Octal Converter

This octal converter turns any decimal whole number into octal, the base eight number system that once underpinned early computing and still turns up today in Unix and Linux file permission codes, such as chmod 755. Octal uses only the digits 0 to 7, and because each octal digit lines up neatly with exactly three binary digits, it became a compact, human-readable stand-in for long strings of binary on older systems, a habit that has stuck around in programming and system administration. To use the calculator, enter a decimal whole number, including negatives if needed, into the single input field. As you type, the tool instantly converts your figure and displays the resulting octal value as the main result, with the equivalent binary and hexadecimal representations shown alongside for quick comparison. This means you get three number bases from one entry, which is handy for checking your own manual working, setting file permissions correctly, or exploring how the same quantity looks across different counting systems. The conversion works by repeatedly dividing the decimal number by 8 and reading the remainders in reverse order, as set out in the worked example and formula below. It suits students learning number systems, programmers wanting a fast cross-check, and anyone curious how computers represent numbers, and it assumes you enter a whole number using the standard integer conversion method.

Decimal whole number

100

Binary1000000

Hexadecimal40

The formula

To convert to octal, repeatedly divide by 8 and record the remainders, then read them from last to first. Each octal digit represents three binary bits.

Worked example

64 divided by 8 is 8 remainder 0, and 8 divided by 8 is 1 remainder 0, so 64 is 100 in octal. That is 1000000 in binary and 40 in hex. Enter 64 to confirm.

Frequently asked questions

What is octal?

Base eight, using digits 0 to 7. Each octal digit equals three binary bits.

Where is octal used today?

Most visibly in Unix and Linux file permissions, such as chmod 755.

What is 64 in octal?

100, because 64 is 8 squared.

Who this calculator is for

This calculator is for students, programmers and anyone exploring number theory.

What this calculator assumes

You enter a whole number within the stated range.
The exact integer algorithm is used.
Very large results are shown grouped for readability.

Formula and sources

Related calculators

Prime Factorization Calculator: break a number into prime factors.
LCM Calculator: lowest common multiple.
GCF Calculator: greatest common factor.

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