Decimal To Octal Converter
Enter the decimal value to convert to octal or Octal to Decimal.
Decimal:
Decimal is the standard Base-10 number system.
Octal:
Octal (Base-8) is used in computing, particularly for Unix file permissions and some legacy systems.
How to Convert Decimal to Octal — Formula:
Repeatedly divide by 8 and record remainders. Read from bottom to top.
Example: 493 ÷ 8 = 61 R5, 61 ÷ 8 = 7 R5, 7 ÷ 8 = 0 R7 → Octal: 755.
Technical Details:
Octal was popular in early computing (PDP-8, UNIVAC) because 3 binary digits map to 1 octal digit. It is still used for Unix permissions and C/C++ octal literals (prefix 0, e.g., 0755).
Decimal To Octal Converter:
Convert decimal numbers to octal format. Useful for setting file permissions in Unix/Linux systems.
Binary ↔ Hex ↔ Octal: Grouping Relationship
Binary → Hex (group by 4 bits):
Binary → Octal (group by 3 bits):
Frequently Asked Questions
How do I convert Decimal to Octal?
Repeatedly divide by 8 and record remainders. Read from bottom to top.
What is the Decimal number system?
Decimal is the standard Base-10 number system.
What is the Octal number system?
Octal (Base-8) is used in computing, particularly for Unix file permissions and some legacy systems.
Where is Decimal to Octal conversion used?
Octal was popular in early computing (PDP-8, UNIVAC) because 3 binary digits map to 1 octal digit. It is still used for Unix permissions and C/C++ octal literals (prefix 0, e.g., 0755).
Can I convert large decimal numbers?
Yes. This converter handles numbers of any practical size. For very large numbers, the conversion is performed using arbitrary-precision arithmetic to ensure accuracy.
How to Convert Decimal to Octal (Base-10 to Base-8)
Decimal-to-octal conversion uses repeated division by 8, similar to decimal-to-binary but with a larger divisor. This conversion is essential for setting Unix file permissions, working with legacy systems, and understanding how early minicomputers represented data.
- Divide the decimal number by 8. Record the remainder (0-7).
- Divide the quotient by 8. Record the new remainder.
- Repeat until the quotient is 0.
- Read the remainders from bottom to top — that is the octal number.
- Example: 100 ÷ 8 = 12 R4, 12 ÷ 8 = 1 R4, 1 ÷ 8 = 0 R1 → 144₈.
Decimal to Octal: Common Values
Frequently used decimal numbers and their octal equivalents:
| Input | Output |
|---|---|
| 7 | 7 |
| 8 | 10 |
| 64 | 100 |
| 100 | 144 |
| 255 | 377 |
| 256 | 400 |
| 493 | 755 |
| 420 | 644 |
| 511 | 777 |
| 512 | 1000 |
| 1000 | 1750 |
| 4096 | 10000 |
Solved Examples: Decimal to Octal
Question 1: Convert decimal 493 to octal to find the file permission.
Solution:
493 ÷ 8 = 61 remainder 5
61 ÷ 8 = 7 remainder 5
7 ÷ 8 = 0 remainder 7
Read bottom to top: 755
Answer: 493₁₀ = 755₈ — this is the classic chmod 755 permission (rwxr-xr-x).
Question 2: Convert decimal 1000 to octal.
Solution:
1000 ÷ 8 = 125 remainder 0
125 ÷ 8 = 15 remainder 5
15 ÷ 8 = 1 remainder 7
1 ÷ 8 = 0 remainder 1
Read bottom to top: 1750
Answer: 1000₁₀ = 1750₈. Verify: 1×512 + 7×64 + 5×8 + 0 = 512 + 448 + 40 + 0 = 1000 ✓.
Question 3: Convert decimal 83 to octal.
Solution:
83 ÷ 8 = 10 remainder 3
10 ÷ 8 = 1 remainder 2
1 ÷ 8 = 0 remainder 1
Read bottom to top: 123
Answer: 83₁₀ = 123₈. Verify: 1×64 + 2×8 + 3 = 64 + 16 + 3 = 83 ✓.
Practice: Decimal to Octal
Try solving these on your own to test your understanding:
- Convert 64 to octal. (Answer: 100)
- Convert 255 to octal. (Answer: 377)
- Convert 420 to octal. (Answer: 644)
- Convert 200 to octal. (Answer: 310)
- Convert 511 to octal. (Answer: 777)
- Convert 4096 to octal. (Answer: 10000)
Setting File Permissions with Octal
The chmod command accepts octal notation directly: chmod 644 file.txt sets rw-r--r--. The three digits represent owner, group, and others. Each digit is a sum: read=4, write=2, execute=1. So 7=4+2+1=rwx, 6=4+2=rw-, 5=4+1=r-x, 4=r--. The most common permissions: 755 for executables/directories, 644 for regular files, 600 for private files, 700 for private executables.
Octal Notation in Programming Languages
In C/C++/Java, prefix with 0: int x = 0755; (which is 493 in decimal). In Python 3, use 0o prefix: permissions = 0o755. In JavaScript strict mode, use 0o: const mode = 0o644. Shell scripts use octal naturally with chmod. Be cautious: in C, int x = 010; assigns 8, not 10. This octal literal trap has caused countless bugs in code that processes zero-padded numbers.
Key Takeaways
- Repeatedly divide by 8, read remainders bottom-to-top.
- Unix permissions: each octal digit = read(4) + write(2) + execute(1).
- Common permissions: 755 (executables), 644 (files), 777 (full access).
- 8 in decimal = 10 in octal (the base transition point).
- In programming, octal literals use 0 prefix (C) or 0o prefix (Python/JS).
- Powers of 8: 8, 64, 512, 4096 are "round numbers" in octal.