Octal to Decimal Converter
Convert octal numbers to decimal format instantly. Enter any octal number and get decimal, binary, and hexadecimal results.
Valid characters: 0-7 only
What is Octal to Decimal Conversion?
Octal to decimal conversion is the process of converting base-8 numbers (octal) to base-10 numbers (decimal). Octal uses digits 0-7, while decimal uses digits 0-9. This conversion involves multiplying each octal digit by increasing powers of 8 (from right to left) and summing the results.
For example, octal 755 equals decimal 493. The conversion works as: (7 × 8²) + (5 × 8¹) + (5 × 8⁰) = (7 × 64) + (5 × 8) + (5 × 1) = 448 + 40 + 5 = 493. This is particularly useful when working with Unix file permissions, where octal notation (like chmod 755) needs to be understood in decimal terms.
Our free octal to decimal converter makes this conversion instant and accurate. Simply enter any octal number (like Unix file permissions 755, 644, or 777) and get the decimal equivalent immediately, along with binary and hexadecimal representations. For the reverse operation, use our Decimal to Octal Converter tool.
How to Convert Octal to Decimal Manually
Understanding the manual conversion process using positional notation:
Positional Notation Method:
- Step 1: Write down the octal number
- Step 2: Assign position numbers from right to left, starting with 0
- Step 3: Multiply each digit by 8 raised to its position
- Step 4: Sum all the results to get the decimal value
Example: Convert 755 to Decimal
Step 1: Octal number 755 Step 2: Assign positions (right to left) Position: 2 1 0 Digit: 7 5 5 Step 3: Calculate each position 7 × 8² = 7 × 64 = 448 5 × 8¹ = 5 × 8 = 40 5 × 8⁰ = 5 × 1 = 5 Step 4: Sum all values 448 + 40 + 5 = 493 Therefore, 755₈ = 493₁₀ Real-world meaning: 755 = rwxr-xr-x (Unix file permissions) 493 is the decimal representation
The key is understanding that each position represents a power of 8, starting from 8⁰ = 1 on the right. For other conversions, check our Octal to Binary Converter or Decimal to Binary Converter.
Octal to Decimal Conversion Table
This reference table shows common octal values and their decimal equivalents:
| Octal | Decimal | Common Use |
|---|---|---|
| 0 | 0 | --- (no permissions) |
| 1 | 1 | --x (execute only) |
| 4 | 4 | r-- (read only) |
| 5 | 5 | r-x (read + execute) |
| 6 | 6 | rw- (read + write) |
| 7 | 7 | rwx (full permissions) |
| 10 | 8 | 1 × 8¹ + 0 × 8⁰ |
| 100 | 64 | 8² = 64 |
| 644 | 420 | rw-r--r-- (common file) |
| 755 | 493 | rwxr-xr-x (executable) |
| 777 | 511 | rwxrwxrwx (full access) |
Pro Tip: Unix file permissions use 3 octal digits representing owner, group, and others. Each digit (0-7) corresponds to different permission combinations.
Why Convert Octal to Decimal?
Octal to decimal conversion is essential in various computing scenarios:
🔐 Understanding Permissions
Convert Unix chmod values (755, 644) to decimal to understand the numeric representation of file permissions.
💻 System Programming
Many system calls and APIs expect decimal values even when documentation uses octal notation.
📊 Data Analysis
Convert octal data from legacy systems to decimal for mathematical operations and reporting.
📖 Educational Learning
Understanding number system conversions is fundamental in computer science education.
🔧 Configuration Files
Some configuration files use octal notation that needs decimal interpretation for validation.
🐛 Debugging
Convert octal debug output to decimal for easier understanding and comparison with expected values.
For performing calculations after conversion, use our Binary Calculator tool.
Common Octal to Decimal Examples
Here are practical octal to decimal conversion examples from real-world scenarios:
📁 chmod 755 (rwxr-xr-x)
Octal 755 = (7×64) + (5×8) + (5×1) = 448 + 40 + 5 = Decimal 493
Most common permission for executable files and directories
📄 chmod 644 (rw-r--r--)
Octal 644 = (6×64) + (4×8) + (4×1) = 384 + 32 + 4 = Decimal 420
Standard permission for regular files
🔒 chmod 600 (rw-------)
Octal 600 = (6×64) + (0×8) + (0×1) = 384 + 0 + 0 = Decimal 384
Private files accessible only by owner
🔐 chmod 777 (rwxrwxrwx)
Octal 777 = (7×64) + (7×8) + (7×1) = 448 + 56 + 7 = Decimal 511
Full permissions for everyone (security risk!)
