Convert Decimal to Octal
Need to change a standard base-10 number into base-8? Use our free decimal to octal converter to instantly transform your values. Whether you're doing math homework or programming, learning how to convert decimal to octal is fast and easy.
Decimal to octal conversion calculator
Quick Reference
Decimal to Octal Conversion Chart
Don't want to use the decimal to octal calculator? We mapped out the most common decimal in octal values for you. Use this chart for a quick decimal octal conversion.
| Decimal | Division / Place Value | Octal |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 7 | 7 | 7 |
| 8 | 1×8¹ + 0×8⁰ | 10 |
| 9 | 1×8¹ + 1×8⁰ | 11 |
| 10 | 1×8¹ + 2×8⁰ | 12 |
| 15 | 1×8¹ + 7×8⁰ | 17 |
| 16 | 2×8¹ + 0×8⁰ | 20 |
| 32 | 4×8¹ + 0×8⁰ | 40 |
| 64 | 1×8² + 0×8¹ + 0×8⁰ | 100 |
| 100 | 1×8² + 4×8¹ + 4×8⁰ | 144 |
| 128 | 2×8² + 0×8¹ + 0×8⁰ | 200 |
| 255 | 3×8² + 7×8¹ + 7×8⁰ | 377 |
| 512 | 1×8³ + 0×8² + 0×8¹ + 0×8⁰ | 1000 |
| 1024 | 2×8³ + 0×8² + 0×8¹ + 0×8⁰ | 2000 |
Step-by-Step
How to Convert Decimal to Octal
Wondering how do you convert decimal to octal manually? The process of converting decimal to octal relies on a simple method: repeated division.
The Method
Decimal is our everyday base-10 system. Octal uses base-8. To convert base 10 to base 8, divide your starting number by 8 over and over. Keep track of your remainders.
Once your division hits zero, you just read the remainders in reverse order to get your final dec to octal result.
How to Change Decimal to Octal — 3 Easy Steps
Write the decimal number
Take the number you want to change. Let's practice with the number 10.
Divide by 8 and record the remainder
10 ÷ 8 = 1 with a remainder of 2. Then divide the quotient (1) by 8. You get 0 with a remainder of 1.
Read from bottom to top
Write those remainders in reverse order. Reading them from last to first gives you 12. So 10₁₀ = 12₈. That is decimal to octal how to made easy!
Decimal vs Octal
Understanding Base 10 and Base 8
We use decimal (base 10) for almost everything in daily life. It uses ten digits (0 through 9). But in computer science, you will often need to convert decimal to octal number formats. Octal uses exactly eight digits (0 through 7).
Why do we use it? Octal acts as a shorthand for binary, grouping long strings of code into readable three-bit chunks. Instead of doing the math manually, using a decimal to octal converter calculator speeds up your workflow.
Whether you call it a dec to oct conversion, or an international conversor decimal a octal, the core math remains exactly the same.
Worked Examples
Sample Decimal to Octal Number Conversions
Let's look at exactly how to convert decimal number to octal with some real-world math. Here are step-by-step breakdowns for popular values.
8 in decimal to octal
8 ÷ 8 = 1 remainder 0, then 1 ÷ 8 = 0 remainder 1. Read backward to get 10₈.
10 in decimal to octal
10 ÷ 8 = 1 remainder 2, then 1 ÷ 8 = 0 remainder 1. The dec to oct result is 12₈.
15 in decimal to octal
15 ÷ 8 = 1 remainder 7, then 1 ÷ 8 = 0 remainder 1. This gives you 17₈.
16 in decimal to octal
16 ÷ 8 = 2 remainder 0, then 2 ÷ 8 = 0 remainder 2. Your octal number is 20₈.
64 in decimal to octal
64 ÷ 8 = 8 remainder 0. Then 8 ÷ 8 = 1 remainder 0. Finally, 1 ÷ 8 = 0 remainder 1. The answer is 100₈.
100 in decimal to octal
100 ÷ 8 = 12 remainder 4. Next, 12 ÷ 8 = 1 remainder 4. Last, 1 ÷ 8 = 0 remainder 1. Your result is 144₈.
255 in decimal to octal
255 ÷ 8 = 31 remainder 7. Next, 31 ÷ 8 = 3 remainder 7. Last, 3 ÷ 8 = 0 remainder 3. This converts to 377₈.
512 in decimal to octal
512 ÷ 8 = 64 remainder 0. Then 64 ÷ 8 = 8 remainder 0. Then 8 ÷ 8 = 1 remainder 0. Finally, 1 ÷ 8 = 0 remainder 1. The total is 1000₈.
FAQ
Frequently Asked Questions
Common questions about performing a decimal to octal conversion.