Tool Octal Number Converter
Enter a number in any base — the tool instantly converts it to octal (base 8), decimal (base 10), binary (base 2), and hexadecimal (base 16). It also includes a visual 3-bit per digit split diagram and a step-by-step mathematical expansion.
Enter an octal number (digits 0–7 only). You can include a minus sign for negative numbers.
Explained How Octal Conversion Works
The octal number system is base 8. It uses the digits 0–7 and each position represents an ascending power of 8. Octal is closely tied to binary because 8 = 2³, meaning each octal digit maps cleanly to exactly 3 binary bits.
The Octal Place Values
| Position | 8³ | 8² | 8¹ | 8⁰ |
|---|---|---|---|---|
| Value | 512 | 64 | 8 | 1 |
17₈ equals 1 × 8¹ + 7 × 8⁰ = 8 + 7 = 15 in decimal. In binary, it is 001 111 = 1111 = 15.Octal vs Other Bases
| Base | Name | Digits Used | Example | Decimal Value |
|---|---|---|---|---|
| 2 | Binary | 0, 1 | 1111 | 15 |
| 8 | Octal | 0–7 | 17 | 15 |
| 10 | Decimal | 0–9 | 15 | 15 |
| 16 | Hexadecimal | 0–9, A–F | F | 15 |
Reading the Visual Diagrams
- Bit diagram: shows the binary expansion of the number, with each bit's power of 2 shown underneath. Highlighted (green) cells mean the bit is 1.
- Octal map: shows how each octal digit maps to a 3-bit binary group. This is the "shortcut" that makes octal and binary so easy to convert without passing through decimal.
chmod 755, chmod 644), embedded systems, and legacy mainframe architectures. Because 3 bits fit cleanly into one octal digit, it acts as an ideal shorthand for binary flags.Reference Octal ↔ Decimal ↔ Binary ↔ Hex
A quick conversion reference for benchmark values in computing.
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 0 | 0000 | 0 | 0 |
| 1 | 0001 | 1 | 1 |
| 2 | 0010 | 2 | 2 |
| 3 | 0011 | 3 | 3 |
| 4 | 0100 | 4 | 4 |
| 5 | 0101 | 5 | 5 |
| 6 | 0110 | 6 | 6 |
| 7 | 0111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 64 | 1000000 | 100 | 40 |
| 255 | 11111111 | 377 | FF |
| 256 | 100000000 | 400 | 100 |
| 512 | 1000000000 | 1000 | 200 |
FAQ Frequently Asked Questions
What is an octal number?
An octal number is a number in base 8, using only the digits 0 through 7. Each position in an octal number represents a power of 8 — like 1, 8, 64, 512, and so on.
How do you convert octal to decimal?
Multiply each octal digit by 8 raised to its position (starting at 0 from the right) and sum the results. For example, 17₈ = 1 × 8¹ + 7 × 8⁰ = 8 + 7 = 15.
How do you convert octal to binary?
Replace each octal digit with its 3-bit binary equivalent. For example, 17₈ → 001 111 → 1111₂. This works because 8 = 2³.
How do you convert octal to hex?
First convert octal → binary, then group the binary digits into sets of 4 and convert each group to hex. For example, 17₈ → 1111₂ → F in hex.
Why is octal used in computing?
Octal (base 8) is a compact way to represent binary data. Each octal digit represents exactly 3 binary bits, making octal useful in Unix file permissions (chmod 755), older computer systems, and low-level programming where binary would be too verbose.
How do I convert decimal to octal?
Repeatedly divide the number by 8 and record the remainders. Then read the remainders from bottom to top. For example, 15 → 15 ÷ 8 = 1 r 7, 1 ÷ 8 = 0 r 1 → octal 17.
What does the visual diagram show?
The bit diagram shows the binary expansion of the number, with each bit highlighted if it's a 1 and shown with its weight (power of 2) underneath. The octal map shows how each octal digit maps to a 3-bit binary group — the "shortcut" for octal ↔ binary conversion.
Can I convert negative numbers?
Yes. Simply prefix the number with a minus sign (-). The tool will preserve the negative sign and convert the magnitude across all bases.