Decimal to Octal Converter
Convert between decimal (base 10) and octal (base 8) numbers instantly
Conversion Mode
Decimal Input
Tip: Supports negative numbers (e.g., -64) and floating point numbers (e.g., 123.45). Decimal 111 = Octal 157.
Educational Mode
Conversion History
Converting Decimal to Octal
Converting decimal (base 10) numbers to octal (base 8) is a fundamental operation in computer science and programming. While decimal uses ten digits (0-9), octal uses only eight digits (0-7). This conversion is particularly useful when working with Unix file permissions, legacy systems, and understanding how computers process numbers.
Our converter supports not only basic integer conversion but also negative numbers and floating point numbers, making it versatile for various use cases. Whether you're a student learning number systems, a programmer working with Unix permissions, or someone working with legacy systems, this tool simplifies the conversion process.
Quick Examples:
64 (decimal) = 100 (octal)
-64 (decimal) = -100 (octal)
123.45 (decimal) ≈ 173.3463146314 (octal)
How to Convert Decimal to Octal
Converting Integers
Division Method:
- Divide the decimal number by 8
- Write down the remainder (this will be a digit from 0-7)
- Replace the number with the quotient (result of division)
- Repeat steps 1-3 until the quotient is 0
- Read all remainders from bottom to top - this is your octal number
Example: Convert 111 (decimal) to octal
Step 1: 111 ÷ 8 = 13 remainder 7
Step 2: 13 ÷ 8 = 1 remainder 5
Step 3: 1 ÷ 8 = 0 remainder 1
Reading bottom to top: 157 (octal)
Converting Negative Numbers
For negative numbers, convert the absolute value (without the minus sign) to octal, then add the minus sign to the result.
Example: Convert -64 (decimal) to octal
Absolute value: 64
64 ÷ 8 = 8 remainder 0
8 ÷ 8 = 1 remainder 0
1 ÷ 8 = 0 remainder 1
Octal: 100
Result: -100 (octal)
Converting Floating Point Numbers
For floating point numbers, convert the integer and fractional parts separately:
Method:
Integer Part:
Use the division method described above
Fractional Part:
- Multiply the fractional part by 8
- Take the integer part as the next octal digit
- Keep only the fractional part
- Repeat until the fractional part is 0 or desired precision is reached
Combine:
octal_integer.octal_fractional
Decimal to Octal Quick Reference
| Decimal | Octal | Decimal | Octal | Decimal | Octal |
|---|---|---|---|---|---|
| 0 | 0 | 16 | 20 | 64 | 100 |
| 1 | 1 | 24 | 30 | 128 | 200 |
| 2 | 2 | 32 | 40 | 256 | 400 |
| 3 | 3 | 40 | 50 | 512 | 1000 |
| 4 | 4 | 48 | 60 | 100 | 144 |
| 5 | 5 | 56 | 70 | 200 | 310 |
| 8 | 10 | 8 | 10 | 365 | 555 |
| 10 | 12 | 15 | 17 | 777 | 1411 |
Common Use Cases
Unix/Linux Permissions
File permissions in Unix/Linux use octal notation. For example, chmod 755 means 7(rwx), 5(r-x), 5(r-x) in octal. Convert decimal permission values to octal.
Computer Science Education
Learning number system conversions is fundamental in computer science. Understanding decimal to octal conversion helps grasp how computers represent and process numbers.
Legacy System Programming
Older computer systems and some embedded systems use octal representation for memory addresses and machine code instructions.
Data Representation
Octal provides a more compact representation than binary for certain applications, making it useful for debugging and data visualization.
Tips & Best Practices
Use Step-by-Step Mode for Learning
Enable the step-by-step calculation display to see exactly how the division method works. This is invaluable for students and anyone learning number system conversions.
Floating Point Precision
For floating point conversions, the tool shows up to 10 fractional digits. Some decimal fractions may not have exact octal representations and will be approximated.
Batch Convert for Efficiency
When working with multiple numbers, use batch conversion mode. Enter one number per line to convert them all at once - saves time and effort.
Verify with Reverse Conversion
After converting to octal, use the Swap button to convert back to decimal and verify you get your original number. This helps catch any input errors.
Track Your Work with History
The conversion history feature keeps track of your recent conversions. Click any history item to quickly reload those values for further work.
Related Number Converters
Octal to Decimal Converter
Convert octal numbers to decimal format
Binary to Text Converter
Convert binary code to readable text
Hex to Decimal Converter
Convert hexadecimal to decimal
Binary to Hex Converter
Convert between binary and hexadecimal
ASCII to Text Converter
Convert ASCII codes to text
All Calculators
Browse all conversion tools
Frequently Asked Questions
How do I convert decimal to octal manually?
Divide the decimal number by 8 repeatedly and keep track of the remainders. When the quotient becomes 0, read all the remainders from bottom to top. That's your octal number. For example: 111 ÷ 8 = 13 R7, 13 ÷ 8 = 1 R5, 1 ÷ 8 = 0 R1. Result: 157.
Can I convert negative decimal numbers to octal?
Yes! This converter supports negative numbers. Simply convert the absolute value to octal and add a minus sign to the result. For example, -64 (decimal) converts to -100 (octal).
What about decimal fractions - can they be converted to octal?
Yes, our tool supports floating point conversion. For the fractional part, multiply by 8 repeatedly and take the integer part as each octal digit. Note that some decimal fractions may not have exact octal representations and will be approximated.
Why does octal only use digits 0-7?
Octal is base 8, meaning it uses 8 unique symbols to represent all numbers. Just as decimal (base 10) uses 0-9, binary (base 2) uses 0-1, octal uses exactly 8 symbols: 0-7. Each position in an octal number represents a power of 8.
Where is decimal to octal conversion used in real life?
The most common use is in Unix/Linux file permissions (e.g., chmod 755). It's also used in legacy systems, embedded programming, computer science education, and understanding the relationship between different number systems.
How many decimal numbers can I convert at once?
Using batch conversion mode, you can convert as many numbers as you need. Simply enter one decimal number per line, and the tool will process them all simultaneously.
Is my data stored when using 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 only in your browser session.