Mayan Numerals Converter
Convert between decimal numbers and ancient Mayan vigesimal (base 20) numerals
Enter a positive integer to convert to Mayan numerals (0-7999)
How to Use This Calculator
Select Conversion Direction
Choose whether you want to convert from decimal to Mayan or from Mayan to decimal.
Enter Your Value
For decimal to Mayan: enter a positive integer. For Mayan to decimal: enter the Mayan numeral using ● (dots) for ones and ━ (bars) for fives, with each level on a separate line.
Click Convert
Press the Convert button to see the result. Mayan numerals are displayed vertically, read from bottom to top.
Formula
Mayan Numeral = Σ(di × 20i)
where di = digit in position i (0-19), and i increases from bottom to top
Base 20 (Vigesimal) System:
The Mayans used a base-20 (vigesimal) positional numeral system, similar to how we use base-10 (decimal).
Digit Representation:
- ● (dot) = 1
- ━━━ (bar) = 5
- ● (shell) = 0
- Numbers 0-19 are represented by combinations of dots and bars
Positional Notation:
Mayan numerals are written vertically. The bottom level represents 20⁰ (ones), the next level up represents 20¹ (twenties), then 20² (four hundreds), and so on.
Example: Converting 123 to Mayan
123 = 6 × 20 + 3
So it's represented as: Level 1 (bottom): ●●● (three dots = 3)
Level 2 (top): ● ━━━ (one dot + one bar = 6)
About Mayan Numerals Converter
The Mayan numeral system was developed by the ancient Maya civilization in Mesoamerica, dating back to around 2000 BCE. This vigesimal (base-20) system was one of the most advanced mathematical systems in the pre-Columbian Americas and is notable for being the first civilization to use zero as a placeholder.
Historical Significance
The Mayan numeral system was revolutionary for several reasons. Most importantly, the Maya developed the concept of zero independently, centuries before it appeared in other civilizations. They used a shell symbol (●) to represent zero, which was crucial for their positional number system.
How Mayan Numerals Work
- Base 20: Each position represents a power of 20
- Three Symbols: Dots (●) for ones, bars (━━━) for fives, and shells (●) for zero
- Vertical Writing: Numbers are written vertically, read from bottom to top
- Positional: Values multiply by 20 as you move up each level
The Vigesimal System
The Mayan base-20 system likely originated from counting fingers and toes (20 digits total). However, in some contexts, particularly for calendar dates, the third position used 18 instead of 20, creating a modified vigesimal system that better matched their 360-day calendar year.
Mayan Calendar System
The Mayans used their numeral system extensively for their sophisticated calendar systems:
- Haab: A 365-day solar calendar (18 months of 20 days + 5 extra days)
- Tzolk'in: A 260-day ritual calendar (13 × 20)
- Long Count: A linear count of days from a mythological creation date
Reading Mayan Numerals
Mayan numerals are read from bottom to top. The bottom level represents ones (20⁰), the next level up represents twenties (20¹), then four hundreds (20²), eight thousands (20³), and so on. Each level uses dots and bars to represent values from 0 to 19.
For example, to write the number 123, you would need 6 twenties (6 × 20 = 120) plus 3 ones (3). So the bottom level would have three dots (● ● ●), and the level above would have one dot and one bar (● ━━━), representing 1 + 5 = 6.
Modern Understanding
Today, the Mayan numeral system is studied for its historical significance and mathematical elegance. It demonstrates that sophisticated mathematical concepts, including positional notation and zero, were developed independently in the Americas. The system's influence can be seen in modern computing and mathematics education.
Frequently Asked Questions
Why did the Mayans use base 20?
The base-20 system likely originated from counting all fingers and toes (20 digits total). This made it natural for the Mayans to group numbers by twenties. Some scholars also suggest it may relate to their calendar system.
Did the Mayans invent zero?
Yes! The Mayans independently developed the concept of zero around 350 CE, using a shell symbol to represent it. This was centuries before zero appeared in other civilizations. However, their use of zero was primarily as a placeholder in their positional system, not as a number for calculation like in modern mathematics.
Why are Mayan numerals written vertically?
Mayan writing, including numerals, was typically written vertically in columns, read from top to bottom and left to right. This vertical orientation was standard for Mayan script and inscriptions on monuments and codices.
What is the modified vigesimal system?
In the Long Count calendar, the third position (representing "months") used 18 instead of 20. This created 18 × 20 = 360 days, which closely matched their 360-day calendar year plus 5 "nameless days." So it was 20 × 18 × 20 × 20... instead of 20 × 20 × 20...
How large numbers could the Mayans represent?
Theoretically, the Mayan system could represent arbitrarily large numbers by adding more levels. In practice, historical inscriptions show numbers in the millions. The Long Count calendar, for example, used this system to track days over very long periods, allowing them to calculate dates thousands of years in the past or future.