How to convert octal to decimal by hand
Example 1: 755 in octal is 493 in decimal
Octal to decimal: add up the place values
Each octal digit is worth its value times 8 raised to the power of its position, counting from 0 on the right.
| Digit | Place value | Digit × place value |
|---|---|---|
| 7 | 8² = 64 | 7 × 64 = 448 |
| 5 | 8¹ = 8 | 5 × 8 = 40 |
| 5 | 8⁰ = 1 | 5 × 1 = 5 |
448 + 40 + 5 = 493
Example 2: 644 in octal is 420 in decimal
Octal to decimal: add up the place values
Each octal digit is worth its value times 8 raised to the power of its position, counting from 0 on the right.
| Digit | Place value | Digit × place value |
|---|---|---|
| 6 | 8² = 64 | 6 × 64 = 384 |
| 4 | 8¹ = 8 | 4 × 8 = 32 |
| 4 | 8⁰ = 1 | 4 × 1 = 4 |
384 + 32 + 4 = 420
Octal to Decimal conversion table
| Octal | Decimal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 10 | 8 |
| 11 | 9 |
| 12 | 10 |
| 13 | 11 |
| 14 | 12 |
| 15 | 13 |
| 16 | 14 |
| 17 | 15 |
| 20 | 16 |
| 40 | 32 |
| 100 | 64 |
| 144 | 100 |
| 200 | 128 |
| 377 | 255 |
| 400 | 256 |
| 1000 | 512 |
| 1750 | 1000 |
| 2000 | 1024 |
Where this conversion comes up
- Unix permissions printed by code: Node's fs.stat and Python's os.stat return the mode as a plain number, so once the file type bits are masked off (mode & 0o777) a 644 file shows as 420.
- Legacy code where a leading zero means octal: in C, 010 is 8, not 10.
Frequently asked questions
Why does 010 equal 8 in some programming languages?
In C, C++ and older JavaScript a leading zero marks an octal literal, so 010 is 1 × 8 + 0 = 8. Python 3 and modern JavaScript require the explicit 0o prefix instead.
Can I convert negative numbers?
Yes. Put a minus sign in front and it is kept in the result, for example -755 becomes -493. The converter does not produce two's complement.
Is there a limit on how big the number can be?
No practical limit. The conversion uses arbitrary precision integers, so long values stay exact. The step-by-step working is shown for numbers up to 24 digits.
Can I convert fractions?
Not with this tool. It converts whole octal numbers to whole decimal numbers.
Other number converters
Going the other way? Use the Decimal to Octal Converter. To see a number in every base at once, try the all-in-one number converter.