This Mayan calendar converter turns a Gregorian date into the three interlocking Maya calendar counts — the Long Count, the 260-day Tzolk'in and the 365-day Haab' — and converts a Long Count back into a Gregorian date. It also shows the Julian Day Number, which is the bridge every one of these conversions actually runs through, and it lets you change the correlation constant so you can see for yourself how much the answer depends on it.
Arb Digital builds free calculators across maths, dates and everyday life. Calendar conversion is a topic where a great many online tools quietly disagree with each other, almost always because they use different correlation constants without saying so. This page states its assumptions up front and gives you the arithmetic to check them.
What This Converter Does
Pick a direction, enter either a Gregorian date or a five-place Long Count, choose a correlation constant, and the tool reports the Long Count, the Tzolk'in day, the Haab' day, the Julian Day Number and the number of days elapsed since 0.0.0.0.0. Years before the common era are entered as negative numbers in astronomical style, so 3114 BCE is −3113.
This is a calendar tool, not a numeral tool, and the distinction matters. Our ancient numeral converter converts whole numbers between decimal and the Babylonian sexagesimal and Maya vigesimal number systems, treating the Long Count as a place-value notation. This page does the calendrical work instead: it anchors that notation to an actual day, runs the two cyclical calendars alongside it, and produces a date rather than a number.
For ordinary Gregorian date arithmetic, the date difference calculator and time duration calculator are the right pages.
How to Use It
- Choose the direction. Gregorian to Maya uses the year, month and day fields; Long Count to Gregorian uses the five Long Count fields. The other set is ignored.
- Enter the date. For years before 1 CE use negative astronomical years — there is no year zero in the historical convention, so 1 BCE is entered as 0 and 3114 BCE as −3113.
- Enter a Long Count in the right ranges. Katun, tun and k'in run 0–19, but uinal runs 0–17, because a tun is 18 uinal rather than 20. This is the one irregularity in the whole system.
- Choose a correlation constant, or enter your own. The default is 584283.
- Read the results and cross-check them against a published correlation before relying on them for anything that matters.
The Formula / How It's Calculated
Everything runs through the Julian Day Number, a continuous count of days that ignores calendars entirely. The Gregorian date is converted to a JDN with the standard integer algorithm, the correlation constant is subtracted to give the number of days since the Long Count's zero date, and that day count is decomposed into the five Long Count places.
The decomposition uses the Maya units directly: 1 k'in = 1 day, 1 uinal = 20 k'in, 1 tun = 18 uinal = 360 days, 1 katun = 20 tun = 7,200 days, 1 baktun = 20 katun = 144,000 days. The 18 in the tun is what makes the Long Count not quite base 20 — it brings the tun close to a solar year, which is presumably why it was chosen.
The two cyclical calendars are simple modular arithmetic anchored at 0.0.0.0.0, which fell on 4 Ajaw 8 Kumk'u. The Tzolk'in number is ((days + 3) mod 13) + 1 and its name is the ((days + 19) mod 20)th of the twenty day names. The Haab' position is (days + 348) mod 365, where 348 is the position of 8 Kumk'u in the Haab' year; the month is that position divided by 20 and the day is the remainder, with positions 360–364 falling in the five-day Wayeb'.
Worked example, which is what the page loads with. 21 December 2012 has Julian Day Number 2456283. Subtracting 584283 gives 1,872,000 days, which is exactly 13 × 144,000, so the Long Count is 13.0.0.0.0. For the Tzolk'in, 1,872,000 is divisible by 13 and by 20, so the number is (0 + 3) mod 13 + 1 = 4 and the name is the 19th index, Ajaw. For the Haab', 1,872,000 mod 365 = 280, and 280 + 348 = 628, which reduces to 263; 263 ÷ 20 = 13 remainder 3, giving 3 K'ank'in in the fourteenth month. The result, 13.0.0.0.0 4 Ajaw 3 K'ank'in, is the most widely published Maya-Gregorian correspondence there is.
