Octal Converter
Master octal-decimal conversion with step-by-step guidance
1Select Conversion Type
Choose your conversion direction:
- Octal to Decimal: Convert base-8 to base-10
- Decimal to Octal: Convert base-10 to base-8
- Real-time conversion: See results as you type
- Step-by-step breakdown: Learn the math behind it
2Enter Your Number
Input the number in the correct format:
- Octal: Use only digits 0-7
- Decimal: Standard base-10 numbers
- No prefixes needed: Just the raw number
- Large numbers supported: Up to JavaScript limits
3View Detailed Results
Get comprehensive conversion information:
Breakdown: (7×8²) + (5×8¹) + (5×8⁰) = 448 + 40 + 5 = 493
4Apply to Real Scenarios
Use in practical applications:
- • Set Unix file permissions (chmod 755)
- • Understand legacy system configurations
- • Learn computer science fundamentals
Understanding Octal Numbers
Learn the fundamentals of the base-8 number system
Octal is a base-8 number system that uses eight distinct digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each position represents a power of 8, making it particularly useful in computing contexts where powers of 2 are common (since 8 = 2³). Historically, octal was popular in early computing systems and remains important today for Unix file permissions.
Octal Digits & Values
Note: Digits 8 and 9 do not exist in octal
Position Values (Powers of 8)
Unix Permissions with Octal
Master file permissions using octal notation
Unix file permissions are the most practical application of octal numbers today. Each permission set (read, write, execute) is represented by 3 bits, making octal the perfect base for representing all 8 possible combinations (0-7).
Permission Values
Common Permission Patterns
Understanding the Three Digits
Each octal permission has three digits representing: Owner, Group, Others
└─7─┘ Owner: rwx (read, write, execute)
└─5─┘ Group: r-x (read, execute)
└─5─┘ Others: r-x (read, execute)
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Frequently Asked Questions
Common questions about octal number conversion and usage
Why is octal used for Unix file permissions?
Octal is perfect for file permissions because each permission set (read, write, execute) uses exactly 3 bits, and 3 bits represent 8 possible values (0-7). This makes octal notation naturally align with permission concepts, where each digit represents the permissions for owner, group, and others respectively.
What's the largest octal number this converter can handle?
Our converter can handle very large octal numbers, limited primarily by JavaScript's number precision (up to about 15-16 significant digits in decimal). For most practical applications including system administration and programming, this range is more than sufficient.
Can octal numbers have digits 8 or 9?
No, octal is a base-8 system that only uses digits 0 through 7. If you see an 8 or 9 in a number, it's not a valid octal number. This is a common source of confusion when working with numbers that might be interpreted as octal but actually contain invalid digits.
How do I remember octal permission values?
Think of each permission as a binary number: read=4, write=2, execute=1. Add them together: rwx = 4+2+1 = 7, r-x = 4+0+1 = 5, r-- = 4+0+0 = 4. Common patterns like 755 (rwxr-xr-x) and 644 (rw-r--r--) will become second nature with practice.
What's the relationship between octal and binary?
Each octal digit represents exactly 3 binary digits. For example, octal 7 equals binary 111, octal 5 equals binary 101. This relationship makes octal a convenient shorthand for binary numbers, especially when working with 3-bit groups in digital systems and permissions.