Decimal to Octal Converter

The divide-by-8 method

Divide the number by 8 and record the remainder, which is always a digit from 0 to 7. Replace the number with the quotient and repeat until it reaches 0, then read the remainders bottom to top. Here is decimal 200:

200 ÷ 8 = 25  remainder 0
 25 ÷ 8 =  3  remainder 1
  3 ÷ 8 =  0  remainder 3
read upward → 310

So decimal 200 is octal 310. Verify it: 3×64 + 1×8 + 0 = 192 + 8 = 200.

The via-binary shortcut

Since one octal digit equals exactly three binary bits, you can convert to binary first and then group the bits in threes from the right. For 200 → binary 11001000 → grouped 011 001 000 → 3 1 0 → 310. This grouping trick is especially handy for permission bytes, where each octal digit corresponds neatly to one rwx triple.

Reference table

Permission codes are the most common reason people convert to octal: 493 → 755 (rwxr-xr-x), 420 → 644 (rw-r--r--), and 511 → 777 (full access). The converter shows octal alongside binary so you can read the rwx bits directly.

Where you'll use it

• Producing chmod and umask values from a decimal permission total.
• Writing octal literals in C, Python and shell scripts.
• Working with legacy file formats and protocols that store octal.
• Teaching base conversion where 3-bit grouping is the focus.