Mayan Numeral Calculator

Convert decimal numbers to the Mayan vigesimal (base-20) number system with visual dot-and-bar notation.

Enter a Decimal Number

= 1 (Dot)
= 5 (Bar)
= 0 (Shell)

Mayan Numeral Result

Decimal Number
--
in Mayan base-20
Number of Levels --
Base-20 Digits --

Step-by-Step Conversion

N = d_k * 20^k + ... + d_1 * 20 + d_0

The Mayan Number System

The ancient Maya civilization developed one of the most sophisticated number systems in the ancient world. Their vigesimal (base-20) system used only three symbols: a dot (representing 1), a bar (representing 5), and a shell symbol (representing 0). The Maya were among the first civilizations to develop the concept of zero independently.

How Mayan Numbers Work

Mayan numbers are written vertically, with the lowest place value at the bottom and higher place values stacked above. Each level represents a power of 20:

Level 0 (Bottom)

The ones place. Values from 0 to 19.

d0 x 200 = d0 x 1

Level 1

The twenties place. Values from 0 to 19, each worth 20.

d1 x 201 = d1 x 20

Level 2

The four-hundreds place. Values from 0 to 19, each worth 400.

d2 x 202 = d2 x 400

Level 3

The eight-thousands place. Values from 0 to 19, each worth 8,000.

d3 x 203 = d3 x 8000

Reading Mayan Numerals

The Three Symbols

  • Dot: Each dot represents the value 1. Up to 4 dots can appear in a single level.
  • Bar: Each horizontal bar represents the value 5. Up to 3 bars can appear in a single level.
  • Shell: The shell (or egg-shaped) symbol represents zero. It is used when a level has no value.

Combining Symbols

Within each level, dots are placed above bars. For example, the number 13 would be shown as 3 dots above 2 bars (3 + 5 + 5 = 13). The number 19 (the maximum single-level value) is 4 dots above 3 bars (4 + 5 + 5 + 5 = 19).

Historical Significance

The Mayan number system was used for astronomical calculations, calendar keeping, and architectural planning. Their accurate astronomical observations and sophisticated mathematical concepts, including the independent invention of zero around 350 CE, demonstrate remarkable intellectual achievement. The Long Count calendar used a modified version of this system to track vast periods of time.