Mayan Numeral Converter

The Mayan Number System The Maya civilization, centered in present-day Mexico, Guatemala, Belize, Honduras, and El Salvador, developed one of the most sophisticated number systems in the ancient world. Their system was vigesimal (base 20), likely because they counted using both fingers and toes.

Symbols The Maya used only three symbols: a dot (worth 1), a bar (worth 5), and a shell shape (worth 0). Using combinations of dots and bars, they could represent any number from 0 to 19 in a single position. Zero was written as the shell, and the Maya were one of the first civilizations to independently discover and use the concept of zero, around 36 BCE. Europe did not get there for another thousand years.

Place Values Like our decimal system uses powers of 10, the Mayan system uses powers of 20. The place values from bottom to top are: 1 (20^0), 20 (20^1), 400 (20^2), 8,000 (20^3), 160,000 (20^4), and so on. Numbers are written vertically, with the lowest place value at the bottom.

Reading Mayan Numbers Each level can hold 0-19 (shown as dots and bars). The value at each level is multiplied by its place value. For example, a dot on the second level means 1 x 20 = 20. Two bars on the bottom level means 10 x 1 = 10. Together they equal 30.

One important exception The Long Count calendar did something different: the third position held 18 rather than 20, making it 360 instead of 400. That was not an error. It made the third place equal the 360 days of the Haab’ year, so the calendar’s place values lined up with the solar year rather than with arithmetic.

Pick the mode above and the calculator does either one. The place values are:

The gap widens fast. At the fourth place the two systems are 800 apart, and by the fifth they differ by 16,000. A date written 9.12.11.5.18 in Long Count notation is 1,386,478 days, and reading those same five digits as pure base 20 gives 1,540,518. That is 154,040 days of difference, or 422 years, from one column being 18 wide instead of 20.

Historical Significance The Maya used this system for astronomical calculations, calendar systems, and architectural planning. Their Long Count calendar tracked dates over millions of years. Mayan mathematicians and astronomers calculated the length of the solar year to within seconds of the modern value.