Base-20 Numerals

How Base-20 Numerals Work

Base-20 numerals use twenty possible digit values in each place. Decimal notation uses ten values, 0 through 9, and then moves to the tens place. A vigesimal system continues through values 10, 11, 12, and so on up to 19 before it moves to the next place. That means a single base-20 digit can represent any value from zero to nineteen.

Mayan numerals are one of the best-known historical examples. The familiar teaching version uses a shell for zero, dots for ones, and bars for fives. With those parts, every value from 0 through 19 can be written as one place. Values above 19 are arranged by place value. In a pure base-20 explanation, the bottom place represents ones, the next place represents twenties, the next represents four hundreds, and the next represents eight thousands. So 33 is one twenty plus thirteen, and 429 is one four-hundred plus one twenty plus nine.

Kaktovik numerals are a modern example of the same base idea. They were developed for an Inupiaq counting context in Alaska and are designed so the symbol shapes carry visual information about the value. A Kaktovik digit set has values 0 through 19, so the decimal value 20 is written as the base-20 digits 10: one group of twenty and zero units. This is the same place-value idea that makes decimal 10 mean one ten and zero ones.

The comparison is useful because Mayan and Kaktovik numerals show two different ways to solve the same notation problem. Mayan numerals are tied to an ancient mathematical and calendrical tradition, while Kaktovik numerals are a recent community-created system built for base-20 arithmetic. Both are now represented in Unicode, so a modern web page can display their digit symbols directly when the browser has a suitable font.

There is one important caution: not every Mayan date is a simple pure base-20 number. The Maya Long Count calendar uses a modified place-value pattern where one position is based on 18 times 20, reflecting calendar structure. For a beginner reference, it is still helpful to learn the pure base-20 model first because it explains why the digit range is 0 through 19 and why larger values stack by powers of twenty.

This page keeps Mayan and Kaktovik numerals separate from the main decimal numeral symbols table. Decimal digit tables compare 0 through 9 across scripts such as Arabic, Devanagari, Thai, and Bengali. Base-20 systems need a wider digit range and a different place-value explanation, so they deserve their own reference page.