Mayan Numeral Calculator — Decimal to Maya Base-20
Enter any whole number and see its Mayan representation using dots (each = 1), bars (each = 5) and the shell glyph (= 0) — with a full base-20 positional decomposition and animated glyph display.
Mayan base-20 notation (high → low): 4 · 12 · 7
Position 0 (× 1)
Position 1 (× 20)
Position 2 (× 400)
Sum of all positions
How does this calculator work?
Mayan numerals are base-20: digits 0–19 use a shell (0), dots (1 each), and bars (5 each). Position values are 1, 20, 400, 8 000, 160 000, … Divide the number by 20 repeatedly to find each digit. For example, 1 847 = 4×400 + 12×20 + 7×1 → written as 4 dots | 2 bars+2 dots | 1 bar+2 dots (top to bottom).
Formula
How this is calculated
The Maya developed a fully positional numeral system in a base-20 (vigesimal) place value structure — one of only a handful of civilisations to independently invent positional notation, alongside India and Mesopotamia. The system uses three symbols: a dot (● = 1), a horizontal bar (= 5), and an oval shell symbol (= 0). Digits from 0 to 19 are written by stacking bars at the bottom and dots on top.
Positional values increase by a factor of 20 from bottom to top: the bottom position represents ones (×1), the next represents twenties (×20), then four-hundreds (×400), eight-thousands (×8 000), and so on. To convert a decimal number, repeatedly divide by 20 and record the remainders — these become the Mayan digits from lowest to highest position. To decode a Mayan number, multiply each digit's face value (0–19) by the positional value (20^n) and sum.
The system was primarily used in the Long Count calendar for counting days, where the second position exceptionally counted only 18 (not 20) uinals per tun, making it a mixed-radix system for calendrical purposes. The pure base-20 arithmetic system used in everyday counting (described here) does not have that exception. Mayan numerals could represent arbitrarily large numbers simply by adding higher positions.
Frequently asked questions
One dot = 1; one bar = 5. To write a digit 0–19: stack bars at the bottom (each worth 5) and add dots above (each worth 1). Zero uses the shell symbol. For example, 17 = three bars (15) + two dots (2). Digits beyond 19 require a new higher position.
Historians believe base-20 systems arose from counting on both fingers and toes (vigesimal = "score-based"). The Maya and many other Mesoamerican peoples used base 20. French also retains traces of it ("quatre-vingts" = 4×20 = 80). By contrast, most modern systems are base-10 (decimal).
Almost. The Long Count calendar uses the same glyphs and base-20 grouping, but with one exception: the third position (tun) counts only 18 winals (18 × 20 = 360 days) instead of 20, to approximate the solar year. Pure arithmetic outside the calendar uses true base-20 throughout.
Also known as
TG we-Calculate Editorial Team. (2026). Mayan Numeral Calculator — Decimal to Maya Base-20 [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/mayan-numeral-calculator
TG we-Calculate Editorial Team. "Mayan Numeral Calculator — Decimal to Maya Base-20." TG we-Calculate. 2026. https://we-calculate.com/calculator/mayan-numeral-calculator.
TG we-Calculate Editorial Team, "Mayan Numeral Calculator — Decimal to Maya Base-20," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/mayan-numeral-calculator
@misc{wecalculate_mayan_numeral_calculator, title = {Mayan Numeral Calculator — Decimal to Maya Base-20}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/mayan-numeral-calculator}}, year = {2026}, note = {TG we-Calculate} }
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