The Correlation Constant Is the Whole Argument
Nothing in Maya inscriptions states which European day a Long Count date falls on. The Long Count is internally consistent and self-dating, but tying it to our calendar requires an external anchor, and that anchor is the correlation constant: the Julian Day Number assigned to 0.0.0.0.0. Change it by one and every Maya date on this page moves by one day.
The constant used here by default is 584283, the Goodman-Martinez-Thompson correlation, built up from Joseph Goodman's work and refined by Juan Martínez Hernández and J. Eric S. Thompson. It is the constant used by the overwhelming majority of Maya scholars, and it is what the Smithsonian National Museum of the American Indian's Maya calendar converter implements. Under it, 0.0.0.0.0 falls on 11 August 3114 BCE in the proleptic Gregorian calendar, which is 6 September 3114 BCE in the Julian calendar.
It is not the only proposal. Kennett and colleagues, writing in Scientific Reports, note that alternative correlation constants span nearly a millennium, and their high-precision radiocarbon dating of a carved wooden lintel from Tikal was undertaken specifically to test between them. That study found strong support for the GMT correlation and no overlap with the alternatives — which is why 584283 is the sensible default, and also why the tool exposes the constant rather than hiding it. A converter that does not tell you which constant it uses is not giving you a date; it is giving you an opinion.
Three Calendars, Not One
The most common misunderstanding about the Maya calendar is that there is a single thing called "the Maya calendar". There are at least three counts running simultaneously, and they do different jobs.
The Tzolk'in pairs a number from 1 to 13 with one of twenty day names. Both advance together, so the pair repeats every 260 days — the lowest common multiple of 13 and 20. It is a ritual and divinatory count with no tie to the solar year at all.
The Haab' is an approximation of the solar year: eighteen months of twenty days plus a short period of five days called Wayeb'. It has no leap-day correction, so it drifts against the seasons by roughly a day every four years — meaning a Haab' date does not stay in the same season across a long inscription.
Together, Tzolk'in and Haab' form the Calendar Round, a pairing that does not repeat for 18,980 days, or about 52 years. That is long enough to date events within a lifetime unambiguously and far too short to date history, which is exactly the gap the Long Count fills: a linear day count from a fixed zero, capable of placing an event thousands of years back without ambiguity.
Where Conventions Genuinely Differ
Beyond the correlation constant, several conventions vary between sources, and you will see the same day written differently in different books.
Haab' day numbering. This page numbers the days of each month 0 to 19. Many older publications number them 1 to 20 instead, and some write the first day as the "seating" of the month rather than as a number. A date written 3 K'ank'in here may appear as 4 K'ank'in in a source using the other convention, and neither is an error.
Orthography. Day and month names are transcribed differently depending on which spelling system a source follows. Kumk'u also appears as Cumku, Tzolk'in as Tzolkin, K'ank'in as Kankin. This page uses a modernised orthography with apostrophes marking glottalised consonants; older literature generally does not.
The Lord of the Night. Inscriptions often add a ninth-day cycle, G1 to G9, which the Smithsonian converter linked above reports alongside the three main counts. It is omitted here rather than implemented on a convention this page cannot properly source.
Julian versus Gregorian. Dates before 1582 are frequently given in the Julian calendar in the older literature and in the proleptic Gregorian calendar in modern tools. The gap between them grows over time and is about a month by 3114 BCE, which is why the zero date is quoted as both 11 August and 6 September depending on the source.
What 2012 Actually Was
13.0.0.0.0 is worth understanding properly because so much was written about it. It is the completion of thirteen baktuns, a round number in a system where thirteen carries weight, and it is a genuinely notable date in the count. It is not an endpoint. The Long Count has higher places above the baktun — the piktun and beyond — and inscriptions exist that project dates far past 2012, which makes the idea of the calendar "ending" difficult to sustain on the epigraphic evidence.
The more interesting fact is arithmetical: 13 baktuns is 1,872,000 days, which is divisible by 13, by 20 and by 260, which is why 13.0.0.0.0 lands on 4 Ajaw — the same Tzolk'in day as 0.0.0.0.0. That recurrence is not a coincidence, and it is visible directly in the calculation above.
