Math
Octal Converter
Pick the base your number is in and the base you want.
Octal (base 8) converts to and from binary by grouping bits in threes, and to decimal by place values of 1, 8, 64, 512. The panel always shows the binary, decimal, hex, and octal forms together, with the grouping and division tables.
Use the digits of the source base you pick below. Octal uses 0-7; a 0o, 0b, or 0x prefix is accepted when it matches.
The base your number is written in.
The base you want. All four are shown in the result anyway.
Try an example
Result
Converted value
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- Decimal
- —
- Binary
- —
- Hexadecimal
- —
- Octal
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Study path
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What the octal converter solves
Octal uses the eight digits 0-7 and each place is worth 8 times the one to its right. Because 8 = 2^3, one octal digit is exactly three bits, which is why Unix file permissions like 755 are written in octal: each digit is a read/write/execute triple. This converter moves between octal and the other common bases in either direction.
Octal to binary table
| Octal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| Binary | 000 | 001 | 010 | 011 | 100 | 101 | 110 | 111 |
| Permission | --- | --x | -w- | -wx | r-- | r-x | rw- | rwx |
How to use it
- Choose the base the number is written in (From) and the base you want (To).
- Type the number using only the digits of the From base; the converter names any digit that does not belong.
- Read the 3-bit grouping table for binary ↔ octal, or the place-value and division tables for decimal conversions.
- Use the four equivalents in the result grid to cross-check.
How to read the answer
The converted value is the main result, and the decimal value is shown for scale. Octal to hex goes through binary: regroup the 3-bit groups into 4-bit groups. The steps list that regrouping when it applies.
Common mistakes and edge cases
- Using 8 or 9 as octal digits. Octal stops at 7; 8 is written 10.
- Grouping binary in fours for octal. Octal needs groups of three, from the right.
- Treating a leading 0 in code (0755) as part of the value. In many languages a leading 0 just marks the literal as octal.
- Fractional octal converts digit by digit to binary but may repeat in decimal.
Worked examples
Octal permissions to binary
755 → binary
Converted value
111101101
Octal to decimal
755 → decimal
Converted value
493
Decimal to octal
493 → octal
Converted value
755
Binary to octal
111101101 → octal
Converted value
755
Octal to hex
777 → hex
Converted value
1FF
Octal fraction
7.4 → decimal
Converted value
7.5
Zero
0 → binary
Converted value
0
Invalid octal digit
78 → decimal
Converted value
—
Frequently asked questions
How do you convert octal to binary?+
Replace each octal digit with its 3-bit pattern: 7 = 111, 5 = 101, 4 = 100. So 755 = 111 101 101.
How do you convert binary to octal?+
Group the bits in threes from the right, pad the leftmost group with zeros, and read each group as a digit 0-7.
How do you convert octal to decimal?+
Multiply each digit by its power of 8 and add: 755 = 7×64 + 5×8 + 5×1 = 493.
Why are file permissions written in octal?+
Each permission set (owner, group, others) has three bits: read, write, execute. Three bits is exactly one octal digit, so 755 means rwx r-x r-x.
How do you convert octal to hex?+
Go through binary: write each octal digit as three bits, then regroup the bits in fours and read each group as a hex digit. 777 = 111 111 111 = 1 1111 1111 = 1FF.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026