Vigesimal Converter

This vigesimal converter turns an ordinary decimal (base 10) whole number into vigesimal, or base 20, the counting system that groups numbers in twenties rather than tens. It is handy if you are studying number systems, exploring how the Maya civilisation and other cultures counted, or you simply want to check a base conversion for homework or curiosity. You enter a decimal whole number into the single field, and the calculator instantly works it out by repeatedly dividing by 20 and reading the remainders, showing the vigesimal result as the large headline figure. Because base 20 needs more than ten symbols, it uses the digits 0 to 9 for the values zero to nine and then the letters A to J for ten to nineteen, so any two-digit result stays easy to read. Alongside the main answer, the calculator also shows the same number converted to duodecimal (base 12) and repeats your original decimal figure, so you can compare all three side by side without doing the sums by hand. The page includes a worked example using 100, which converts to 50 in vigesimal, plus a short explanation of the method, background on where base 20 has been used historically, and answers to common questions. Enter any whole number to see its vigesimal equivalent update immediately as you type.

Decimal whole number

Duodecimal (base 12)84

Decimal100

The formula

To convert to base 20, repeatedly divide by 20 and record the remainders as digits, with ten to nineteen written A to J, then read them from last to first.

Worked example

100 divided by 20 is 5 remainder 0, so 100 in vigesimal is 50. The number 19 is written J, and 20 is 10. Enter 100 to confirm.

Frequently asked questions

What is vigesimal?

Base 20, using digits 0 to 9 then A to J for ten to nineteen.

Who used base 20?

The Maya civilisation used a vigesimal system, and traces survive in languages such as French and Danish.

What is 100 in base 20?

50, because 100 is exactly 5 twenties.

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

Related calculators

Scientific Calculator: general scientific maths.
Percentage Calculator: percentages and changes.
Ratio Calculator: simplify and scale ratios.

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