Mayan Numeral Converter

What is the Mayan Numeral System?

The ancient Maya civilization developed one of the most sophisticated, mathematically elegant positional number systems in human history. Operating on a vigesimal (base-20) base rather than the decimal (base-10) system common today, Mayan mathematics was capable of recording astronomical cycles, counting millions of days, and performing arithmetic with remarkable simplicity.

The Maya were also among the earliest civilizations to independently discover and systematically use the concept of zero (represented by a stylized turtle shell or snail shell glyph) as both a placeholder and a numerical value.

The Three Core Mayan Symbols

Every Mayan number from 0 to 19 is built from just three intuitive geometric symbols:

• A Shell Glyphs ($\text{𝋠}$): Represents the quantity zero ($0$).
• A Dot ($\bullet$): Represents the quantity one ($1$). Between 1 and 4 dots are placed horizontally in a row.
• A Horizontal Bar (—): Represents the quantity five ($5$). Up to 3 horizontal bars are stacked below the dots.

For example, the number $8$ is written as three dots over one horizontal bar ($3 + 5 = 8$), and the number $19$ (the largest single-digit Mayan numeral) is written as four dots over three horizontal bars ($4 + 3 \times 5 = 19$).

Positional Base-20 Values

While modern Arabic numerals write places horizontally from left to right (ones, tens, hundreds), Mayan numerals are written vertically from bottom to top in ascending powers of 20:

• Level 1 (Bottom): Units place ($20^0 = 1$)
• Level 2: Twenties place ($20^1 = 20$, known as K'al)
• Level 3: Four-hundreds place ($20^2 = 400$, known as Bak')
• Level 4: Eight-thousands place ($20^3 = 8,000$, known as Pic)
• Level 5: Hundred-sixty-thousands place ($20^4 = 160,000$, known as Calab)

For instance, to represent the decimal number $2026$:

$$2026 = 5 \times 400 + 1 \times 20 + 6 \times 1$$

In Mayan notation, this is displayed as a three-level vertical stack: Level 3 has a single bar ($5$), Level 2 has a single dot ($1$), and Level 1 has one dot over a bar ($6$).

The Mayan Long Count Calendar System

When recording astronomical dates in the Long Count calendar, the Maya modified the third position so that it multiplied by 360 instead of 400. This closely approximated the solar year of 365.24 days:

• Kin: 1 single day ($1$)
• Uinal: 20 Kin ($20$ days / 1 Maya month)
• Tun: 18 Uinal ($18 \times 20 = 360$ days / 1 Maya year)
• Katun: 20 Tun ($20 \times 360 = 7,200$ days / approx. 19.7 years)
• Baktun: 20 Katun ($20 \times 7,200 = 144,000$ days / approx. 394.3 years)

You can switch between the Pure Vigesimal system and the Long Count Calendar system using the dropdown options in our converter.

How to Use the Mayan Numeral Converter

1. Enter a Decimal Number: Type any positive integer into the input box or pick from quick presets.
2. Select the Calculation Mode: Choose between standard mathematical base-20 or the Long Count calendar system.
3. Inspect the Glyphs: Observe the authentic vertical stack of dots, bars, and shell zero glyphs rendered in real time.
4. Copy the Breakdown: Copy the text export containing individual positional weights and mathematical decompositions.

Explore other ancient numbering systems with our Roman Numerals Converter and base converters like the Binary Calculator.