Octal to Decimal Converter
Convert between octal (base 8) and decimal (base 10) instantly
Conversion Mode
Octal Input
Tip: Octal numbers use digits 0-7. For example, octal 157 equals decimal 111.
Educational Mode
Conversion History
What is the Octal Number System?
The octal number system (also known as base 8) is a positional numeral system that uses eight distinct digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each position in an octal number represents a power of 8, just as each position in a decimal number represents a power of 10.
Octal was widely used in early computing systems, particularly in systems programming and machine code representation. It provides a more compact representation than binary while being easier to convert to and from binary than hexadecimal (one octal digit represents exactly three binary digits).
Example Conversion:
Octal 157 = (1 × 8²) + (5 × 8¹) + (7 × 8⁰)
= (1 × 64) + (5 × 8) + (7 × 1)
= 64 + 40 + 7
= 111 (decimal)
Today, while hexadecimal has largely replaced octal in most applications, understanding octal is still valuable for working with Unix file permissions, legacy systems, and learning about number systems in computer science education.
How to Convert Between Octal and Decimal
Octal to Decimal
Method:
- Write down the octal number
- Starting from the rightmost digit, multiply each digit by 8 raised to its position (0, 1, 2, ...)
- Add all the results together
Example: Convert 752 (octal) to decimal
Position 2: 7 × 8² = 7 × 64 = 448
Position 1: 5 × 8¹ = 5 × 8 = 40
Position 0: 2 × 8⁰ = 2 × 1 = 2
Total: 448 + 40 + 2 = 490 (decimal)
Decimal to Octal
Method:
- Divide the decimal number by 8
- Record the remainder
- Replace the number with the quotient
- Repeat steps 1-3 until the quotient is 0
- Read the remainders from bottom to top
Example: Convert 490 (decimal) to octal
490 ÷ 8 = 61 remainder 2
61 ÷ 8 = 7 remainder 5
7 ÷ 8 = 0 remainder 7
Reading bottom to top: 752 (octal)
Octal to Decimal Quick Reference
| Octal | Decimal | Octal | Decimal | Octal | Decimal |
|---|---|---|---|---|---|
| 0 | 0 | 10 | 8 | 20 | 16 |
| 1 | 1 | 11 | 9 | 30 | 24 |
| 2 | 2 | 12 | 10 | 40 | 32 |
| 3 | 3 | 13 | 11 | 50 | 40 |
| 4 | 4 | 14 | 12 | 60 | 48 |
| 5 | 5 | 15 | 13 | 70 | 56 |
| 6 | 6 | 16 | 14 | 100 | 64 |
| 7 | 7 | 17 | 15 | 200 | 128 |
Common Use Cases
Unix File Permissions
Unix and Linux systems use octal notation for file permissions. For example, chmod 755 sets read, write, and execute permissions using octal values.
Legacy Systems
Older computer systems and programming languages used octal notation for representing machine code and memory addresses.
Computer Science Education
Learning octal helps students understand positional number systems, binary-to-octal conversions, and the fundamentals of how computers process numbers.
Digital Electronics
Octal representation is sometimes used in digital electronics and circuit design as a compact way to represent binary values.
Tips & Best Practices
Use Step-by-Step Mode
Enable the step-by-step calculation display to understand exactly how the conversion works. This is especially helpful for learning and verifying manual calculations.
Batch Conversion for Multiple Values
When you need to convert multiple numbers, use batch conversion mode. Enter one number per line to convert them all at once and save time.
Remember: Only Digits 0-7
Octal numbers can only contain digits 0 through 7. If you see an 8 or 9 in what you think is an octal number, it's actually in a different number system.
Use History Feature
The conversion history keeps track of your recent conversions. Click on any history item to quickly reload those values and perform additional conversions.
Quick Verification with Swap
After converting a number, click the Swap button to reverse the conversion and verify that you get back to your original value.
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Frequently Asked Questions
What is the difference between octal and decimal?
Decimal (base 10) uses digits 0-9 and each position represents a power of 10. Octal (base 8) uses digits 0-7 and each position represents a power of 8. For example, the decimal number 64 equals octal 100 because 1×8² + 0×8¹ + 0×8⁰ = 64.
Why does octal only use digits 0-7?
Octal is base 8, meaning it uses 8 unique symbols (0-7) to represent all numbers. This is similar to how decimal (base 10) uses 10 symbols (0-9) and binary (base 2) uses 2 symbols (0-1). Each number system uses exactly as many symbols as its base.
Where is octal used today?
The most common use of octal today is in Unix/Linux file permissions (e.g., chmod 755). It's also used in some legacy systems, embedded systems, and computer science education to teach number system concepts.
How do I convert large octal numbers?
Our converter supports large numbers automatically. Simply enter the octal number, and the tool will handle the conversion. For very large numbers, JavaScript can handle integers up to 2⁵³-1 (about 9 quadrillion) accurately.
Can I convert multiple numbers at once?
Yes! Switch to "Batch Conversion" mode and enter multiple numbers, one per line. The tool will convert all of them simultaneously and show the results in a formatted list.
What's the relationship between octal and binary?
Each octal digit represents exactly 3 binary digits. For example, octal 7 = binary 111, octal 5 = binary 101. This makes octal useful as a shorthand for binary, though hexadecimal (base 16) has largely replaced it for this purpose.
Is my data stored when I use this converter?
No! All conversions happen entirely in your browser using JavaScript. Your numbers never leave your computer, ensuring complete privacy. The conversion history is stored locally in your browser session only.