Calendar Converter

Harys Dalvi


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Julian Day Gregorian Islamic Hindu Hebrew Persian Indian Civil Mayan/Mesoamerican Julian ISO-8601 Martian Calendar Maker

Julian Day

Julian day:


Astronomers, unlike historians, frequently need to do arithmetic with dates. For example: a double star goes into eclipse every 1583.6 days and its last mid-eclipse was measured to be on October 17, 2003 at 21:17 UTC. When is the next? Well, you could get out your calendar and count days, but it's far easier to convert all the quantities in question to Julian day numbers and simply add or subtract.

Julian days simply enumerate the days and fraction which have elapsed since the start of the Julian era, which is defined as beginning at noon on Monday, 1st January of year 4713 B.C.E. in the Julian calendar. This date is defined in terms of a cycle of years, but has the additional advantage that all known historical astronomical observations bear positive Julian day numbers, and periods can be determined and events extrapolated by simple addition and subtraction. Julian dates are a tad eccentric in starting at noon, but then so are astronomers (and systems programmers!)—when you've become accustomed to rising after the “crack of noon” and doing most of your work when the Sun is down, you appreciate recording your results in a calendar where the date doesn't change in the middle of your workday. But even the Julian day convention bears witness to the eurocentrism of 19th century astronomy—noon at Greenwich is midnight on the other side of the world. But the Julian day notation is so deeply embedded in astronomy that it is unlikely to be displaced at any time in the foreseeable future. It is an ideal system for storing dates in computer programs, free of cultural bias and discontinuities at various dates, and can be readily transformed into other calendar systems, as the source code for this page illustrates. Use Julian days and fractions (stored in 64 bit or longer floating point numbers) in your programs, and be ready for Y10K, Y100K, and Y1MM!

Modified Julian day:

While any event in recorded human history can be written as a positive Julian day number, when working with contemporary events all those digits can be cumbersome. A Modified Julian Day (MJD) is created by subtracting 2400000.5 from a Julian day number, and thus represents the number of days elapsed since midnight (00:00) Universal Time on November 17, 1858. Modified Julian Days are widely used to specify the epoch in tables of orbital elements of artificial Earth satellites. Since no such objects existed prior to October 4, 1957, all satellite-related MJDs are positive.

Gregorian Calendar


The Gregorian calendar was proclaimed by Pope Gregory XIII and took effect in most Catholic states in 1582, in which October 4, 1582 of the Julian calendar was followed by October 15 in the new calendar, correcting for the accumulated discrepancy between the Julian calendar and the equinox as of that date. When comparing historical dates, it's important to note that the Gregorian calendar, used universally today in Western countries and in international commerce, was adopted at different times by different countries. Britain and her colonies (including what is now the United States), did not switch to the Gregorian calendar until 1752, when Wednesday 2nd September in the Julian calendar dawned as Thursday the 14th in the Gregorian.

The Gregorian calendar is a minor correction to the Julian. In the Julian calendar every fourth year is a leap year in which February has 29, not 28 days, but in the Gregorian, years divisible by 100 are not leap years unless they are also divisible by 400. How prescient was Pope Gregory! Whatever the problems of Y2K, they won't include sloppy programming which assumes every year divisible by 4 is a leap year since 2000, unlike the previous and subsequent years divisible by 100, is a leap year. As in the Julian calendar, days are considered to begin at midnight.

The average length of a year in the Gregorian calendar is 365.2425 days compared to the actual solar tropical year (time from equinox to equinox) of 365.24219878 days, so the calendar accumulates one day of error with respect to the solar year about every 3300 years. As a purely solar calendar, no attempt is made to synchronise the start of months to the phases of the Moon.

While one can't properly speak of “Gregorian dates” prior to the adoption of the calendar in 1582, the calendar can be extrapolated to prior dates. In doing so, this implementation uses the convention that the year prior to year 1 is year 0. This differs from the Julian calendar in which there is no year 0—the year before year 1 in the Julian calendar is year −1. The date December 30th, 0 in the Gregorian calendar corresponds to January 1st, 1 in the Julian calendar.

A slight modification of the Gregorian calendar would make it even more precise. If you add the additional rule that years evenly divisible by 4000 are not leap years, you obtain an average solar year of 365.24225 days per year which, compared to the actual mean year of 365.24219878, is equivalent to an error of one day over a period of about 19,500 years; this is comparable to errors due to tidal braking of the rotation of the Earth.