🎯 Simple Octal 12
Octal 12 = (1×8) + (2×1) = 8 + 2 = Decimal 10
Benefits of Using Our Online Converter
ProURLMonitor's free octal to decimal converter offers multiple advantages:
- ✓Instant Conversion: Convert any octal number to decimal in milliseconds without manual calculation.
- ✓Multiple Formats: Get decimal, binary, and hexadecimal results simultaneously.
- ✓Step-by-Step Breakdown: See the positional calculation showing how each digit contributes to the final result.
- ✓Input Validation: Automatically checks for valid octal digits (0-7 only).
- ✓Perfect for chmod: Understand Unix file permission values in decimal format.
- ✓100% Free: No registration, downloads, or hidden costs. Use unlimited times.
- ✓Mobile Friendly: Works on all devices—desktop, tablet, and smartphone.
- ✓Educational Value: Learn the conversion process with detailed examples and power calculations.
Understanding Octal Number System
The octal number system is a base-8 positional numeral system that uses eight distinct digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each position represents a power of 8, making it useful for representing binary data in a more compact form.
Octal Position Values:
Example: To understand octal 755 in decimal:
Octal was historically popular in computing because early computers used 12-bit, 24-bit, or 36-bit words (divisible by 3). Modern systems use 8-bit bytes, making hexadecimal more common, but octal remains essential for Unix file permissions.
Related Binary Conversion Tools
Explore our complete suite of binary and number system converters:
🔄 Octal to Binary Converter
Convert octal numbers to binary format—see the bit-level representation.
🔢 Binary to Octal Converter
Convert binary numbers to octal format—essential for Unix file permissions.
📊 Decimal to Binary Converter
Convert decimal numbers to binary format for computer operations.
🔢 Binary to Decimal Converter
Convert binary numbers to decimal format for human-readable values.
🔷 Hex to Binary Converter
Convert hexadecimal numbers to binary format—perfect for analyzing hex codes.
🔷 Binary to Hex Converter
Convert binary numbers to hexadecimal format used in modern programming.
🧮 Binary Calculator
Perform arithmetic operations on binary numbers (add, subtract, multiply, divide).
🔤 Binary Translator
Convert text to binary code and decode binary back to readable text.
📚 Frequently Asked Questions (FAQs)
Q: How do I convert octal 755 to decimal?
A: Calculate (7×64) + (5×8) + (5×1) = 448 + 40 + 5 = 493 in decimal.
Q: What is octal 7 in decimal?
A: Octal 7 equals decimal 7. Single-digit octal numbers 0-7 have the same decimal value.
Q: Why multiply by powers of 8?
A: Octal is base-8, so each position represents 8⁰, 8¹, 8², etc., from right to left. This is how positional number systems work.
Q: What does chmod 644 mean in decimal?
A: Octal 644 = Decimal 420. This represents rw-r--r-- permissions (owner: read+write, group: read, others: read).
Q: Can I enter octal numbers with a leading 0?
A: Yes, you can enter 0755 or just 755—both work. Leading zeros don't change the value but indicate octal notation in programming.
Q: What happens if I accidentally enter 8 or 9?
A: The converter will show an error because octal only uses digits 0-7. Numbers 8 and 9 don't exist in the octal system.
Q: Is this converter accurate for large octal numbers?
A: Yes, 100% accurate! It uses JavaScript's built-in parseInt() with base-8, supporting octal numbers up to JavaScript's safe integer limit.
Q: Why is octal still used if hexadecimal is more common?
A: Octal remains essential for Unix/Linux file permissions (chmod). It's also easier to convert between octal and binary (3:1 bit ratio) for certain applications.
🚀 Start Converting Octal to Decimal Now!
Use our free octal to decimal converter to convert any octal number instantly. Perfect for Unix administrators understanding chmod permissions, programmers working with system programming, students learning number systems, and anyone needing to convert octal notation. Get results in decimal, binary, and hexadecimal formats with detailed positional calculation breakdown.
No registration required. Unlimited conversions. Completely free forever!
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