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Mayan Numerals

Tool to convert to/from Mayan numbers system. The Maya numeral system uses a mix of base 20 (vigesimal) and base 5 (and also 360) numerals

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Mayan Numerals -

Tag(s) : Numeral System, History, Symbol Substitution

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# Mayan Numerals

## Mayan to Decimal/Arabic Numbers Converter

 Mode Base 20 then 360 (see FAQ) Base 20 (Classical Vigesimal System)

## Decimal/Arabic to Mayan Numbers Converter

 Displaynumbers With images (symbols above) With dashes - and dots . With symbols ➖ and • With Unicode symbols 𝋮 (v14+ needed)
 Mode Base 20 then 360 (see FAQ) Base 20 (Classical Vigesimal System)

## Answers to Questions (FAQ)

### What are Maya numerals? (Definition)

In the Maya culture, numbers consist of simple glyphs/symbols: the dots . and the - (horizontal) lines.

The mathematical peculiarity of Maya numeration is the writing of numbers in base 20 (called vicesimal or vigesimal base) contrary to the writing in base 10 usual nowadays.

In the Maya civilization, the writing of numbers is generally vertical (the units are placed under the tens/twenties, under the (four-)hundreds etc.)

### How to write Maya numbers?

In Mayan culture, numbers are written in base 20 (called vigesimal base). The 20 Mayan digits are composed of simple glyphs/symbols that can be added: dots . associated to value $1$ (units) and horizontal bars - associated to value $5$. The mayan civilization used a vertical writing for the numbers (units under tens/twenties, under (four-)hundreds, etc.).

Example: The number $14$ (English/hindu-arabic numeral in base 10) is written in Mayan (2 bars and 4 dots: $2 \times 5 + 4 \times 1 = 14$)

Example: $26$ is written (in 2 rows: 1 dot on the first line: $1 \times 20 = 20$ and 1 dot and 1 bar on the second line $1 + 5 = 6$, total $20 + 6 = 26$)

Example: $0$ (zero) is noted (originally a shell shape, but some say an egg or an American football/rugby ball)

From 360, the writing of Mayan numbers diverges. The written traces show 2 notations, including a specific rule, a modified vigesimal system particularly when they spoke of dates. The variant takes place at the third tier/line, which then stops at $360$ (base 10).

Example: In base 20 $360$ is normally written , but in modified base 20, $360$ is written (which equals $400$ in unmodified base 20). In the same way, the number $7200$ is written $8000$.

### How to convert Mayan numbers?

Converting Mayan numerals to English/Arabic numerals is made by counting dots and bars symbols on each rows and treat it as base 20 writing, before converting it to base 10.

Example: a single row with 2 dots and 3 bars: $2 \times 1 + 3 \times 5 = 17$

Example: A number on two rows with 1 dot then (under) 2 dots: $1 \times 20 + 2 \times 1 = 22$

For numbers that are greater than or equal to 360, be sure to know the variant used.

### How to write a date with Mayan numbers?

The dates in Maya are based on the kin (plural kinob), which is 1 day, then the uinal (plural unialob) which is 20 days, the tun, an 18 uinalob period which is therefore 360 days, about 1 year (365.24 days), then the katun (20 tunob = 7200 days = about 20 years), then the baktun (20 katunob, 144000 days = about 394 years). Day 0 seems to match August 11, 3114 BC of our era (precision to be relativised with the Gregorian / Julian calendar chosen)

To write a birthdate or anniversary date in a contemporary way, dCode recommends to use the values of the 3 numbers (day, month, year) written in Maya and separated by a dash - or a bar / (slash), the year with the font changed to 360.

### How to count using Mayan numerals?

The first Mayan numbers are:

For others maya numbers (up to 1000, 10000, 100000, 1000000 etc.), use the form above.

### Why does maya notation change after 19 (from 20)?

Today, for counting, base 10 is used, up to 9, the 10 digits 0,1,2,3,4,5,6,7,8,9 use only one character/symbol /glyph, beyond 9, it is necessary to use 2 symbols/numbers to write 10 (a 1 and a 0). Similarly, the Mayan numeral uses base 20 to count, so beyond 19 it is necessary to use 2 symbols/glyphs.

### Why does maya notation use base 20?

It is assumed that men today count in base 10 because they have 10 fingers on their hands. It is likely that the Maya considered a process including the toes, or 20 fingers.

### Why is 20 not written with 4 bars?

It's mostly unusual and confusing so avoid it. It's a bit like asking the question why not write 10 with a new symbol, like , some may understand, some may not.

### How to recognize Mayan numbers?

Maya numeration uses generally stacked lines and dots.

The Mayan civilization lived in Central America around -2000 BC as their pyramids testify.

Although there are similarities, the Mayan civilization is different from the Aztecs or the Incas.

Any reference to Mexico, Belize, Guatemala, El Salvador or Honduras (current areas where the Mayans lived) are clues.

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Mayan Numerals on dCode.fr [online website], retrieved on 2023-09-27, https://www.dcode.fr/mayan-numbers

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