Convert decimal integers to octal with a step-by-step division-by-eight breakdown showing remainders and the final octal string.
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Number Systems
The decimal to octal converter translates decimal (base-10) integers into their octal (base-8) equivalents. Enter a decimal number and see the octal result with a step-by-step division breakdown.
Repeatedly divide the decimal number by 8 and record the remainder at each step. Read the remainders from bottom to top to form the octal result.
For example, decimal 100 divided by 8 gives quotient 12 remainder 4, then quotient 1 remainder 4, then quotient 0 remainder 1, producing octal 144.
Octal notation is most commonly seen in Unix and Linux file permissions. The permission triplet for owner, group, and others is specified as a three-digit octal number, such as 755 for full owner access with read-execute for others.
Frequently asked questions
Only digits 0 through 7. Any digit 8 or 9 would be invalid in base 8.
Each permission set (read, write, execute) maps to three bits, and three bits map perfectly to one octal digit, making octal a natural fit.
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