The famous Aztec calendar stone is not actually a calendar
The great carved disc in Mexico City's National Museum of Anthropology is often called the Aztec calendar stone, but it is the sun stone. The real calendar meshed a 365-day solar year with a 260-day sacred count, and the two lined up again only once every 52 years, a moment the Aztecs feared.
The sacred count, the tōnalpōhualli, paired a number from 1 to 13 with one of twenty day signs. Each day both advanced together, so 1 Crocodile was followed by 2 Wind, 3 House and so on to 13 Reed, after which the numbers restarted while the signs carried on, giving 1 Jaguar. Only after 260 days, thirteen times twenty, did the sequence return to 1 Crocodile. The days fell into twenty groups of thirteen, which scholars call trecenas from the Spanish for thirteen; the Florentine Codex records the Nahuatl name as a family of days. Each group had its own patron deity, and each day sign was tied to a cardinal direction. The signs match those used by the Mixtecs.
The solar year, the xiuhpōhualli, was treated as the agricultural calendar. It held eighteen periods of twenty days, now called veintenas, making 360 named days, plus five nameless days, the nēmontēmi, regarded as unlucky. Its months followed a count of days rather than the moon, and each twenty-day period opened on Crocodile with a festival. Years themselves were named by four signs combined with thirteen numbers, creating the 52-year cycle often called Xiuhmolpilli, though Xiuhnelpilli is the more accurate Nahuatl word.
The 52-year span carried cosmic weight. The Aztecs believed they lived in the Fifth Sun, the latest of a series of worlds each destroyed by its own flaws, and that at the end of any cycle the gods could take everything back.
Reconstructing the exact correlation with European dates remains contested. Rafael Tena of Mexico's national institute of anthropology argues the Mexica year began on February 23 of the Gregorian calendar. Rival models by Ruben Ochoa and José Genaro Emiliano Medina Ramos tie the year to the spring equinox, but scholars point out they clash with evidence about when the Mexica day began and the absence of any leap day in Mesoamerican calendars.
Source: Aztec calendar