How the Mayan number system works
The Mayan numeral system used three symbols: a dot (1), a bar (5) and a shell (0). Each glyph can represent 0-19: bars stack up to 3 (15), then dots are added. Digits are written in a vertical column, and each level up is worth 20 times the one below: 1, 20, 400, 8,000, 160,000.
| Number | Base 20 digits | Glyphs |
|---|---|---|
| 19 | 19 | |
| 20 | 1, 0 | |
| 100 | 5, 0 | |
| 365 | 18, 5 | |
| 401 | 1, 0, 1 | |
| 1,000 | 2, 10, 0 | |
| 2,000 | 5, 0, 0 | |
| 7,999 | 19, 19, 19 |
The Long Count exception
For calendar dates the Maya changed one rule. In the Long Count, the third level counts 360 days (18 × 20) instead of 400, so that one unit, the tun, matches a year of 18 twenty-day months. Levels are then worth 1 (kin), 20 (winal), 360 (tun), 7,200 (katun) and 144,000 (baktun) days. Switch "System" to Long Count to see a number written that way.
History
The Maya developed one of the most sophisticated number systems in the ancient world and used a sign for zero by the 4th century AD, independently of the zero later spread from India. The system is vigesimal (base 20), likely because people counted on both fingers and toes. The 260-day sacred calendar (Tzolk'in) and the 365-day solar calendar (Haab') were both counted with it, and the Long Count tracked thousands of years from a starting date in 3114 BC.