Maya Numerals
Convert integers to Maya vigesimal numerals (dots, bars, shell).
Overview
The Maya Numerals converter turns a base-10 integer into the vigesimal (base-20) numerals used by the Classic Maya civilisation. The Maya wrote numbers as a vertical stack of place values, with each digit composed of dots (one each, up to four) and bars (each worth five), plus a shell shape for zero — making this one of the earliest known number systems to use a positional zero.
It is useful for history and archaeology students writing about Mesoamerica, museum exhibit designers labelling artefacts, and anyone preparing flavour text for an adventure novel set in pre-Columbian Yucatán. Long-tail queries it covers include "convert number to Maya numerals", "Maya base 20 vigesimal system" and "Maya zero shell symbol".
How it works
The converter divides the input by powers of 20 — but with one well-known quirk. In the standard Maya counting system, the second-from-bottom place is multiplied by 20 as expected, but for calendar use the third place becomes 18 × 20 = 360 (a tun) instead of 20 × 20 = 400. The tool defaults to the pure mathematical base-20 system; calendar mode is available as a switch.
Each digit from 0 to 19 is then rendered as the right combination of bars and dots: zero is a shell, 1-4 are that many dots, 5 is one bar, 6-9 are one bar with extra dots, 10 is two bars, 19 is three bars plus four dots. Place values are stacked vertically, highest on top.
Examples
0 → (shell)
7 → one bar + two dots
20 → one dot (in second place) over zero shell
2024 → 5 × 400 + 1 × 20 + 4 → one bar (5) / one dot (1) / four dots (4)
FAQ
Did the Maya really have a zero?
Yes, and it was a positional zero — used as a placeholder in a positional number system — centuries before the concept reached Europe. India had developed a positional zero independently around the same time.
Why is base 20 instead of base 10?
Many Mesoamerican cultures used a base-20 system, possibly derived from counting fingers and toes. Some languages still encode this: French uses "quatre-vingts" (four twenties) for 80.
What's the difference between the math and calendar systems?
In the calendar Long Count, the third place is 18 × 20 = 360 instead of 20 × 20 = 400, to give a useful approximation of the year. Above the third place, every higher place is multiplied by 20 again.
How are place values stacked visually?
Top to bottom, highest place value at the top. A 2-digit Maya number reads top-as-twenties, bottom-as-ones, the opposite of decimal "tens then ones" written left to right.
Why is the shell used for zero?
The shell symbol resembles an empty conch and conveys the idea of "nothing here" or "complete". It was used both as positional zero and as a separate concept of completion in calendar inscriptions.