اسلامی تقویم



The Islamic calendar is purely lunar and consists of twelve alternating months of 30 and 29 days, with the final 29 day month extended to 30 days during leap years. Leap years follow a 30 year cycle and occur in years 1, 5, 7, 10, 13, 16, 18, 21, 24, 26, and 29. Days are considered to begin at sunset. The calendar begins on Friday, July 16th, 622 C.E. in the Julian calendar, Julian day 1948439.5, the day of Muhammad's flight from Mecca to Medina, with sunset on the preceding day reckoned as the first day of the first month of year 1 A.H.—“Anno Hegiræ”—the Arabic word for “separate” or “go away”.

In the Gregorian calendar, days begin at midnight. In the Islamic calendar, days begin with sunset. For this reason, you should select coordinates above because sunset times vary from place to place. In some places at high latitudes in the winter and summer, the sun sets at odd hours or doesn't set at all. In these places some people use a calendar from Mecca. For this reason, in this calendar you can specify that the calendar should be calculated as if you are in Mecca.

In Islamic prayer, Muslims find the direction of Mecca. This calendar can find the direction to Mecca if you specify your coordinates above. The direction to Mecca is known as the “Qibla.”

Each cycle of 30 years thus contains 19 normal years of 354 days and 11 leap years of 355, so the average length of a year is therefore ((19 × 354) + (11 × 355)) / 30 = 354.365… days, with a mean length of month of 1/12 this figure, or 29.53055… days, which closely approximates the mean synodic month (time from new Moon to next new Moon) of 29.530588 days, with the calendar only slipping one day with respect to the Moon every 2525 years. Since the calendar is fixed to the Moon, not the solar year, the months shift with respect to the seasons, with each month beginning about 11 days earlier in each successive solar year.

The calendar presented here is the most commonly used civil calendar in the Islamic world; for religious purposes months are defined to start with the first observation of the crescent of the new Moon.

اسلامی تقویم چاند کے ساتھ سیدھ رکھتا ہے۔ بارہ مہینے ہیں، اور ہر ایک میں یا تو ۳۰ یا ۲۹ دن ہوتے ہیں۔ آخری مہینے ذو الحجہ میں دونوں ۲۹ اور ۳۰ دن ہو سکتے ہیں۔ ہر ۳۰ سالوں میں ذو الحجہ میں ۳۰ دن ہوتے ہیں پہلے، 5ویں، 7ویں، 10ویں، 13ویں، 16ویں، 18ویں، 21ویں، 24ویں، 26ویں، اور 29ویں سالوں میں۔ اسلامی تقویم کا پہلا دن جمعہ، ۱۹ جولائی، ۶۲۲ء ہے۔ یہ پہلا نیا چاند ہے محمد کے مکّے سے مدینے جانے کے بعد۔

عیسوی تقویم میں، دن آدھی رات کو شروع ہوتے ہیں۔ اسلامی تقویم میں، سورج کے ڈوبنے سے شروع ہوتے ہیں۔ اِس لئے اِس تقویم کے لئے ضروری ہے کہ آپ ایک جگہ اوپر چن لیں، کیوں کہ ہر جگہ میں سورج الگ-الگ وقتوں پہ ڈوبتا ہے۔ اونچے لَیٹِیٹیُوڈز پر کئی جگہوں میں گرمیوں اور سردیوں میں سورج عجیب وقتوں پہ ڈوبتا ہے، اور کبھی-کبھی ڈوبتا ہی نہیں۔ اِن جگہوں میں کئی لوگ مکّے کے تقویم کا استعمال کرتے ہیں۔ اِس لئے اِس تقویم میں آپ کہہ سکتے ہیں کہ تقویم کو ہونا ہے جیسے آپ مکّے میں ہیں۔

اسلامی نماز میں، مسلمان مکّے کی طرف ڈھونڈتے ہیں۔ یہ تقویم مکّے کی طرف ڈھونڈ سکتا ہے اگر آپ اپنی جگہ اوپر دے دیں۔ مکّے کی طرف کو ”قبلہ“ کہتے ہیں۔

اسلامی تقویم میں اوسط سال 354.365 دن کا ہے، اور اوسط مہینہ 29.53055 دن کا ہے۔ اصل میں چاند دنیا کا گول کرتا ہے ہر 29.530588 دن۔ اسلامی تقویم اِس سے اتنا قریب ہے کہ ہر 2525 سال، تقویم میں بس ایک ہی دن کی غلطی آ جاتی ہے۔ اسلامی تقویم چاند کے ساتھ سیدھ رکھتا ہے اور سورج کے ساتھ نہیں؛ اِس لئے رُتوں سے ہر سال تقریباً ۱۱ دنوں کا فرق ہو جاتا ہے۔

