Octal to Decimal Calculator
Convert an octal number to decimal.
Digits 0-7 only
Results update as you type.
How it works
Octal is the base-8 number system, and this calculator converts an octal value into ordinary decimal. You enter an octal number using only the digits 0 through 7, and it returns the decimal equivalent. Octal uses eight symbols per digit, and conversion works by place value: each position is a power of eight, so from right to left the places are 1, 8, 64, 512, and so on. Each digit is multiplied by its place value and the results are summed. For example, octal 17 has a 1 in the eights place and a 7 in the ones place, giving eight plus seven, or fifteen. Octal was historically important in early computing because it groups binary digits neatly, three bits per octal digit, making it a compact way to represent binary data before hexadecimal became more common. It still appears in some contexts, most notably in Unix and Linux file permissions, where numbers like 755 or 644 are octal representations of read, write, and execute bits. Understanding octal-to-decimal conversion helps computer science students and anyone working with file permissions or legacy systems. This calculator accepts only valid octal digits, 0 through 7, and returns an error for anything containing an 8, 9, or other character. Enter an octal number to convert it to decimal.
decimal = Σ digitᵢ × 8ⁱ
An octal number is converted to decimal using place values that are powers of eight, increasing from right to left as 1, 8, 64, and so on. Each octal digit, from 0 to 7, is multiplied by its place value and the results are summed to give the decimal number.
Source:Number systems
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Worked example
How to use this calculator
- 1
Enter your values
Enter octal number.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Decimal value updates instantly as you type — no button to press.
Frequently asked questions
How do you convert octal to decimal?
Give each octal digit a place value that is a power of eight, starting at 1 on the right. Multiply each digit by its place value and add the results. Octal 17 is one times eight plus seven, which equals fifteen. The calculator does this automatically from the octal number you enter.
What is octal?
Octal is the base-8 number system, using only the digits 0 through 7. Each position represents a power of eight. It was widely used in early computing because three binary digits map to exactly one octal digit, making it a compact way to write binary data before hexadecimal became the common choice.
Where is octal still used?
Octal appears most visibly in Unix and Linux file permissions, where values like 755 or 644 are octal codes for the read, write, and execute permissions of a file's owner, group, and others. It also shows up in some legacy systems and programming contexts, though hexadecimal has largely replaced it for representing binary.
Why does each octal digit equal three bits?
Because eight is two to the third power, each octal digit can represent exactly three binary digits, from 000 to 111. This clean mapping made octal a convenient shorthand for binary in early computers with word sizes divisible by three, letting programmers write long binary values more compactly and readably.
What if my input has an 8 or 9?
Octal uses only the digits 0 through 7, so an 8 or 9 is not a valid octal digit. If your input contains one, or any non-octal character, it is not a valid octal number, and the calculator returns an error instead of a value. Check that your number uses only digits 0 to 7.