Decimal to Octal Converter
Enter a base-10 number (integer or fractional) to convert it into base-8 format.
What is Decimal to Octal Conversion?
Decimal to octal conversion means changing a number from the decimal system (base 10) into the octal system (base 8). Decimal uses digits 0 through 9, while octal uses only 0 through 7. This base conversion is common in computer science, digital electronics, and number-system education.
A decimal to base-8 converter helps you avoid manual errors and instantly get accurate results for both whole numbers and decimal fractions. This calculator supports negative values and can show a detailed breakdown of the conversion process.
How to Use This Calculator
- Type a decimal number in the input field (for example, 100, -26, or 19.75).
- Choose the fractional precision (how many octal digits appear after the decimal point).
- Click Convert to Octal.
- Read the octal output and the conversion steps displayed below.
Decimal to Octal Formula and Method
1) Integer Part: Repeated Division by 8
For whole numbers, keep dividing the decimal number by 8 and note each remainder. The octal value is formed by reading those remainders from bottom to top.
Repeat with quotient until quotient = 0
Octal integer = remainders read in reverse order
2) Fractional Part: Repeated Multiplication by 8
For decimal fractions, multiply the fractional part by 8 repeatedly. Each integer part you get becomes the next octal digit to the right of the point.
Repeat until fraction = 0 or desired precision reached
Worked Examples
Example A: 83 (decimal) to octal
- 83 ÷ 8 = 10 remainder 3
- 10 ÷ 8 = 1 remainder 2
- 1 ÷ 8 = 0 remainder 1
Read remainders upward: 123₈. So, 83₁₀ = 123₈.
Example B: 45.625 (decimal) to octal
Integer part (45):
- 45 ÷ 8 = 5 remainder 5
- 5 ÷ 8 = 0 remainder 5
Integer result: 55₈
Fraction part (0.625):
- 0.625 × 8 = 5.0 → digit 5
Fraction result: .5₈ so the final value is 55.5₈.
Quick Decimal to Octal Reference Table
| Decimal | Octal | Decimal | Octal |
|---|---|---|---|
| 8 | 10 | 24 | 30 |
| 9 | 11 | 32 | 40 |
| 10 | 12 | 64 | 100 |
| 15 | 17 | 100 | 144 |
| 16 | 20 | 255 | 377 |
Where Octal Is Useful
- Computer systems: historical systems and low-level representations.
- Permissions in Unix/Linux: file permissions like 755 and 644 are octal-based.
- Learning number systems: understanding links among binary, octal, decimal, and hexadecimal.
- Embedded systems: compact digit grouping for binary patterns.
Common Conversion Mistakes
- Reading integer remainders in the wrong direction.
- Using digits 8 or 9 in octal output (invalid in base 8).
- Stopping fractional conversion too early and losing precision.
- Forgetting to keep the negative sign for negative values.
Final Thoughts
This decimal to octal conversion calculator gives you fast, accurate base-10 to base-8 results along with step-by-step logic. Whether you're studying digital logic, working with Linux permissions, or reviewing number-system fundamentals, this tool can save time and improve accuracy.