اِس تقویم کا استعمال اسلامی ملکوں میں ہوتا ہے سِوِل کیلنڈر کے لئے؛ مذہب کے لئے مہینے چاند کے ہلال کی نظر پہ شروع ہوتے ہیں۔

हिंदू पंचांग


हफ़्ते का दिन:


The Hindu calendar is lunisolar: months align with the moon while years align with the sun. In this calendar the month can begin with either the new moon (amavasya) or the full moon (purnima). The stars complete a full revolution in a year, and for this reason the Hindu calendar completes a cycle in a year. Since it is aligned with both the stars and the moon, sometimes a month must occur twice in a year, if the sun is in the same zodiac sign for two months in a row. When this happens, the first is considered “extra” (adhik) and the second “pure” (shuddh). Besides Hindus, this calendar is used by South Asian farmers and followers of other Indian religions.

Day Number Day Name
1/16 Pratipada
2/17 Dwitiya
3/18 Tritiya
4/19 Chaturthi
5/20 Panchami
6/21 Shashthi
7/22 Saptami
8/23 Ashtami
9/24 Navami
10/25 Dashami
11/26 Ekadashi
12/27 Dwadashi
13/28 Trayodashi
14/29 Chaturdashi
15/30 Amavasya (New moon)
Poornima (Full moon)

The dates in the boxes here are called tithis. This is a lunar day. In one cycle of the moon there are 30 tithis, but this is separate from our days: they don't start at midnight or any one specific time. For this reason, the name of the tithi it was at sunrise is taken as the divasa for everyday life. A tithi is slightly shorter than a day because one cycle of the moon is about 29.5 days, but 30 tithis. There are two pakshas (fortnights) in a month. Unless it is amavasya or poornima, the name of the fortnight must be specified to know whether the moon is waxing (shukla paksha) or waning (krishna paksha). For example, if it is three days after Amavasya, the day is called Shukla Tritiya. If it is three days after Poornima, the day is called Krishna Tritiya.

Every year the stars fall back 0.014°. The amount they have fallen back from the Earth and the sun is known as ayanamsa. After 25771.5 years, ayanamsa will have gone a full 360°! For this reason in order to stay with the seasons it is necessary that the months' zodiac signs change about every 2147.62 years. However, the Surya Siddhantha says that ayanamsa cycles between 27° and -27°. The Surya Siddhantha values are used here for calculating seasons and months. The zodiac signs are not calculated from the Surya Siddhantha ayanamsa values.

The first month of the year is usually Chaitra, but in the Bengali calendar it is Vaisakh. In ancient times many used the Kali Yuga era, but these days Vikram and Shaka are most used. Today the Shaka era is used in the Indian National Calendar. In Nepal, Vikram Samvat is used. When the Indian government made its national calendar, it also said that the Hindu calendar should be calculated from 23.2°N, 82.5°E. Generally this is done, but you can change this with the “From India?” button.

हिंदू पंचांग महीने चांद से गिनता है लेकिन साल सूरज से गिनता है। इस पंचांग में महीना दोनों अमावस और पूनम पे शुरू हो सकता है। तारे साल में पूरा गोल करते हैं, और इसलिए हिंदू पंचांग भी एक साल में गोल करता है। दोनों तारों और चांद के साथ जाने की वजह से, कभी-कभी महीने को साल में दो बार होना पड़ता है। जब ये होता है, पहला महीना “अधिक” होता है और दूसरा “शुद्ध”। हिंदुओं के अलावा देसी किसान और अलग-अलग भारतीय धर्मों के लोग इस पंचांग का इस्तेमाल करते हैं।

यहाँ के बक्सों के तारीख़ों को “तिथि” कहते है। ये चांद का दिन है। चांद के एक गोल में 30 तिथियाँ हैं, मगर ये हमारे दिनों से जुदा है: ना आधीरात को ना किसी एक घंटे को शुरू होते हैं। इसलिए जो तिथि थी जब सूरज पिछली बार चढ़ गया, वो दिवस बन जाती है आम ज़िंदगी के लिए। एक तिथि हमारे दिन से थोड़ी छोटी है क्योंकि चांद के एक गोल में तक़रीबन 29.5 दिन हैं, मगर 30 तिथियाँ हैं। महीने में दो पक्ष या पाख होते हैं। अगर न पूनम न अमावस है, पाख का नाम कहना है ताकि पता हो कि क्या चांद उतर रहा है (कृष्ण पक्ष/पाख) या बढ़ रहा है (शुक्ल पक्ष/पाख)। जैसे, अगर अमावस से तीन दिन बाद है तो दिन का नाम “शुक्ल तीज” होगा। अगर पूनम से तीन दिन बाद है तो दिन का नाम “कृष्ण तीज” होगा।