Checking a Result Before You Trust It
Any converter, this one included, should be cross-checked before its output goes anywhere permanent. The quickest check is the one built into this page: load it with no changes and confirm that 21 December 2012 returns 13.0.0.0.0, 4 Ajaw 3 K'ank'in at Julian Day Number 2456283. If that matches, the correlation constant and all three counts are aligned with the standard published values.
A second check is the zero date itself: enter Long Count 0.0.0.0.0 and confirm you get 11 August of astronomical year −3113, which is 3114 BCE, with Tzolk'in 4 Ajaw and Haab' 8 Kumk'u. A third is any date from a published inscription with an accepted reading. If a tool passes all three it is very unlikely to be wrong about anything in between, because the arithmetic is purely linear once the anchor is right. For everyday date arithmetic in the Gregorian calendar, the age calculator and date difference calculator handle the ordinary cases, and the Roman numeral converter covers another historical notation.
Arb Digital maintains a large library of free tools covering dates, maths, money and everyday planning. Have a look, or get in touch.
Browse Free Tools Contact Arb DigitalCommon Mistakes to Avoid
- Treating the Long Count as pure base 20 — a tun is 18 uinal, not 20, and ignoring that irregularity throws every date off by a growing margin.
- Comparing results from tools using different constants — a two-day difference between converters is almost always the correlation constant, not a bug in either one.
- Entering historical BCE years directly — the fields use astronomical years, where 1 BCE is 0 and 3114 BCE is −3113, because there is no year zero in the historical convention.
- Assuming a Haab' date stays in the same season — the Haab' has no leap correction and drifts by about a day every four years against the solar year.
- Mixing Julian and Gregorian dates for early periods — the two diverge by roughly a month by the fourth millennium BCE, which is why the zero date is quoted two different ways.
Related Free Tools From Arb Digital
For the number system rather than the calendar, use the ancient numeral converter, which handles Babylonian sexagesimal and Maya vigesimal notation. For ordinary date arithmetic, the date difference calculator, time duration calculator and age calculator cover the common cases, and the Roman numeral converter handles another historical notation. Browse the free online tools hub for everything else.
Frequently Asked Questions
584283 by default, the Goodman-Martinez-Thompson correlation used by most Maya scholars and by the Smithsonian's own converter. You can switch to 584285 or enter your own value, and doing so shifts every date the page produces by the difference between the constants.
Almost always because they use different correlation constants, and often without stating which. The Long Count itself is unambiguous; tying it to a European calendar requires an external anchor, and that anchor has been the subject of a long scholarly argument.
Under the 584283 constant it was 13.0.0.0.0 in the Long Count, 4 Ajaw in the Tzolk'in and 3 K'ank'in in the Haab', at Julian Day Number 2456283. That is the completion of the thirteenth baktun, and it is the correspondence this page loads with so you can verify the arithmetic.
No. Thirteen baktuns is a round and significant figure, but the Long Count has higher places above the baktun and inscriptions exist projecting dates far beyond 2012. The count continues past 13.0.0.0.0 in exactly the same way it continued past every earlier baktun completion.
The Tzolk'in is a 260-day ritual count pairing a number from 1 to 13 with one of twenty day names. The Haab' is a 365-day approximation of the solar year, eighteen months of twenty days plus a five-day Wayeb'. Together they form a Calendar Round that repeats about every 52 years.
Because the tun contains 18 uinal rather than 20, which is the single irregularity in an otherwise vigesimal system. The effect is to bring the unit close to a solar year, which makes the Long Count far more useful for tracking years than a pure base-20 count would be.
Because there are two conventions. This page numbers the days of each month 0 to 19; many older publications number them 1 to 20, and some write the first day as the seating of the month instead. Neither is wrong, but they differ by one, so always check which a source is using.
This tool implements published correlation arithmetic and states the constant it uses. Maya calendar scholarship involves genuine disagreement over correlation and over transcription conventions, so for academic or published work, verify any result against a specialist source rather than against a web converter alone.
