Octal to decimal converter
Type an octal number with digits 0 to 7 to get its decimal value. 377 becomes 255 and 755 becomes 493. Put each number on its own line to convert a whole list.
Show the working
Runs in your browser. Nothing you type is uploaded.
How to convert octal to decimal
- Write the place values under the digits from the right: 1, 8, 64, 512 and so on. Each one is 8 times the one before.
- Multiply each octal digit by the place value under it.
- Add the results. The total is the decimal number.
Open "Show the working" under the tool to see this sum for the first number you type. It lists every digit, its power of 8 and the running total.
Octal to decimal formula
For an octal number with digits dn ... d1 d0, the decimal value is dn × 8n + ... + d1 × 8 + d0. So 1000 in octal is 1 × 83 = 512, and 17 is 1 × 8 + 7 = 15. To go the other way, use the decimal to octal converter.
Worked examples
| Octal | Working | Decimal |
|---|---|---|
| 17 | 1 × 8 + 7 | 15 |
| 36 | 3 × 8 + 6 | 30 |
| 144 | 1 × 64 + 4 × 8 + 4 | 100 |
| 275 | 2 × 64 + 7 × 8 + 5 | 189 |
| 377 | 3 × 64 + 7 × 8 + 7 | 255 |
| 755 | 7 × 64 + 5 × 8 + 5 | 493 |
| 777 | 7 × 64 + 7 × 8 + 7 | 511 |
A quick check: an octal number can never contain 8 or 9. If you see one, the number is probably decimal already, and the tool marks the digit for you.
Octal fractions
Digits after the point use negative powers of 8. In 17.4 the 4 is worth 4 × 8-1 = 0.5, so 17.4 in octal is 15.5 in decimal. Type a number with a point and the converter does the same.
What is the octal number system?
Octal is base 8, one of the bases from 2 to 36 that the base converter handles. It uses the digits 0 to 7, and the next number after 7 is written 10. Each octal digit stands for exactly 3 bits, which is why programmers use it as short binary. The octal to binary converter shows those 3 bits for each digit. The place you see it most today is Unix file permissions, written as octal numeric modes: chmod 644 and chmod 755 are octal numbers, and 755 is 493 in decimal.
Frequently asked questions
How do I convert octal to decimal?
Multiply each digit by its power of 8, with 1 for the digit on the right, then add the results. For 275 that is 2 × 64 + 7 × 8 + 5 = 189.
What is 275 octal in decimal?
189. The working is 128 + 56 + 5.
What is 36 octal in decimal?
30, because 3 × 8 + 6 = 30.
What is 8 in octal?
8 in decimal is written 10 in octal. Octal has no digit 8, so it carries over, just as decimal does after 9.
Can I convert several octal numbers at once?
Yes. Put each number on its own line or separate them with spaces, and every result appears in the same order.