The decimal mathematical system widely used today originated by counting with the fingers a person has. Counting with the fingers and toes started the Maya vigesimal system. So it is based on groups of twenty units. Just as the decimal system goes by 1, 10, 100, 1000, 10000, etc., the Maya vigesimal system goes 1, 20, 400, 8000, 160000, etc. While in the decimal system there are ten possible digits for each placeholder [0 - 9], in the Maya vigesimal system each placeholder has a possible twenty digits [0 - 19]. For example, in the decimal system 31 = 10 * 3 + 1 while in the vigesimal system 31 = 20 + 11. The Maya discovered and used the zero. Their zero is represented by an ovular shell.

Characteristics of The Maya Mathematical System:

a) It is vigesimal, this means that it is based on 20 units [0 - 19] instead of the 10 units [0 - 9] of the decimal system. This table shows the first 20 numbers and their Arabic equivalents. Learn the Maya mathematical system fast using THE MAYA CALCULATION ASSISTANT. The Mayan names for numbers are here.

b) It only uses three symbols, alone or combined, to write any number. These are: the dot - worth 1 unit, the bar - worth 5 units and the zero simbolized by a shell.
c) It also uses a vigesimal positioning system, in which numbers in higher places grow multiplied by 20´s instead of the 10´s of the decimal system, compare number 168,421 in both systems:

Place Number
Decimal value
Equals & is
Vigesimal value
Equals & is
6th 1 X 100,000= 100,000 3'200,000  
5th 6 X 10,000 = 60,000 160,000
4th 8 X 1,000 = 8,000 8,000
3rd 4 X 100 = 400 400
2nd 2 X 10 = 20 20
1st 1 X 1 = 1 1
TOTAL   Arabic 168,421 Maya 168,421

d) Numbers in the Maya system can be written vertically or horizontally. In vertical writing, the bars are placed horizontally and the dots go on top of them, in this case the vigesimal positions grow up from the base. When written horizontally, the bars are placed vertically and the dots go to their left and higher vigesimal positions grow to the left of the first entry.

The Maya would write 168,421 (previous example) as:

Thus when writing vertically the vigesimal positioning system, to write 20 a zero is placed in the first position (base) with a dot on top of it, in the second position. The dot in this place means one unit of the second order which equals to 20. To write 21, the zero would change to a dot (1 unit) and for the subsequent numbers the original 19 number count will follow in the first position. As they in turn reach 19 again another unit (dot) is added to the second position. Any number higher than 19 units in the second position is written using units of the third position. A unit of the third position is worth 400 (20 x 20), so to write 401 a dot goes in the first position, a zero in the second and a dot in the third. Positions higher than the third also grow multiplied by twenties from the previous ones. Examples of the numbers mentioned above follow:

(Note : the Maya made one exception to this order, only in their calendric calculations they gave the third position a value of 360 instead of 400, the higher positions though, are also multiplied by 20.)

Mayan Names For Numbers

0 xix im 10 lahun
1 hun 11 buluc 20 hun kal 400 hun bak
2 caa 12 lahca 40 ca kal 800 ca bak
3 ox 13 oxlahun 60 ox kal 1200 ox bak
4 can 14 canlahun 80 can kal 1600 can bak
5 hoo 15 hoolahun 100 hoo kal 2000 hoo bak
6 uac 16 uaclahun 120 uac kal 8,000 pic
7 uuc 17 uuclahun 140 uuc kal 160,000 calab
8 uaxac 18 uaxaclahun 200 ka hoo kal 3'200,000 kinchil
9 bolon 19 bolonlahun 300 ox hoo kal 64,000,000 alau

back to top