From Base-8 to Base-10 in Seconds

Our Octal to Decimal Converter is an online utility that simplifies the conversion of numbers from the octal (base-8) system to the more familiar decimal (base-10) system. The octal system, which uses digits 0 through 7, was historically popular in computing as a compact representation of binary numbers. While less common than hexadecimal today, it's still an important concept in computer science and is used in some specific applications, such as file permissions in Unix/Linux systems.

Understanding the decimal value of an octal number is key to grasping its real-world magnitude. For example, the file permission 755 in octal represents the decimal value 493. Manually calculating this involves multiplying each octal digit by powers of 8, which can be tedious. This tool automates the process, providing instant and accurate results for students learning number theory and professionals working with legacy systems or specific computing environments.

How to Use the Octal to Decimal Converter

1. Enter the Octal Number: Type or paste your octal value (using digits 0-7) into the input box.
2. Click Convert: Press the "Convert to Decimal" button.
3. View the Result: The decimal equivalent will immediately appear in the output field below.
4. Copy if Needed: Use the "Copy Result" button to quickly copy the decimal value to your clipboard.

Frequently Asked Questions About Octal to Decimal Conversion

How do I convert octal to decimal?

To convert an octal number to decimal, you multiply each digit of the octal number by the appropriate power of 8 and sum the results. Starting from the rightmost digit (which is 8^0), each position to the left increases the power by one (8^1, 8^2, etc.).

How to convert octal to decimal in scientific calculator?

Most scientific calculators have a base conversion mode. You would typically switch to 'OCT' (octal) mode, enter your number (e.g., 514), and then switch back to 'DEC' (decimal) mode to see the converted result (332).

How do you convert 514 octal to decimal?

To convert 514 from octal to decimal, you calculate (5 * 8^2) + (1 * 8^1) + (4 * 8^0). This equals (5 * 64) + (1 * 8) + (4 * 1), which sums to 320 + 8 + 4 = 332.

What is the octal number 714 to the decimal number?

The decimal equivalent of octal 714 is calculated as (7 * 8^2) + (1 * 8^1) + (4 * 8^0). This is (7 * 64) + 8 + 4 = 448 + 8 + 4, which equals 460.

How do you convert 123 octal to decimal?

For the octal number 123, the decimal conversion is (1 * 8^2) + (2 * 8^1) + (3 * 8^0). This equals 64 + 16 + 3, giving a final decimal result of 83.