Maya Numbers: Dots, Bars, the Shell Zero and Base 20 (with 2026 Worked Out)

Maya numbers use three signs: a dot for 1, a bar for 5 and a shell-shaped sign for 0. Numbers from 1 to 19 are dots and bars added together; from 20 upward the places stack vertically in powers of 20 (1s at the bottom, then 20s, 400s and 8,000s), so 20 is a dot written above a shell.

In short: Count dots as 1 and bars as 5, at most four dots and three bars in one place. Each place up the column is worth 20 times the one below. To write a big number, divide by 400 and 20 and draw each remainder. Worked out below: 2026 = 5 | 1 | 6 (a bar, a dot, a dot over a bar). Calendar dates are the exception: their third place counts 360, not 400.

The three signs

The teachers’ guidebook to the Casa K’inich Maya Learning Center in Copán, Honduras (Copan Association, 2005) puts it in one line: the ancient Maya wrote their base numbers (0 to 19) with three symbols, a shell-like oval for zero, a dot for 1 unit and a bar for 5 units. Mark Pitts’s Maya Numbers and the Maya Calendar, a teaching book hosted by UC Berkeley’s Multiverse project, gives the same rule: count each dot as one and each bar as five, and use the right number of each to add up to the number you want.

• Zero. Pitts shows four popular ways the Maya wrote zero and notes that the last two look like shells: shells are often empty containers, holding nothing. He counts the invention of zero among the great achievements of the ancient Maya.
• Base 20. Pitts says the Maya based their system on 20 instead of 10, from a total of 20 fingers and toes. The STARLAB planetarium curriculum, also on the Multiverse site, says the same.
• Bars and dots. Pitts notes that the Maya wrote numbers with horizontal bars and the dots above them, and could also draw the bars vertically; they also used fancier number glyphs.

Maya numbers 0 to 20

Within a single place, write the dots above the bars (the horizontal style Pitts uses). Pitts’s rule is never more than four dots in one group, since five dots make a bar; and as four bars would make 20, which moves up a place, a single place never holds more than three bars.

Rule from Pitts, Casa K’inich and STARLAB; the Smithsonian’s Color and Discover activity book prints the same chart as glyphs for 0 to 29.

Why 20 needs two places. Pitts explains that the Maya used zero as a place holder, as we do in 10. The number 20 has one twenty and zero ones, so it is written as a dot in the second position and a shell in the first, with the two signs clearly separated and the dot higher than the shell. He puts the places in boxes for learners and notes that the Maya did not: the spacing alone showed which place a sign belonged to. That spacing is the difference between 11 (one dot over two bars, in one place) and 30 (one dot in the 20s place, two bars in the 1s place).

Place values: 1, 20, 400, 8,000

To read a stacked number, multiply what is drawn in each place by that place’s value and add. Pitts’s own examples:

The Casa K’inich guide adds a warning about reading digits the decimal way: Maya digits 3, 2, 8 stacked in the 400s, 20s and 1s places make 3 x 400 + 2 x 20 + 8 = 1,248, not 328.

Worked examples: 2026 and a birth year

The method is the same for any number under 8,000: divide by 400, then divide what is left by 20, and draw each result in its place. These examples are computed for this page with that method.

2026.

• 2026 divided by 400 = 5, remainder 26. Draw 5 (one bar) in the 400s place.
• 26 divided by 20 = 1, remainder 6. Draw 1 (one dot) in the 20s place.
• 6 is left. Draw 6 (one dot over one bar) in the 1s place.
• Check: 5 x 400 + 1 x 20 + 6 = 2,000 + 20 + 6 = 2026.

1990, a birth year.

• 1990 divided by 400 = 4, remainder 390. Draw four dots in the 400s place.
• 390 divided by 20 = 19, remainder 10. Draw four dots over three bars in the 20s place.
• 10 is left. Draw two bars in the 1s place.
• Check: 4 x 400 + 19 x 20 + 10 = 1,600 + 380 + 10 = 1990.

2000, with zeros.

• 2000 divided by 400 = 5, remainder 0: one bar in the 400s place, then a shell in the 20s place and a shell in the 1s place.
• Check: 5 x 400 + 0 + 0 = 2000.

Calendar dates use 360, not 400

The plain base-20 places above are for counting. The STARLAB curriculum notes that the third place would be 400 except for measurements of time, which used the third place as 360. Pitts explains why: in the Long Count, the day (k’in) is grouped into a winal of 20 days, and 18 winals make a tun of 360 days. After that the count is in 20s again: 20 tuns make a k’atun, and 20 k’atuns a b’ak’tun. Worked through, the five places of a Long Count date are worth 144,000 days (a b’ak’tun, 20 x 7,200), 7,200 (a k’atun, 20 x 360), 360, 20 and 1, not the counting values in the table above. How the 260-day Cholq’ij and the 365-day Haab fit together, and what the day names mean, is on our Maya calendar (Cholq’ij) explainer.

Counting aloud in a Mayan language today

The Casa K’inich guidebook teaches counting in Ch’orti’, the Mayan language spoken around Copán, with recordings it says were made with girls and boys from Jocotán, Guatemala: jun (1), cha (2), ush (3), chan (4), jo (5), written as a Spanish speaker would say them. At the site, it suggests looking for bars and dots on the stelae and saying the numbers aloud. For carved Maya stelae on the Guatemalan side of the border, see our Quiriguá guide and our Tikal guide. The K’iche’ Maya creation book is explained on our Popol Vuh page.

For classroom use, the Milwaukee Public Museum’s educator guide asks students to find a Maya number on an exhibited object and write it, and the Smithsonian’s activity book asks children to write their own age and a friend’s in Maya numbers and add them.

Sources

All read 10 November 2026.

• Mark Pitts, Maya Numbers and the Maya Calendar (PDF), hosted by UC Berkeley’s Multiverse project: dots, bars, zero, base 20, place values and examples, the Long Count units.
• STARLAB curriculum (PDF), hosted by UC Berkeley’s Multiverse project: base 20, the third place as 360 for time.
• Copan Association, Casa K’inich guidebook (PDF), 2005: three symbols, the 1,248 example, counting in Ch’orti'.
• Smithsonian, Color and Discover: A Journey Through Central America’s Past (PDF): number chart 0 to 29 and age exercise.
• Milwaukee Public Museum, Maya Educators Guide (PDF), February 2018: classroom exercises.