Convert Octal to Decimal
1 Octal (oct) = 1 Decimal (dec). Use the free converter below to instantly convert any octal value to decimal, or view the full conversion table and formula.
1 oct = 1 dec
Octal to Decimal Conversion Table
How to Convert Octal to Decimal
To convert octal to decimal, multiply each digit by 8 raised to the power of its position (rightmost = 0), then sum all values. For example, 755 in octal: (7×8²) + (5×8¹) + (5×8⁰) = 448 + 40 + 5 = 493 in decimal.
Worked Example: Convert 10 oct to dec
Start with the value in octal
10 oct
Apply the formula
Expand each 10 digit × 8^position, sum all values
Calculate the result
10 oct = 8 dec
Octal to Decimal Examples
0 oct is equal to 0 dec. Using the formula Expand each octal digit × 8^position, sum all values, 0 oct converts to 0 dec.
1 oct is equal to 1 dec. Using the formula Expand each octal digit × 8^position, sum all values, 1 oct converts to 1 dec.
7 oct is equal to 7 dec. Using the formula Expand each octal digit × 8^position, sum all values, 7 oct converts to 7 dec.
10 oct is equal to 8 dec. Using the formula Expand each octal digit × 8^position, sum all values, 10 oct converts to 8 dec.
17 oct is equal to 15 dec. Using the formula Expand each octal digit × 8^position, sum all values, 17 oct converts to 15 dec.
20 oct is equal to 16 dec. Using the formula Expand each octal digit × 8^position, sum all values, 20 oct converts to 16 dec.
77 oct is equal to 63 dec. Using the formula Expand each octal digit × 8^position, sum all values, 77 oct converts to 63 dec.
100 oct is equal to 64 dec. Using the formula Expand each octal digit × 8^position, sum all values, 100 oct converts to 64 dec.
Converting Decimal to Octal
Need the reverse conversion? Use the table below for a quick reference converting decimal back to octal.
| Decimal (dec) | Octal (oct) |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 7 | 7 |
| 8 | 10 |
| 10 | 12 |
Octal to Decimal FAQ
What is octal?
Octal is a base-8 number system using digits 0-7. It was historically popular in computing because early systems used 12-bit, 24-bit, or 36-bit words, which divide evenly into 3-bit octal groups.
How do I convert octal to decimal?
Multiply each octal digit by 8 raised to the power of its position (starting from 0 on the right), then sum all values. For example, 77 in octal = (7×8¹) + (7×8⁰) = 56 + 7 = 63.
Where is octal used today?
Octal is commonly used in Unix/Linux file permissions (e.g., chmod 755), and occasionally in programming with the 0o prefix notation.
Understanding Octal and Decimal
What is an Octal (oct)?
The octal (oct) is a specialized unit of number systems. It is commonly abbreviated as oct and relates to decimal by a factor of 1.
What is a Decimal (dec)?
The decimal (dec) is a specialized unit of number systems. It is commonly abbreviated as dec and relates to octal by a factor of 1.