Decimal to Octal

Convert decimal numbers to octal (base 8) and back.

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Decimal to Octal Converter

Turn decimal numbers into octal – base 8 – and convert octal back to decimal. Paste a list with one number per line; every line is converted as you type. For example 8 becomes 10, 64 becomes 100, and 493 becomes 755.

What is the octal number system?

Octal uses only the digits 0 to 7. Each position is worth eight times the position to its right, so the octal number 755 means 7 × 64 + 5 × 8 + 5 = 493. Because 8 is a power of two, every octal digit corresponds to exactly three binary digits, which is why octal was popular on early computers with 12-, 24-, and 36-bit words.

Converting decimal to octal step by step

Divide the decimal number by 8 and keep the remainder, then divide the quotient again until it reaches zero. Reading the remainders from bottom to top gives the octal result. For 493: 493 ÷ 8 = 61 r 5, 61 ÷ 8 = 7 r 5, 7 ÷ 8 = 0 r 7 → 755. The tool follows exactly this method but with exact big-integer math, so long numbers never lose precision.

Where octal is still used

  • Unix and Linux permissions – chmod 644 or chmod 755 are octal numbers; each digit holds the read (4), write (2), and execute (1) bits for owner, group, and others.
  • Escape sequences – C and many shells accept \101 for the character A.
  • Legacy formats – tar headers and some aviation and telecom protocols store numbers in octal.

Options

Enable Prefix to get Python- and JavaScript-style literals such as 0o755, or Group digits to split long results into blocks of three. Negative values keep their sign and decimal fractions are converted too (0.5 → 0.4). Need the other bases as well? The All Number Converter shows binary, octal, decimal, and hex together.

Frequently Asked Questions

Repeatedly divide by 8 and write down each remainder. When the quotient reaches 0, read the remainders in reverse order. 100 in decimal, for example, is 144 in octal.

755 in octal is 493 in decimal, but for permissions the digits are read separately: 7 (rwx) for the owner and 5 (r-x) for the group and for others.

Octal is base 8, so each position can hold eight different values. The digit 8 would already be a carry into the next position, written as 10.

Yes. Choose the Octal to Decimal mode or press the swap button, then paste your octal numbers one per line.