Decimal to Octal Converter
Free online tool to instantly convert decimal (Base 10) to octal (Base 8). Includes quick conversion tables and step-by-step mathematical explanations.
How to convert Decimal to Octal
Converting from Decimal (Base 10) toOctal (Base 8) involves positional value evaluation.
Convert Decimal to Octal
Divide the decimal value repeatedly by 8. Record the remainders after each division. The final octal representation is formed by reading the remainders in reverse order (bottom to top).
Decimal to Octal Quick Conversion Table
Common values converted between Decimal (Base 10) and Octal (Base 8):
| Decimal (10) | Octal (8) |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 10 |
| 9 | 11 |
| 10 | 12 |
| 11 | 13 |
| 12 | 14 |
| 13 | 15 |
| 14 | 16 |
| 15 | 17 |
| 16 | 20 |
| 32 | 40 |
| 64 | 100 |
| 100 | 144 |
| 255 | 377 |
Decimal to Octal Frequently Asked Questions
Common questions and step-by-step mathematical answers about converting Decimal (Base 10) to Octal (Base 8).
1How do you convert decimal to octal?↓
Use the successive division-by-8 method. Record each remainder after division by 8 until the quotient is 0, then reverse the remainder sequence.
2What is the formula for decimal to octal conversion?↓
The formula expresses the decimal integer as a sum of powers of 8: N₁₀ = oₙ·8ⁿ + ... + o₁·8¹ + o₀·8⁰.
3How do you convert decimal to octal manually?↓
Example with 83: 83÷8 = 10 (rem 3), 10÷8 = 1 (rem 2), 1÷8 = 0 (rem 1). Result: 123₈.
4What is 10 in octal?↓
10 ÷ 8 = 1 with remainder 2; 1 ÷ 8 = 0 with remainder 1 → 12₈.
5What is 25 in octal?↓
25 ÷ 8 = 3 with remainder 1; 3 ÷ 8 = 0 with remainder 3 → 31₈.
6What is 100 in octal?↓
100 ÷ 8 = 12 (rem 4), 12 ÷ 8 = 1 (rem 4), 1 ÷ 8 = 0 (rem 1) → 144₈.
7How do you convert decimal fractions to octal?↓
Example: 0.375 × 8 = 3.0 → Integer part is 3, fractional part is 0. Result is 0.3₈.
8What is the difference between decimal and octal?↓
Decimal groups values by powers of 10, whereas Octal groups values by powers of 8, making octal compact for 3-bit binary computer operations.
9How does the decimal to octal conversion method work?↓
By dividing by 8, you repeatedly peel off the least significant octal digit as the remainder, shifting the remaining value down by one octal place.
10How do you calculate octal values from decimal numbers?↓
Both methods produce identical results: repeated division by 8 is direct, while decimal → binary → octal is fast for mental math.