Maya Numerals Converter
Convert numbers to Maya numerals and back, drawn as dots, bars and shells stacked in base 20. Choose plain vigesimal or the Long Count calendar, where the third place is 360.
How to Use
- Choose decimal to Maya or Maya to decimal.
- Pick the system: pure base 20, or the Long Count used for dates, whose third place is 18 × 20 = 360.
- Type a whole number, or the levels from the top down separated by dots, such as 5.1.6.
- Read the levels and the decimal value; the drawing stacks the levels with dots, bars and shells.
- Show Work divides by 20 (or by 18 at the winal place).
Worked Example
2026 in Maya numerals. Divide by 20: 2026 ÷ 20 = 101 r 6; 101 ÷ 20 = 5 r 1; 5 ÷ 20 = 0 r 5. Stacked from the top: 5.1.6. The top level is one bar (5), the middle one dot (1), the bottom a bar and a dot (6). Check: 5 × 400 + 1 × 20 + 6 = 2,026.
The same number as a Long Count day count. The third place is now 360, not 400: 2026 = 5 × 360 + 11 × 20 + 6, which is 5.11.6: 5 tun, 11 winal and 6 kʼin.
The common mistake: using 400 for calendar dates. In the Long Count, 18 winal (not 20) make a tun, so 1.0.0 is 360 days, not 400. Converting a date with pure base 20 gives a day count that is too large by 40 days for every tun.
Show Work
Formulas
Counting Days in the Maya World
The dot-and-bar numerals were used across Mesoamerica, by the Olmec and Zapotec before the Maya, and the Maya carved them on stelae and painted them in their books. The Dresden Codex, one of four Maya books to survive, has tables of Venus’s cycles and eclipses written in these numerals with a shell for zero.
The Long Count numbered days from a starting date in 3114 BC in the proleptic Gregorian calendar. Its mixed base, with 18 winal in a tun, kept the third unit close to a solar year of 365 days. The end of the 13th bʼakʼtun on 21 December 2012 was a calendar milestone, not, as some claimed, a prophecy of the end of the world.
About This Calculator
This converter writes whole numbers as Maya numerals in pure base 20 or as Long Count day counts, and reads dotted level notation back, checking that every level is in range. It draws the column of levels with dots, bars and shells and labels each with its place value, and in the Long Count with its unit name.
Everything runs in your browser; nothing is sent anywhere. To turn a Long Count into a calendar date, use the calendar converter.
Related calculators: Babylonian Numerals, Roman Numeral Converter, and Calendar Converter.
Frequently Asked Questions
How do Maya numerals work?
Each level shows a number from 0 to 19 with three signs: a dot for 1, a bar for 5 and a shell for 0. So 6 is a bar with one dot, and 19 is three bars and four dots. Levels are stacked vertically, the lowest worth 1, the next 20, the next 400 and so on, because the system is base 20.
How do I write 2026 in Maya numerals?
2026 = 5 × 400 + 1 × 20 + 6. Top level: 5, one bar. Middle level: 1, one dot. Bottom level: 6, a bar and a dot. Reading the levels from the top, 5.1.6.
What is the Long Count?
The Maya calendar counted days in a mixed base: 20 kʼin make a winal, but 18 winal make a tun of 360 days, then 20 tun a kʼatun (7,200 days) and 20 kʼatun a bʼakʼtun (144,000 days). Dates are written like 13.0.0.0.0, the end of the 13th bʼakʼtun on 21 December 2012, which is 1,872,000 days from the start of the count.
Did the Maya have a zero?
Yes. The Maya used a shell sign for zero as a placeholder in the Long Count by at least the 4th century, one of only a few independent inventions of zero, along with the Babylonian placeholder and the Indian digit that spread to Europe.
Why base 20?
Probably from counting fingers and toes. Many Mesoamerican languages count in twenties, and traces of base 20 survive elsewhere too: French quatre-vingts (four twenties) for 80, Danish numbers, and the English score.
How do I use the Maya Numerals Converter?
Just type or paste your value. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Is it free? Does it work without internet?
Yes to both. It is free with no sign-up, and once the page has loaded it keeps working even with no internet.
Where does my data go?
Nowhere — every calculation runs on your own device. Nothing you enter is uploaded, logged, or stored.
Common Use Cases
Years
2026 = 5.1.6: a bar, a dot, and a bar with a dot.
Long Count
13.0.0.0.0 is 1,872,000 days, the bʼakʼtun ending of 21 December 2012.
Day counts
2026 days in the Long Count is 5.11.6: 5 tun, 11 winal, 6 kʼin.
Teaching
19 is the largest single level: three bars and four dots.
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