Decimal to Octal Converter
Convert decimal (base 10) numbers to octal (base 8) instantly. Shows the full division process step by step. Important for Linux file permissions and system programming.
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What is Octal (Base 8)?
The octal system uses digits 0–7. It was historically used in computing because 3 octal digits = 1 byte in some systems, and it maps cleanly to groups of 3 binary bits (2³ = 8). Today it is most commonly seen in Unix/Linux file permissions.
Linux File Permissions in Octal
In chmod 755: 7 (owner: rwx = 4+2+1), 5 (group: r-x = 4+1), 5 (others: r-x = 4+1). Each permission group uses 3 bits: r=4, w=2, x=1.
How to Convert Decimal to Octal
Divide the number by 8 repeatedly, record remainders (0–7), read them bottom-up. Example: 65 ÷ 8 = 8 R1, 8 ÷ 8 = 1 R0, 1 ÷ 8 = 0 R1 → octal = 101.
Frequently Asked Questions
How do I convert decimal to octal?
Divide by 8 repeatedly, note each remainder (0–7), read remainders bottom-up. Example: 8 → 8÷8=1 R0, 1÷8=0 R1 → octal 10.
What is 255 in octal?
255 in octal is 377. (255÷8=31 R7, 31÷8=3 R7, 3÷8=0 R3 → 377₈)
Why does chmod use octal?
Linux permissions use 3 bits per group (read=4, write=2, execute=1). 3 bits = one octal digit. So 3 octal digits represent all 9 permission bits for owner, group, and others.