Summary: convert octal to decimal, free and private
An octal to decimal converter turns a base-8 number, which uses only the digits 0 to 7, into the ordinary base-10 number it stands for. To convert octal to decimal free and privately, type the octal number into Octal Input above, for example 157, and the answer, 111, appears under Decimal Output. Nothing is uploaded: the conversion runs in your browser.
The method is place value. Each octal digit is multiplied by 8 to the power of its position, counting from 0 at the right, and the products are added: decimal = Σ dᵢ × 8ⁱ. So 157 = 1 × 8² + 5 × 8¹ + 7 × 8⁰ = 64 + 40 + 7 = 111. For the other direction, switch the mode or use the decimal to octal converter.
Table of Use: octal inputs and their decimal results
| Octal input | Decimal result | What it shows |
|---|---|---|
| 10 | 8 | The first number that needs two octal digits |
| 0o17 | 15 | The 0o prefix used in Python and JavaScript is accepted |
| 377 | 255 | The largest value of one byte, 11111111 in binary |
| 644 | 420 | chmod rw-r--r--, a common file mode |
| 755 | 493 | chmod rwxr-xr-x, a common program or folder mode |
| 777 | 511 | chmod rwxrwxrwx, every permission for everyone |
| -17 | -15 | A leading minus sign is kept |
| 7.4 | 7.5 | A fraction: 4 × 8⁻¹ = 0.5 |
To work a conversion by hand, you need the place values, which are the powers of 8.
| Position from the right | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Place value | 1 | 8 | 64 | 512 | 4,096 | 32,768 | 262,144 |
Features
- Both directions. Octal → Decimal is the default, Decimal → Octal is one click away, and Swap feeds the result back in reversed.
- Exact results. Whole numbers up to 10,000 digits are converted without rounding, and octal fractions are exact in decimal.
- Forgiving input. A sign, a 0o prefix, a fraction, spaces and underscores are all accepted. A digit 8 or 9 gets a clear error message.
- Step-by-Step Calculation. Show Steps lists each digit times its power of 8, then the total, for numbers of up to 64 digits.
- Batch Conversion. One number per line, with an optional results-only list for spreadsheets.
- Educational Mode, Conversion History, Copy and Download. History holds your last 20 conversions in the open page, and Download saves octal-to-decimal.txt.
Octal is also the shorthand for binary in which each digit stands for three bits. For related bases, see the hex to binary converter, the binary to hex converter and the binary to text converter.
How to Use the Octal to Decimal Converter
- Under Conversion Mode, keep Octal → Decimal selected.
- Choose Single Value, or Batch Conversion for a list with one number per line.
- Type or paste your number into Octal Input.
- Read the answer under Decimal Output, or Batch Results for a list. A red message explains any invalid digit.
- Click Show Steps under Step-by-Step Calculation to see the working.
- Click Copy or Download to keep the result, Swap to convert it back, and Reset to start over.
Who Can Use an Octal to Decimal Converter
System administrators check file modes and umask values on Linux and macOS. Programmers decode octal literals and the octal escape codes found in C-style strings, and can compare them with character codes in the ASCII to text converter or the text to ASCII converter. Students in computer science and digital electronics use the steps to check homework, and the scientific calculator helps with the arithmetic. Anyone reading older computer manuals will meet octal too, and the Base64 encoder covers a different way to write bytes.
FAQs
How do I convert octal to decimal?
Multiply each octal digit by 8 raised to its position, counting from 0 at the right, then add the results. Octal 157 = 1 × 64 + 5 × 8 + 7 × 1 = 111 in decimal. Type the number into Octal Input to get the answer, and click Show Steps to see this working for your own number.
What is 755 in decimal, and why does chmod use octal?
Octal 755 is decimal 493 (7 × 64 + 5 × 8 + 5). Chmod uses octal because each permission digit is read 4 plus write 2 plus execute 1, a sum from 0 to 7 that fits exactly one octal digit. So 755 means rwxr-xr-x. The decimal 493 matters only where a program asks for the mode as a plain integer.
What is the difference between octal and decimal?
Decimal is base 10: it uses the digits 0 to 9 and each position is a power of 10. Octal is base 8: it uses only 0 to 7 and each position is a power of 8. Decimal 64 is therefore octal 100. Because 8 and 9 do not exist in octal, the converter shows an error if your number contains either.
Can I convert negative octal numbers and octal fractions?
Yes. A leading minus sign is kept, so octal -17 is decimal -15. Fractions work too: octal 7.4 is decimal 7.5, because 4 × 8⁻¹ = 0.5. Every octal fraction has an exact decimal value, so nothing is rounded. A 0o prefix, as in 0o755, is accepted, and spaces or underscores inside the number are ignored.
How large an octal number can I convert?
Up to 10,000 digits. The converter uses arbitrary-precision integers, so results stay exact beyond 2⁵³, the limit of ordinary JavaScript numbers. The step-by-step working is shown for numbers of up to 64 digits; longer numbers still get the exact result without the steps.
How do I convert a list of octal numbers at once?
Click Batch Conversion and enter one octal number per line. Each line is converted on its own, and a line that is not valid octal is marked with its line number. Tick "Results only, one per input line" to get just the decimal values in the same order, ready to paste into a spreadsheet column.
How do I convert octal to decimal in Python or JavaScript?
In Python, int("755", 8) returns 493. In JavaScript, parseInt("755", 8) returns 493, and the literal 0o755 is also 493. Both read whole numbers only, and parseInt loses precision above 2⁵³. For fractions, very long numbers or a quick check with the working shown, use this converter.
Is my data stored or sent anywhere?
No. The conversion runs in your browser with JavaScript, and nothing you type is uploaded; the Network tab in your browser's DevTools will show no request carrying your numbers. Conversion History keeps your last 20 conversions in the open page only, and it disappears when you reload or close the tab.