दिन का नंबर दिन का नाम (हिन्दी/संस्कृत)
१/१६ परिवा/प्रतिपदा
२/१७ दूज/द्वितीया
३/१८ तीज/तृतीया
४/१९ चौथ/चतुर्थी
५/२० पंचमी
६/२१ छठ/षष्ठी
७/२२ सप्तमी
८/२३ अष्टमी
९/२४ नौमी/नवमी
१०/२५ दसमी/दशमी
११/२६ ग्यारस/एकादशी
१२/२७ बारस/द्वादशी
१३/२८ तेरस/त्रयोदशी
१४/२९ चौदस/चतुर्दशी
१५/३० अमावस/अमावस्या

तारे हर साल तक़रीबन 0.014° पीछे हो जाते हैं। जितने पीछे हुए हैं दुनिया और सूरज से, इसको “अयनांश” कहते हैं। 25771.5 सालों बाद, अयनांश पूरा 360° चला होगा! इसलिए रुतों के साथ चलने के लिए ज़रूरी है कि महीनों की राशियाँ बदलें लगभग हर 2147.62 साल। मगर सूर्यसिद्धान्थ में कहा है कि अयनांश 27° और -27° के बीच हमेशा रहता है गोल मारके। इधर सूर्यसिद्धान्थ के हिसाब का इस्तेमाल होता है रुतों और महीनों के लिए। राशियाँ सूर्यसिद्धान्थ के हिसाब के अयनांश से नहीं गिनी जाती हैं।

साल का पहला महीना ज़्यादातर चैत है, मगर बंगाली पंचांग में बैसाख है। पुराने ज़मानों में बहुत लोग कलियुग का इस्तेमाल करते थे, मगर आज-कल ज़्यादातर विक्रम और शक का इस्तेमाल होता है। आज भारतीय राष्ट्रीय पंचांग में शक संवत का इस्तेमाल होता है। नेपाल में विक्रम संवत का इस्तेमाल होता है। जब भारत सरकार ने अपना राष्ट्रीय पंचांग बनाया, ये भी कहा था कि हिंदू पंचांग को 23.2°उ. 82.5°पू. से हिसाब करना है। ज़्यादातर यही होता है, मगर आप इसे बदल सकते हैं “भारत में?” वाले बटन से।

הַלּוּחַ הָעִבְרִי


The Hebrew (or Jewish) calendar attempts to simultaneously maintain alignment between the months and the seasons and synchronise months with the Moon—it is thus deemed a “lunisolar calendar”. In addition, there are constraints on which days of the week on which a year can begin and to shift otherwise required extra days to prior years to keep the length of the year within the prescribed bounds. This isn't easy, and the computations required are correspondingly intricate.

Years are classified as common (normal) or embolismic (leap) years which occur in a 19 year cycle in years 3, 6, 8, 11, 14, 17, and 19. In an embolismic (leap) year, an extra month of 29 days, “Adar Bet” (אֲדָר ב׳), is added to the end of the year after the month “Adar”, which is designated “Adar Aleph” (אֲדָר א׳) in such years. Further, years may be deficient, regular, or complete, having respectively 353, 354, or 355 days in a common year and 383, 384, or 385 days in embolismic years. Days are defined as beginning at sunset, and the calendar begins at sunset the night before Monday, October 7, 3761 B.C.E. in the Julian calendar, or Julian day 347995.5. Days are numbered with Sunday as day 1, through Saturday: day 7.

The average length of a month is 29.530594 days, extremely close to the mean synodic month (time from new Moon to next new Moon) of 29.530588 days. Such is the accuracy that more than 13,800 years elapse before a single day discrepancy between the calendar's average reckoning of the start of months and the mean time of the new Moon. Alignment with the solar year is better than the Julian calendar, but inferior to the Gregorian. The average length of a year is 365.2468 days compared to the actual solar tropical year (time from equinox to equinox) of 365.24219 days, so the calendar accumulates one day of error with respect to the solar year every 216 years.

