The Maya Calendar: Long Count, Tzolk'in and Haab' Explained

Few calendars in history are as intricate as those of the ancient Maya. Across southern Mexico and Central America, Maya astronomers and scribes developed a set of interlocking cycles that tracked days, years and vast stretches of time with impressive precision. Rather than one calendar, they used several at once, much like gears turning together in a machine.

The Tzolk'in: a sacred count of 260 days

The first cycle is the Tzolk'in, a count of 260 days. It combines the numbers 1 to 13 with a sequence of 20 named days. Both run at the same time, so a day might be 1 Imix, followed by 2 Ik', 3 Ak'bal and so on. When the numbers reach 13 they start again at 1, while the names carry on to the twentieth. Because 13 and 20 share no common factor, it takes 260 days before the same number and name meet again.

Why 260 days? Scholars have suggested several reasons. It is close to the length of human pregnancy. In parts of the Maya region it matches the interval between certain passages of the Sun overhead. It also works neatly with the Maya counting system, which was based on twenty. The Tzolk'in was used for ceremonies, divination and naming children, and some Maya communities in Guatemala still keep it today.

The Haab': a year of 365 days

Alongside the sacred count ran the Haab', a solar year of 365 days. It was made of eighteen months of 20 days each, plus a short period of five days called Wayeb'. Those final five days were considered unlucky, a time when the boundary between the human world and the underworld was thin.

Like the Egyptian year, the Haab' had no leap day, so it slowly drifted against the true solar year. The Maya were well aware of the real length of the year, but the Haab' was kept as a fixed count.

The Calendar Round: 52 years

When you combine a Tzolk'in date with a Haab' date, you get a full Maya date such as 4 Ahau 8 Kumk'u. Because the two cycles have different lengths, the same combination comes round only once every 18,980 days, which is almost exactly 52 years. This larger cycle is called the Calendar Round.

For most people a 52-year cycle was enough to identify any date within a lifetime. The completion of a Calendar Round was an important moment, and for the later Aztecs, who used a similar system, it was marked by the New Fire ceremony.

The Long Count: measuring history

To record events across centuries, the Maya used a third system, the Long Count. It counted the number of days since a fixed starting point, using units based mostly on twenty:

• 1 k'in = 1 day

• 1 winal = 20 days

• 1 tun = 360 days

• 1 k'atun = 7,200 days, about 20 years

• 1 b'ak'tun = 144,000 days, about 394 years

A Long Count date is written as five numbers, such as 9.12.11.5.18, which marks the death of the famous king Pakal of Palenque in AD 683. Using the most widely accepted correlation, the starting point of the count falls on 11 August 3114 BC in our calendar.

The Maya wrote these numbers with dots for ones, bars for fives and a shell symbol for zero. The Maya were among the first people in the world to use a true zero, centuries before it reached Europe.

The Dresden Codex

Most Maya books were destroyed after the Spanish conquest. Only four are known to survive, and the finest is the Dresden Codex, a folding book of bark paper painted around the thirteenth century and kept in Dresden, Germany, since 1739. One of its pages appears on the cover of this post. Its pages contain astronomical tables, including a careful record of the cycle of Venus and tables that could predict eclipses. It shows how closely calendar keeping and astronomy were linked in Maya thought.

What really happened in 2012

On 21 December 2012 the Long Count reached 13.0.0.0.0, the end of the thirteenth b'ak'tun. Popular stories claimed the Maya had predicted the end of the world. They had not. For the Maya the completion of a large cycle was a moment of renewal, much like a car's odometer rolling over. Maya inscriptions even mention dates thousands of years beyond 2012.

A lasting achievement

The Maya calendar is a masterpiece of human ingenuity, built without telescopes, metal tools or modern mathematics. It reminds us that there is more than one way to organize time, and that the calendars we take for granted are only one of many brilliant solutions to the same ancient question: what day is it?

Cover image: Dresden Codex p09, Public domain, via Wikimedia Commons.