Octal Converter
Convert octal to decimal and vice versa
Frequently Asked Questions
What is the octal number system?
Octal is base-8, using digits 0-7. Each octal digit represents exactly 3 binary bits. The decimal number 255 is 377 in octal (3×64 + 7×8 + 7×1). Octal was historically used in computing before hexadecimal became dominant.
How do I convert between octal and decimal?
Octal to decimal: multiply each digit by 8^position. 375₈ = 3×64 + 7×8 + 5×1 = 253. Decimal to octal: repeatedly divide by 8 and read remainders bottom-up. 253 ÷ 8 = 31 R5, 31 ÷ 8 = 3 R7, 3 ÷ 8 = 0 R3 → 375₈.
Where is octal still used today?
Octal is used in Unix/Linux file permissions (chmod 755), some programming languages (C/C++ octal literals with 0 prefix like 0777), and digital electronics. It provides a compact way to represent groups of 3 binary bits.
How do Unix file permissions use octal?
Each permission set (owner, group, others) uses one octal digit: read=4, write=2, execute=1. chmod 755 means owner=7 (rwx), group=5 (r-x), others=5 (r-x). The calculator converts between symbolic and octal notation.
How do I convert between octal and hexadecimal?
Convert through binary as an intermediate. Each octal digit = 3 bits, each hex digit = 4 bits. 375₈ = 011 111 101₂ = 0FD₁₆. The calculator handles direct conversion between any number bases.