گاه‌شماری ایرانی‎

روزِ هفته

The modern Persian calendar was adopted in 1925, supplanting (while retaining the month names of) a traditional calendar dating from the eleventh century. The calendar consists of 12 months, the first six of which are 31 days, the next five 30 days, and the final month 29 days in a normal year and 30 days in a leap year.

Each year begins on the day in which the March equinox occurs at or after solar noon. Days begin at midnight. There is no leap year rule; 366 day years do not recur in a regular pattern but instead occur whenever that number of days elapse between equinoxes at the reference meridian. The calendar therefore stays perfectly aligned with the seasons. No attempt is made to synchronise months with the phases of the Moon.

There is some controversy about the reference meridian at which the equinox is determined in this calendar. Various sources cite Tehran, Esfahan, and the central meridian of Iran Standard Time as that where the equinox is determined. In this implementation, Iran Standard Time is used. In Iran, it appears the Iran Standard Time longitude is used today. This is 52°30' E (52.5° E), or GMT+3:30. As this calendar is proleptic for all years prior to 1925 C.E., historical considerations regarding the capitals of Persia and Iran do not seem to apply.

In Iran, although the Persian calendar is separate from the Islamic calendar, it has the same starting year of 622 C.E. marking the Hijra (flight) from Mecca to Medina. The Kurdish calendar is also a version of the Persian calendar, but beginning earlier, in 612 B.C.E. This year is relevant to Kurdish history because of its importance in the life of the Median king Cyaxares (Hevexştre). King Phraortes (Frevertîş), the father of Cyaxares, was killed in battle by Assyrians. Media was then conquered by Scythians. Cyaxares overthrew the Scythians and began to fight against Assyria. In 612 B.C.E., Cyaxares took the Assyrian capital of Nineveh, a crushing defeat for the Assyrians. Because the modern Kurds consider themselves to have a common heritage with the ancient Median people, this date is used for the beginning of the Kurdish calendar.

This implementation allows you to choose between both the Hijri (Islamic) and Kurdish (Median) year counts. Only the year number is affected; months and days remain the same.

भारतीय राष्ट्रीय पंचांग

हफ़्ते का दिन:

A bewildering variety of calendars have been and continue to be used in the Indian subcontinent. In 1957 the Indian government's Calendar Reform Committee adopted the National Calendar of India for civil purposes and, in addition, defined guidelines to standardise computation of the religious calendar, which is based on astronomical observations. The civil calendar is used throughout India today for administrative purposes, but a variety of religious calendars remain in use. We present the civil calendar here.

The National Calendar of India is composed of 12 months. The first month, Chaitra, is 30 days in normal and 31 days in leap years. This is followed by five consecutive 31 day months, then six 30 day months. Leap years in the Indian calendar occur in the same years as as in the Gregorian calendar; the two calendars thus have identical accuracy and remain synchronised.

Years in the Indian calendar are counted from the start of the Shaka Era, the equinox of March 22nd of year 79 in the Gregorian calendar, designated day 1 of month Chaitra of year 1 in the Shaka Era. The calendar was officially adopted on 1 Chaitra, 1879 Shaka Era, or March 22nd, 1957 Gregorian. Since year 1 of the Indian calendar differs from year 1 of the Gregorian, to determine whether a year in the Indian calendar is a leap year, add 78 to the year of the Shaka era then apply the Gregorian calendar rule to the sum.

Mesoamerican Calendars

Mayan Long Count
. . . .
Calendar type:  

The Mayans employed three calendars, all organised as hierarchies of cycles of days of various lengths. The Long Count was the principal calendar for historical purposes, the Haab was used as the civil calendar, while the Tzolkin was the religious calendar. All of the Mayan calendars are based on serial counting of days without means for synchronising the calendar to the Sun or Moon, although the Long Count and Haab calendars contain cycles of 360 and 365 days, respectively, which are roughly comparable to the solar year. Based purely on counting days, the Long Count more closely resembles the Julian Day system and contemporary computer representations of date and time than other calendars devised in antiquity. Also distinctly modern in appearance is that days and cycles count from zero, not one as in most other calendars, which simplifies the computation of dates, and that numbers as opposed to names were used for all of the cycles.

The Long Count calendar is organised into the hierarchy of cycles shown at the right. Each of the cycles is composed of 20 of the next shorter cycle with the exception of the tun, which consists of 18 uinal of 20 days each. This results in a tun of 360 days, which maintains approximate alignment with the solar year over modest intervals—the calendar comes undone from the Sun 5 days every tun.

