Octal Converter
Octal is base 8, using only the digits 0-7. Enter an octal number below to get its decimal, binary, and hexadecimal equivalents at once. For example, octal 52₈ = decimal 42₁₀ = binary 101010₂ = hex 2A₁₆.
Octal Number Converter
Convert a whole octal integer to decimal, binary, and hexadecimal.
About Octal
Octal is a base-8 number system using only the digits 0 through 7 — it never needs letters the way hexadecimal does. It shows up most often in Unix/Linux file permissions, where chmod values such as 755 or 644 are written in octal. Because each octal digit maps to exactly 3 binary bits, it was also a common compact stand-in for binary on early computers with 12-, 24-, or 36-bit words.
For example, octal 52 equals decimal 42, binary 101010, and hex 2A: 5×8¹ + 2×8⁰ = 40 + 2 = 42. To go from decimal or binary into octal, see the Binary to Octal Converter or the Binary Converter.
Octal Digit Reference (0-7)
| Octal | Decimal | Binary (3-bit) |
|---|---|---|
| 0 | 0 | 000 |
| 1 | 1 | 001 |
| 2 | 2 | 010 |
| 3 | 3 | 011 |
| 4 | 4 | 100 |
| 5 | 5 | 101 |
| 6 | 6 | 110 |
| 7 | 7 | 111 |
Where Octal Conversion Is Used
- Unix/Linux permissions:
chmodvalues such as 755 (rwxr-xr-x) or 644 (rw-r--r--) - Legacy systems: older architectures and file formats that use octal notation
- Escape sequences: some languages accept octal escapes such as
\755 - Computer science education: a standard example for teaching positional number systems
Related Converters
Octal to Decimal
Full positional-notation breakdown of octal to decimal.
Octal to Binary
3-bit grouping method for octal to binary.
Binary to Octal
Convert binary numbers to octal notation.
Binary Converter
Broad binary conversion hub, including text encoding.
Hex Converter
Broad hexadecimal conversion hub.
Two's Complement Calculator
Represent negative numbers in binary or hex at a fixed bit width.
Frequently Asked Questions
What formats does this octal converter support?
It converts a whole octal (base-8) integer to decimal, binary, and hexadecimal at once, using exact BigInt arithmetic. For a step-by-step positional-notation breakdown of one conversion, see the Octal to Decimal or Octal to Binary converters linked below.
Do I need to include the 0o prefix?
No. Enter the octal digits directly, such as 52 instead of 0o52. Input written with a 0o prefix is rejected with a message rather than silently stripped.
What happens if I enter 8 or 9?
The converter shows an error. Octal only uses the digits 0-7 — unlike hexadecimal, it has no extra digit symbols, so 8 and 9 are always invalid octal digits.
Can I enter octal numbers with a leading zero?
Yes. 0755 and 755 convert to the same value. Leading zeros do not change the value, though they conventionally mark a number as octal in code.
Can I convert negative octal values?
Not directly. A minus sign in front of an octal number isn't how computers represent negative values — that requires a fixed bit width and a format such as two's complement. Use the Two's Complement Calculator, linked below, for signed conversions.
What's the largest octal value this tool can convert?
There is no fixed size limit. Conversion uses BigInt built directly from the validated octal string, so arbitrarily long octal numbers convert exactly rather than losing precision the way JavaScript's native Number type does beyond 2^53 - 1 (9,007,199,254,740,991).
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