Mayan Numerals Converter

Convert between decimal and ancient Maya numbers

Convert numbers between the modern decimal system and the ancient Mayan vigesimal (base-20) number system using traditional symbols.

Example Conversions

Try these examples to understand Mayan numerals

Simple Number

decimalToMayan

Convert a basic number to Mayan

Decimal: 19

Result: —••••

Multiple Levels

decimalToMayan

Number requiring multiple position levels

Decimal: 365

Result: •|—•••|⌘

Simple Mayan

mayanToDecimal

Convert Mayan symbols to decimal

Mayan: —•••

Result: 9

Complex Mayan

mayanToDecimal

Multi-level Mayan number

Mayan: ••|—••|•••

Result: 463

Other Titles
Understanding Mayan Numerals: A Comprehensive Guide
Explore the ancient Maya vigesimal number system and learn to convert between decimal and Mayan numerals

What are Mayan Numerals?

  • The Vigesimal System
  • Historical Context
  • Symbol Meanings
Mayan numerals represent one of the most sophisticated number systems developed by ancient civilizations. The Maya civilization, which flourished in Mesoamerica from approximately 2000 BCE to 1500 CE, created a vigesimal (base-20) number system that was remarkably advanced for its time.
The Vigesimal Foundation
Unlike our decimal (base-10) system, the Mayan system is based on 20. This likely originated from counting with both fingers and toes, providing a natural base-20 foundation. Each position in a Mayan number represents a power of 20, making it fundamentally different from our positional decimal system.
Sacred and Practical Applications
The Maya used their number system for astronomical calculations, calendar systems, and architectural measurements. Their mathematical precision allowed them to predict eclipses, track planetary movements, and create incredibly accurate calendars that rival modern systems.
Symbol System
Mayan numerals use three basic symbols: a dot (•) representing 1, a horizontal bar (—) representing 5, and a shell-like symbol (⌘) representing 0. These symbols can be combined within each positional level to represent numbers 0-19.

Basic Symbol Examples

  • • = 1
  • —— = 10
  • ⌘ = 0
  • —••• = 8

Step-by-Step Guide to Converting Mayan Numerals

  • Decimal to Mayan Conversion
  • Mayan to Decimal Conversion
  • Multi-level Numbers
Converting between decimal and Mayan numerals requires understanding the vigesimal positional system. Each level represents increasing powers of 20, starting from 20⁰ = 1 at the bottom.
Converting Decimal to Mayan
To convert a decimal number to Mayan: 1) Divide the number by 20 repeatedly, keeping track of remainders. 2) The remainders represent the values for each level, starting from the bottom. 3) Convert each remainder (0-19) to Mayan symbols using dots, bars, and shells.
Converting Mayan to Decimal
To convert Mayan to decimal: 1) Identify each level from bottom to top. 2) Convert each level's symbols to its decimal value (0-19). 3) Multiply each level's value by the appropriate power of 20. 4) Sum all the products to get the final decimal number.
Reading Multi-level Numbers
Mayan numbers are written vertically, with the most significant digit at the top. Each level can contain 0-19 using combinations of dots and bars. When a level equals 0, the shell symbol is used.

Conversion Examples

  • 365 = 1×20² + 8×20¹ + 5×20⁰
  • •|—•••|—••• = 1×400 + 8×20 + 8×1 = 568
  • ⌘ represents an empty level (zero)

Real-World Applications of Mayan Numerals

  • Archaeological Studies
  • Educational Value
  • Cultural Preservation
Understanding Mayan numerals provides valuable insights into ancient Maya civilization and their mathematical achievements. This knowledge has practical applications in various fields today.
Archaeological and Historical Research
Archaeologists and historians use Mayan numeral knowledge to decipher ancient texts, stelae, and codices. Understanding the number system helps interpret Maya astronomical observations, historical dates, and mathematical concepts recorded in stone and bark paper.
Mathematics Education
Studying alternative number systems like Mayan numerals helps students understand that mathematical concepts can be expressed in various ways. It demonstrates the cultural relativity of mathematical notation while reinforcing universal mathematical principles.
Cultural Heritage and Tourism
Knowledge of Mayan numerals enhances appreciation of Maya cultural heritage. Museums, educational centers, and archaeological sites use this information to provide richer experiences for visitors interested in ancient civilizations.

Practical Applications

  • Deciphering dates on Maya stelae
  • Understanding Maya calendar calculations
  • Teaching alternative number systems
  • Cultural tourism enhancement

Common Misconceptions and Correct Methods

  • System Limitations
  • Symbol Combinations
  • Position Values
Several misconceptions exist about Mayan numerals that can lead to errors in conversion and interpretation. Understanding these common mistakes helps ensure accurate work with the system.
Misconception: Unlimited Symbol Stacking
A common error is thinking you can stack unlimited dots and bars in a single level. In reality, each level can only represent values 0-19. Once you reach 20, you must move to the next higher level. For example, 25 is not written as five bars in one level, but as •|— (1 in the twenties place, 5 in the ones place).
Misconception: Horizontal Reading
Unlike many modern writing systems, Mayan numerals are read vertically, not horizontally. The bottom level represents the ones place (20⁰), the next level up represents twenties (20¹), then four-hundreds (20²), and so on.
Misconception: Decimal Position Values
The biggest mistake is applying decimal thinking to the vigesimal system. Each position represents powers of 20, not powers of 10. The positions are: 1, 20, 400, 8000, 160000, etc., not 1, 10, 100, 1000 as in decimal.

Correct vs. Incorrect Methods

  • Wrong: ————— for 25
  • Correct: •|— for 25
  • Wrong: Reading left to right
  • Correct: Reading bottom to top

Mathematical Derivation and Advanced Examples

  • Positional Notation Theory
  • Large Number Conversions
  • Calendar Mathematics
The mathematical foundation of Mayan numerals lies in positional notation with base 20. Understanding this system deeply reveals the sophistication of Maya mathematical thinking.
Positional Value Formula
Any Mayan number can be expressed as: N = Σ(dᵢ × 20ⁱ) where dᵢ is the digit value (0-19) at position i, and i starts from 0 at the bottom level. This formula allows conversion of any Mayan number to decimal.
Large Number Examples
Consider the number 9,999 in Mayan numerals: 9999 ÷ 8000 = 1 remainder 1999, 1999 ÷ 400 = 4 remainder 399, 399 ÷ 20 = 19 remainder 19, 19 ÷ 1 = 19 remainder 0. This gives us •|••••|——————••••|——————••••.
Calendar Applications
The Maya used their number system for complex calendar calculations. The Long Count calendar uses modified vigesimal notation where the third position represents 360 (not 400) to align with their 360-day approximate year. This shows how they adapted their mathematical system for astronomical purposes.

Mathematical Examples

  • Basic: 23 = •|•••
  • Complex: 1,234 = •••|•|——••••
  • Calendar: 9.12.19.14.3 (Long Count date)
  • Large: 160,000 = •|⌘|⌘|⌘|⌘