Decimal to Octal Converter
Enter the decimal number you want to convert to octal.
Table of Contents
- How does decimal to octal conversion work?
- Decimal to octal conversion formula
- Conversion process
- Examples
- Decimal to octal conversion table
- Frequently Asked Questions
How does decimal to octal conversion work?
The decimal system is base 10 and the octal system is base 8. To convert a decimal number to octal, repeatedly divide the number by 8 and record the remainders. Then, read the remainders in reverse order (from bottom to top) to obtain the base-8 number.
Decimal to octal conversion formula
To convert a decimal number N to octal:
Where the coefficients oi (remainders) take values from 0 to 7, obtained by successively dividing N by 8. The octal number is formed by reading the remainders from bottom to top.
Conversion process
- Divide the decimal number by 8 and note the remainder (0–7).
- Take the quotient obtained and repeat the division by 8 until you reach 0.
- Write the remainders in reverse order (from bottom to top) to obtain the octal number.
Examples
25₁₀ to octal| Division | Quotient | Remainder |
|---|---|---|
| 25 ÷ 8 | 3 | 1 |
| 3 ÷ 8 | 0 | 3 |
Reading the remainders from bottom to top: 31₈.
Result: 25₁₀ = 31₈.
100₁₀ to octal| Division | Quotient | Remainder |
|---|---|---|
| 100 ÷ 8 | 12 | 4 |
| 12 ÷ 8 | 1 | 4 |
| 1 ÷ 8 | 0 | 1 |
Reading the remainders from bottom to top: 144₈.
Result: 100₁₀ = 144₈.
Decimal to octal conversion table
Quick reference values for small decimal numbers.
| Decimal | Octal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 10 |
| 9 | 11 |
| 10 | 12 |
| 16 | 20 |
| 32 | 40 |
| 64 | 100 |
| 128 | 200 |
| 256 | 400 |
| 512 | 1000 |
| 1024 | 2000 |
Frequently Asked Questions
How do you convert a decimal number to octal?
To convert a decimal number to octal, repeatedly divide the number by 8, write down the remainders, and then read them from bottom to top.
Why is base 8 used in the octal system?
Because each octal digit represents exactly 3 binary bits, which makes conversions between binary and octal quick and straightforward.
Cite this page
You can use the following citation format when referencing this calculator in academic or professional work.
Ramos, J., Decimal to octal converter, Available at: https://calcuclub.com/convert/decimal-to-octal/ (Accessed: 27 November 2025).