How does octal convert to decimal?

Octal is base 8, so each digit's value is the digit multiplied by 8 raised to the power of its position, counting from zero at the rightmost digit. Summing all those terms gives the decimal value.

Which digits are valid in octal?

Only the digits 0 through 7. There is no digit 8 or 9 in octal, just as there is no single digit for ten in decimal.

Where is octal still used?

Octal is most common in Unix and Linux file permissions, where modes like 755 or 644 are octal. It groups three bits per digit, which suits the read/write/execute permission triplets.

Why is 10 in octal equal to 8 in decimal?

In octal, the number after 7 rolls over to 10, just as decimal rolls over after 9. So octal 10 means one eight plus zero ones, which is 8 in decimal.

Can it handle large octal numbers?

Yes. The converter uses exact big-integer arithmetic, so even very long octal strings convert to decimal without any rounding error.

Octal to Decimal Converter

Converting octal to decimal is a frequent need for anyone working with Unix file permissions, older computing systems or low-level data, since octal packs neatly into groups of three bits. This converter evaluates a base-8 number positionally and shows the full working.

How it works

Octal is a base-8 positional system using the digits 0 through 7. The value of a number is the sum of each digit multiplied by 8 raised to the power of that digit’s position, where positions are counted from zero starting at the rightmost digit. So the rightmost digit is multiplied by 8 to the power 0 (which is 1), the next by 8 to the power 1 (which is 8), the next by 64, and so on.

The tool walks the string from right to left, computes each digit’s place value as a power of 8, multiplies, and accumulates the total using exact big-integer arithmetic.

Example

Convert the Unix permission 755. The expansion is 7 × 8² + 5 × 8¹ + 5 × 8⁰ = 7 × 64 + 5 × 8 + 5 × 1 = 448 + 40 + 5 = 493. So octal 755 equals decimal 493.

Tips and notes

Octal is most familiar from chmod permission modes, where each octal digit encodes the read, write and execute bits for owner, group and others. If you enter a digit of 8 or 9 the tool flags it, since those are not valid octal digits. All processing happens locally in your browser.