Decimal to Octal Converter
Convert any decimal number (base 10) to octal (base 8) and back instantly. Step-by-step division method, supports large numbers, and runs entirely in your browser. Free, private, and no signup required.
Convert Decimal to Octal
Enter a decimal number (base 10) and get its octal equivalent (base 8). The calculator shows the full division method step by step.
0-9 for input. Example: 64 → 100, 100 → 144, 255 → 377
What is a decimal to octal converter?
A decimal to octal converter is a tool that transforms a number from the decimal number system (base 10) into the octal number system (base 8). Decimal uses ten digits — 0 through 9 — while octal uses only eight — 0 through 7. The value stays exactly the same; only the representation changes.
Converting between these two systems is a common task in computing. Octal numbers appear in Unix file permissions (like chmod 755), in some programming languages for compact binary representation, and in historical computer architectures that used 3-bit groups. Being able to switch between decimal and octal quickly saves time and prevents errors.
This tool does the conversion both ways, shows every step of the division method, and supports very large numbers. Everything runs locally in your browser — no data is sent to a server.
How to convert decimal to octal
The standard method is called repeated division by 8. Here's how it works:
- Divide the decimal number by 8.
- Record the remainder (a value from 0 to 7).
- Repeat with the quotient from the previous step.
- Stop when the quotient reaches 0.
- Read the remainders from bottom to top — that's your octal number.
8 ÷ 8 = 1 remainder 0
1 ÷ 8 = 0 remainder 1
Read remainders bottom to top: 100
To go the other way (octal to decimal), use positional multiplication: multiply each octal digit by 8 raised to the power of its position, then sum the results.
= 1 × 64 + 4 × 8 + 4 × 1
= 64 + 32 + 4
= 100
Conversion formulas
Position starts at 0 from the rightmost digit.
0 → 000, 1 → 001, 2 → 010, 3 → 011
4 → 100, 5 → 101, 6 → 110, 7 → 111
Why use this decimal to octal converter?
Bidirectional conversion
Convert decimal to octal and octal to decimal in the same tool. No need to open a second page or app.
Step-by-step working
See every division, remainder, and multiplication. Perfect for students, teachers, and anyone learning number systems.
Handles large numbers
Uses JavaScript's BigInt for very large values, so you can convert numbers that would overflow in other tools.
Quick reference table
A full decimal ↔ octal ↔ binary ↔ hex table with search and click-to-copy. Great for programming quick lookups.
100% private
Everything runs in your browser. The numbers you enter never leave your device — no server, no logs, no tracking.
Works offline
Once the page loads, you can use the converter without an internet connection. Perfect for exam prep and remote work.
Real-world uses for decimal to octal conversion
Unix and Linux file permissions
The most common modern use of octal is Unix file permissions. When you run chmod 755 file.sh, the 755 is an octal number. Each digit encodes permissions for user, group, and others. Understanding octal is essential for system administrators and DevOps engineers.
Computer science education
Number base conversions are a foundational topic in computer science curricula. Learning octal — and the related shortcuts for binary and hexadecimal — builds intuition for how computers represent data at the lowest level.
Programming and debugging
Some languages and tools use octal literals. In C, C++, Java, and Python, a leading 0 historically indicates an octal literal. Debugging legacy code often requires reading and converting octal values.
Embedded systems and hardware
Octal appears in some embedded systems and hardware documentation because each octal digit maps neatly to 3 bits, which aligns with certain hardware word sizes and instruction encodings.
Data compression and encoding
Octal is occasionally used in file formats and protocols where a compact representation of binary data is needed. Some historic file formats and networking protocols used octal for encoding byte values.
Decimal to octal quick reference
Here are some of the most commonly needed conversions. The full table is available in the "Conversion Table" tab above.
| Decimal | Octal | Decimal | Octal |
|---|---|---|---|
| 1 | 1 | 20 | 24 |
| 2 | 2 | 25 | 31 |
| 3 | 3 | 32 | 40 |
| 4 | 4 | 40 | 50 |
| 5 | 5 | 50 | 62 |
| 6 | 6 | 64 | 100 |
| 7 | 7 | 100 | 144 |
| 8 | 10 | 128 | 200 |
| 9 | 11 | 200 | 310 |
| 10 | 12 | 255 | 377 |
| 12 | 14 | 256 | 400 |
| 15 | 17 | 512 | 1000 |
| 16 | 20 | 1024 | 2000 |
| 17 | 21 | 4096 | 10000 |