Duodecimal Converter
This duodecimal converter turns a decimal whole number into its duodecimal, or base 12, equivalent, a system also known as dozenal. Base 12 rarely gets used for everyday counting, but it interests mathematicians and dozenal enthusiasts for a practical reason: twelve divides evenly by two, three, four and six, so fractions like a half, a third and a quarter come out as tidy whole digits, unlike in base ten, where a third becomes a recurring decimal. Traces of base 12 show up in 12-hour clocks, dozens of eggs, and twelve inches to a foot. To use the calculator, type a decimal whole number into the input box. As you type, the tool returns three results: the number written in duodecimal using the digits 0 to 9 followed by A for ten and B for eleven, the same number written in binary for comparison, and your decimal value grouped with thousands separators so you can confirm the entry. The method is repeated long division: the number is divided by 12 over and over, each remainder recorded as a digit, and those digits read in reverse to build the final figure. This is exact arithmetic, not an estimate, so the result is precise for any whole number entered, whether you are exploring number systems, working on a dozenal project, or simply curious what a familiar number looks like in base 12.
The formula
To convert to base 12, repeatedly divide by 12 and record the remainders as digits, with ten written A and eleven written B, then read them from last to first.
Worked example
100 divided by 12 is 8 remainder 4, and 8 divided by 12 is 0 remainder 8, so 100 in duodecimal is 84. Enter 100 to confirm.
Frequently asked questions
What is duodecimal?
Base 12, using digits 0 to 9 then A (ten) and B (eleven). It is also called the dozenal system.
Why would anyone use base 12?
Twelve divides evenly by 2, 3, 4 and 6, so common fractions come out neatly, which appeals to dozenal enthusiasts.
What is 100 in base 12?
84, because 100 is 8 twelves plus 4.
Who this calculator is for
This calculator is for students and anyone needing a quick, reliable result.
What this calculator assumes
- You enter valid numbers.
- The standard formula is applied.
- Results are rounded for display.
Formula and sources
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