Decimal to Octal Conversion Calculator
The decimal number system, which uses base 10, is the most familiar to us in daily life. But in computing and electronics, octal (base-8) plays an important role—especially in simplifying binary values. This tool helps you easily convert decimal numbers into octal format, while also explaining the steps and reasoning behind the conversion.
What Are Decimal Numbers?
Decimal numbers are base-10 numbers, meaning they use digits from 0 to 9. Each digit's position represents a power of 10, which makes the decimal system intuitive for daily use.
237= 2×10² + 3×10¹ + 7×10⁰ = 237
What Are Octal Numbers?
Octal numbers are base-8 numbers. They use digits from 0 to 7 and are commonly used in computing environments such as file permissions in Unix systems or simplifying binary sequences. Octal representations are shorter than binary but still align well with hardware-level data structures.
101₈, 755₈ (common in Unix permissions), 46₈
How to Convert Decimal to Octal
To convert a decimal number into an octal number manually, follow these steps:
- Start with the decimal number.
- Divide the number by 8 and record the remainder.
- Use the quotient as the new number and repeat division by 8.
- Continue until the quotient becomes 0.
- Read the remainders from bottom to top to get the octal value.
65 ÷ 8 = 8 R1 → 8 ÷ 8 = 1 R0 → 1 ÷ 8 = 0 R1
Octal = 101₈
Decimal to Octal Conversion Table
| Decimal | Octal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 5 | 5 |
| 8 | 10 |
| 15 | 17 |
| 22 | 26 |
| 45 | 55 |
| 65 | 101 |
| 85 | 125 |
| 100 | 144 |
Why Use an Online Converter?
For fast, error-free conversions, especially with large numbers, an online Decimal to Octal Converter saves time and increases accuracy. It’s especially useful for:
- Students learning number systems
- Software engineers working with Unix systems
- Developers needing quick checks while coding