Mayan Numeral Converter
Convert between decimal numbers and the ancient Mayan vigesimal (base-20) numeral system.
See the dot-and-bar representation used by the Maya civilization.
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 represented by the shell — the Maya were one of the first civilizations to independently discover and use the concept of zero, around 36 BCE.
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 This calculator implements the pure base-20 system described above, which is what the Maya used for ordinary counting. Their 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. If you are converting a Long Count date rather than a plain number, the 400s column will not match.
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.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
SuperGlobalCalculator is independently built and maintained. See how we build and verify our calculators.