Mayan Numerals Converter
Convert between decimal numbers and ancient Mayan vigesimal (base-20) numerals
Convert Numbers to Mayan Numerals
Choose conversion direction
Enter a positive integer or simple expression (supports +, -, *, /)
Please enter a valid number
Example Conversions
Example 1: Number 344
Decimal: 344
Division process:
344 ÷ 20 = 17 remainder 4
17 ÷ 20 = 0 remainder 17
Base-20: 17 4
Mayan: Three lines + two dots (17) over four dots (4)
Example 2: Number 52
Decimal: 52
Calculation: 52 = 2×20¹ + 12×20⁰
Base-20: 2 12
Mayan: Two dots (2) over two lines + two dots (12)
Example 3: Expression 72+19
Expression: 72 + 19 = 91
Division: 91 ÷ 20 = 4 remainder 11
Base-20: 4 11
Mayan: Four dots (4) over two lines + one dot (11)
Mayan Symbol Guide
Dot
Represents 1
Line
Represents 5
Shell
Represents 0
Vigesimal System
Base-20
Uses 20 symbols (0-19)
Like fingers and toes!
Vertical Layout
Read from top to bottom
Higher powers on top
Infinite Range
Can represent any number
Add more levels as needed
Quick Tips
5 dots = 1 line (combine automatically)
Maximum 4 lines per level (19 max)
Used for astronomy and calendars
No negative numbers in original system
Understanding the Mayan Numeral System
Historical Background
The Mayan civilization developed one of the most sophisticated numeral systems in the ancient world. Their vigesimal (base-20) system was used for complex astronomical calculations, calendar systems, and architectural measurements. Unlike our decimal system based on 10 fingers, the Mayan system likely originated from counting both fingers and toes.
Symbol Meaning
- •Dot (●): Represents the value 1
- •Line (═══): Represents the value 5
- •Shell (🐚): Represents zero, a revolutionary concept
Conversion Process
Decimal → Base-20 → Mayan Symbols
Divide by 20 repeatedly, read remainders from bottom to top
Mathematical Formula
N = a₀×20⁰ + a₁×20¹ + a₂×20² + ...
Where each aᵢ is a digit from 0 to 19
Advanced Examples and Applications
Large Number Example: 3,193,619
Step-by-step division:
3,193,619 ÷ 20 = 159,680 remainder 19
159,680 ÷ 20 = 7,984 remainder 0
7,984 ÷ 20 = 399 remainder 4
399 ÷ 20 = 19 remainder 19
19 ÷ 20 = 0 remainder 19
Base-20: 19 19 4 0 19
Powers: 19×20⁴ + 19×20³ + 4×20² + 0×20¹ + 19×20⁰
Astronomical Applications
- Venus Calendar: 584-day cycles calculated precisely
- Solar Year: 365.2420 days (remarkably accurate)
- Long Count: Dates spanning millions of years
- Eclipse Prediction: Complex astronomical tables
Historical Note: The Mayan understanding of zero predates its use in Europe by several centuries, making their mathematical system remarkably advanced for its time.