Decimal to Octal Converter
Enter a decimal number (integer or fraction), then click convert.
Conversion Steps
What is a Decimal to Octal Calculator?
A decimal to octal calculator converts a base-10 number into base-8 format. Decimal is the number system we use every day (0–9), while octal uses only digits 0–7. This tool helps you quickly convert values without manually dividing by 8 over and over.
How to Use This Tool
- Type a decimal number into the input field.
- Set fractional precision if your number has a decimal part.
- Click Convert to Octal.
- Read the octal result and optional step-by-step breakdown.
Decimal vs. Octal: Quick Comparison
Decimal (Base 10)
Decimal uses ten symbols: 0,1,2,3,4,5,6,7,8,9. Each position represents a power of 10.
For example, 347 means 3×10² + 4×10¹ + 7×10⁰.
Octal (Base 8)
Octal uses eight symbols: 0,1,2,3,4,5,6,7. Each position represents a power of 8.
For example, 347₈ means 3×8² + 4×8¹ + 7×8⁰.
How Decimal to Octal Conversion Works
For Whole Numbers
Repeatedly divide the decimal integer by 8 and record each remainder. The octal number is formed by reading remainders from bottom to top.
Example: 156₁₀
156 ÷ 8 = 19 remainder 4
19 ÷ 8 = 2 remainder 3
2 ÷ 8 = 0 remainder 2
Reverse remainders → 234₈.
For Fractional Numbers
Keep the integer conversion method above for the whole part. For the fractional part, repeatedly multiply the fraction by 8. Each integer digit produced (0–7) becomes the next octal digit after the point.
Example: 0.625₁₀
0.625 × 8 = 5.0 → first digit 5
So 0.625₁₀ = 0.5₈.
Useful Examples
10₁₀ = 12₈64₁₀ = 100₈255₁₀ = 377₈45.625₁₀ = 55.5₈-42₁₀ = -52₈
Where Octal Is Used
Octal appears less often today than decimal, hexadecimal, or binary, but it still matters in computing contexts:
- Legacy systems and older programming environments.
- Unix/Linux file permissions (e.g.,
755,644). - Compact representation of binary values in groups of 3 bits.
FAQ
Can this calculator convert negative decimals?
Yes. The sign is preserved, and the magnitude is converted to octal.
Does it support decimal fractions?
Yes. You can control how many octal fractional digits are generated using the precision field.
Why do some fractions look long in octal?
Some decimal fractions do not terminate cleanly in base 8, so the result can be repeating or long. Precision limits the displayed length.
Final Note
If you work with number systems, this decimal to octal calculator saves time and reduces manual errors. Use the built-in step display whenever you want to learn or verify the conversion process.