The Mayan Numerals

maya7.tif (35990 bytes)

The Maya of Central America used a zero hundreds of years before 876 AD, its earliest known use in India. When Europeans arrived in the Americas, they found that the abacus was in use in both Mexico and Peru.

Instead of ten digits like we have today, the Maya used a base number of 20. Base twenty was also used in their calendar, developed by astronomers for keeping track of time.  They used a system of bar and dot as "shorthand" for counting. A dot stood for one and a bar stood for five.

In the following table, you can see how the system of dots and bars works to create Mayan numerals and the equivalent Roman numerals 0-19.

0.gif (470 bytes)
1.gif (187 bytes)
2.gif (225 bytes)
3.gif (261 bytes)
4.gif (288 bytes)
5.gif (195 bytes)
6.gif (255 bytes)
7.gif (303 bytes)
8.gif (314 bytes)
9.gif (363 bytes)
10.gif (266 bytes)
11.gif (323 bytes)
12.gif (362 bytes)
13.gif (395 bytes)
14.gif (410 bytes)
15.gif (304 bytes)
16.gif (374 bytes)
17.gif (399 bytes)
18.gif (437 bytes)
19.gif (460 bytes)

Because the base of the number system was 20, larger numbers were written down in powers of 20. We do that in our decimal system too: for example 32 is 3*10+2. In the Maya system, this would be 1*20+12, because they used 20 as base.

Numbers were written from bottom to top. Below you can see how the number 32 was written:

20's 1.gif (187 bytes)(1)
1's 12.gif (362 bytes)(12)

It was very easy to add and subtract using this number system, but they did not use fractions. Here's an example of a simple addition:

8000's 1.gif (187 bytes) 1.gif (187 bytes) 2.gif (225 bytes)
400's 3.gif (261 bytes) 6.gif (255 bytes) 9.gif (363 bytes)
20's 12.gif (362 bytes) + 1.gif (187 bytes) = 13.gif (395 bytes)
1's 9.gif (363 bytes) 5.gif (195 bytes) 14.gif (410 bytes)
9449 + 10425 = 19874

As you can see, adding is just a matter of adding up dots and bars! Maya merchants often used cocoa beans, which they layed out on the ground, to do these calculations.

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Copyright © 1997 Saxakali
Last modified: July 09, 2000

The data for this page was provided by Michielb, a graduate astronomy student living in The Netherlands. It is based on a written summary of a lecture Dawn Jenkins gave on the topic of Maya Astronomy at the February 13, 1995, at the regular meeting of the Cuyahoga Astronomical Association. The HTML version was made by Michiel Berger, who added some information and graphics here and there by Michielb.