Octal (Base 8) to Decimal (Base 10) Converter
Convert octal numbers to decimal.
377 (base 8) = 255 (base 10)
Digits in base 8: 0 to 7. Digits in base 10: 0 to 9.
How to convert Octal to Decimal
Every positional number system works the same way: a digit is worth its own value times the base raised to the power of its position. In base 8 the place values, from the right, are 80 = 1, 81 = 8, 82 = 64 and so on.
To get from base 8 to decimal, multiply each digit by 8 raised to the power of its position, counting from 0 on the right, and add the results.
The method
decimal value = each digit × its place value, all added upplace values in base 8: 1, 8, 64, 512, 4096, and so ondigits in base 8: 0 to 7digits in base 10: 0 to 9
Worked example 1: 55 from octal to decimal
55 (base 8) = 5 × 81 + 5 × 80= 40 + 5= 4555 (base 8) = 45 (base 10)
Digits that are 0 add nothing to the sum, so they are left out of the expansion.
Worked example 2: 377 from octal to decimal
377 (base 8) = 3 × 82 + 7 × 81 + 7 × 80= 192 + 56 + 7= 255377 (base 8) = 255 (base 10)
Worked example 3: 1750 from octal to decimal
1750 (base 8) = 1 × 83 + 7 × 82 + 5 × 81= 512 + 448 + 40= 1,0001750 (base 8) = 1000 (base 10)
Need the other direction? Open the Decimal to Octal converter.
Octal to Decimal examples
The decimal number 255 is written 377 in octal and 255 in decimal.
| Octal | Decimal |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 7 | 7 |
| 10 | 8 |
| 12 | 10 |
| 17 | 15 |
| 20 | 16 |
| 40 | 32 |
| 100 | 64 |
| 144 | 100 |
| 377 | 255 |
| 1750 | 1000 |
Where Octal to Decimal comes up
Octal uses the digits 0 to 7, and each octal digit stands for exactly three bits. Unix file permissions such as chmod 755 are written in octal, and it also appears in older machine listings where word sizes divide by three.
Decimal is the base 10 system everyone learns first, with the digits 0 to 9. It is the form people read: prices, measurements, ages and IDs. It is also the base we calculate in by hand, which is why the worked steps on this page pass through decimal.
Going to a larger base packs more value into each digit, so the result is shorter. The number 255 needs 3 digits in octal and 3 in decimal.
Octal to Decimal FAQ
How do I convert octal to decimal?
Multiply each base 8 digit by 8 raised to the power of its position, counting from 0 on the right, then add everything up.
Which digits does octal use?
Base 8 uses the digits 0 to 7. For example, 8 is not a valid digit in base 8.
Will the decimal number be longer or shorter?
Shorter. Going to a larger base packs more value into each digit, so the result is shorter. Roughly 0.9 decimal digits for every octal digit. The number 255 needs 3 digits in octal and 3 in decimal.
What is 377 in decimal?
377 in octal is 255 in decimal. Both are the decimal number 255.
Can I convert negative numbers or fractions?
The converter handles whole numbers, and a leading minus sign works for negatives. Fractions use a different method, where you repeatedly multiply the fractional part by the new base, and they are not supported here.