Octal to Decimal Converter

How to Convert Octal to Decimal

Converting octal to decimal by hand is straightforward once you know the routine. The converter above does it instantly, but working through the steps yourself is the fastest way to understand what is actually happening to the digits.

1. Write down the octal number and number each digit by its position, starting with 0 at the rightmost digit.
2. Multiply every digit by 8 raised to the power of its position.
3. Add all the products together. The total is the decimal value.

Worked example: 3736

Result: (3736)⁸ = (2014)¹⁰

The Octal System

Octal is the base 8 numeral system and uses the digits 0 through 7. Its usefulness comes from the fact that one octal digit maps exactly onto three binary digits, so it is a compact way to write binary without doing real arithmetic. Octal was common on early minicomputers with 12, 24, and 36 bit words. Today the place most developers still meet it is Unix file permissions, where a command such as chmod 755 sets read, write, and execute bits three at a time.

Octal uses the digits 0 through 7.

The Decimal System

Decimal is the base 10 system that almost every human culture settled on, most likely because we have ten fingers. It uses the digits 0 through 9, and each position is worth ten times the position to its right. The number 2345.67 means 2 thousands, 3 hundreds, 4 tens, 5 ones, 6 tenths, and 7 hundredths. It is the default for everything people read, which is why converting to and from decimal is the most common base conversion a programmer performs.

Decimal uses the digits 0 through 9.

Octal to Decimal Conversion Examples

Octal to Decimal Conversion Chart

A full reference table for the values 1 to 256. Use it to check a conversion quickly or to look up a common value without typing anything.

Need a different pair of bases? Browse every number converter tool including binary, octal, decimal, and hexadecimal in both directions.