Mayan Numeral
Convert any decimal number to its ancient Mayan vigesimal (base-20) representation using dots, lines, and shell symbols. Free online Mayan numeral converter for students, historians, and math enthusiasts.
About This Calculator
The Mayan Numeral Converter converts any positive decimal (base-10) whole number into the ancient Mayan vigesimal numeral system. The Maya civilization developed one of the earliest fully functional place-value systems in human history, using a base-20 (vigesimal) counting system that supported advanced astronomical calculations, calendar keeping, and commerce across Mesoamerica for over a thousand years.
To convert a number, the calculator repeatedly divides it by 20 to extract each base-20 digit. Every digit from 0 to 19 is then rendered using three symbols: dots ● for units of 1, horizontal lines ─ for units of 5, and a shell ◎ for zero. For example, the number 344 becomes 17x20¹ + 4x20^0, which is displayed as three lines and two dots above four dots -- representing the Mayan reading of 344. The glyphs are stacked vertically from bottom (20^0 position) to top (highest power of 20), following authentic Mayan notation.
Usage notes: Enter any positive whole number. The output shows both the Mayan stacked glyph representation and the vigesimal digit grouping (e.g., 17:4 for 344). Each level of the stack represents a power of 20, making it easy to understand the base-20 place values.
Frequently Asked Questions
How does the Mayan numeral converter work?
The calculator takes a decimal (base-10) number and repeatedly divides it by 20 to extract the vigesimal (base-20) digits from right to left. Each digit between 0 and 19 is then converted into a combination of Mayan symbols: dots (each representing 1), lines (each representing 5), and a shell symbol representing 0. The final output stacks the symbols vertically from bottom (20^0) to top (20ⁿ) following the authentic Mayan notation.
What symbols did the Mayans use for numbers?
The Mayan numeral system used just three basic symbols: a dot (●) representing 1, a horizontal line (─) representing 5, and a stylized shell (◎) representing 0. Numbers 1 through 4 were written with the corresponding number of dots. The number 5 was a single line, and numbers 6 through 19 combined lines and dots -- for example, 17 was three lines and two dots. For numbers 20 and above, they stacked these glyphs vertically in a place-value system where each level represented a power of 20.
What is the vigesimal (base-20) number system?
The vigesimal system is a base-20 numeral system used by the ancient Maya civilization for astronomy, calendar calculations, and commerce. Unlike the decimal (base-10) system we use today, each digit position in a vigesimal number represents a power of 20 instead of 10. For example, the number 344 in decimal equals 17x20¹ + 4x20^0, which is written as a glyph for 17 above a glyph for 4 in Mayan notation.
Can I convert large numbers to Mayan numerals?
Yes, this calculator supports any positive whole number up to several billion. Larger numbers will produce taller Mayan numeral stacks with additional vigesimal place-value levels. Each level represents a higher power of 20, stacked from bottom (20^0) to top (20ⁿ). The result also shows the base-20 digit grouping separated by colons for easy understanding.
Did the Mayans have a symbol for zero?
Yes, the Maya were one of the first civilizations in the world to develop a concept and symbol for zero, which they represented as a shell or seashell glyph (◎). This was a revolutionary mathematical achievement that allowed their place-value vigesimal system to function properly, much like our modern zero enables decimal place values. Their use of zero dates back to at least the 3rd century CE, predating its use in European mathematics.
How do Mayan numerals differ from Babylonian numerals?
Both civilizations developed base-based place-value systems, but they used different bases and symbols. The Babylonians used a sexagesimal (base-60) system with wedge-shaped cuneiform symbols representing 1 and 10. The Maya used a vigesimal (base-20) system with dots for 1, lines for 5, and a shell for 0. Babylonians wrote numbers horizontally with place values separated by spaces, while Mayans stacked their glyphs vertically.
Is this Mayan numeral converter free to use?
Yes, all calculators on Calculy are completely free to use with no registration, subscription, or hidden fees. You can convert any decimal number to Mayan numerals instantly in your browser with no server-side processing.