Cycle Composed of Total
kin   1  
uinal 20 kin 20  
tun 18 uinal 360 0.986
katun 20 tun 7200 19.7
baktun 20 katun 144,000 394.3
pictun 20 baktun 2,880,000 7,885
calabtun 20 piktun 57,600,000 157,704
kinchiltun 20 calabtun 1,152,000,000 3,154,071
alautun 20 kinchiltun 23,040,000,000 63,081,429

The Mayans believed that at the conclusion of each pictun cycle of about 7,885 years the universe is destroyed and re-created. Those with apocalyptic inclinations will be relieved to observe that the present cycle will not end until Columbus Day, October 12, 4772 in the Gregorian calendar. Speaking of apocalyptic events, it's amusing to observe that the longest of the cycles in the Mayan calendar, alautun, about 63 million years, is comparable to the 65 million years since the impact which brought down the curtain on the dinosaurs—an impact which occurred near the Yucatán peninsula where, almost an alautun later, the Mayan civilisation flourished. If the universe is going to be destroyed at the end of the current pictun, there's no point in writing dates using the longer cycles, so we dispense with them here.

Dates in the Long Count calendar are written, by convention, as:

baktun . katun . tun . uinal . kin

and thus resemble present-day Internet IP addresses!

For civil purposes the Mayans used the Haab calendar in which the year was divided into 18 named periods of 20 days each, followed by five Wayeb days not considered part of any period. Dates in this calendar are written as a day number (0 to 19 for regular periods and 0 to 4 for the days of Wayeb) followed by the name of the period. This calendar has no concept of year numbers; it simply repeats at the end of the complete 365 day cycle. Consequently, it is not possible, given a date in the Haab calendar, to determine the Long Count or year in other calendars. The 365 day cycle provides better alignment with the solar year than the 360 day tun of the Long Count but, lacking a leap year mechanism, the Haab calendar shifted one day with respect to the seasons about every four years.

The Mayan religion employed the Tzolkin calendar, composed of 20 named periods of 13 days. Unlike the Haab calendar, in which the day numbers increment until the end of the period, at which time the next period name is used and the day count resets to 0, the names and numbers in the Tzolkin calendar advance in parallel. On each successive day, the day number is incremented by 1, being reset to 1 after reaching 13, and the next in the cycle of twenty names is affixed to it. Since 13 does not evenly divide 20, there are thus a total of 260 day number and period names before the calendar repeats. As with the Haab calendar, cycles are not counted and one cannot, therefore, convert a Tzolkin date into a unique date in other calendars. The 260 day cycle formed the basis for Mayan religious events and has no relation to the solar year or lunar month.

The Mayans frequently specified dates using both the Haab and Tzolkin calendars; dates of this form repeat only every 52 solar years.

The Aztecs used a calendar very similar to the Mayan calendar. They lacked a long count and used different words for days and months. Mayan Haab dates do not correspond to their Aztec counterpart, called Xiuhpōhualli in Nahuatl, although both have 365 days. Both had a 260 day religious cycle and a 365 day civil cycle. Here you may choose between the Mayan and Aztec calendars.

Los mayas utilizaban tres calendarios, todos organizados como jerarquías de ciclos de días de varias duraciones. La cuenta larga era el calendario principal para propósitos históricos, el haab era usado como calendario civil y el tzolkin era el calendario religioso. Todos los calendarios mayas son basadas en contando días en serie sin medio para sincronizar el calendario con el sol ni la luna, aunque la cuenta larga y el haab contienen ciclos de 360 y 365 días respectivamente, que son aproximadamente comparable al año solar. Basada puramente en contando días, la cuenta larga parece al sistema del día juliano y representaciones contemporáneas en informática de la fecha y la hora más que otros calendarios ideados en la antigüedad. Además, algo claramente moderno en el aspecto es que días y ciclas cuentan de cero, no de uno como en la mayoría de otros calendarios, algo que simplifica la computación de fechas, y que se usaban números en vez de nombres para todos los ciclos.

El calendario de la cuenta larga es organizado con la jerarquía de ciclos mostrado a la derecha. Cada ciclo es compuesto de 20 del próximo ciclo más corto con la excepción del tun, que consiste en 18 uinal cada de 20 días. Esto da como resultado un tun de 360 días, que mantenga alineación aproximada con el año solar durante intervalos moderados—el calendario se deshace del sol 5 días cada tun.

Ciclo Compuesto de Días
kin   1  
uinal 20 kin 20  
tun 18 uinal 360 0.986
katún 20 tun 7200 19.7
baktún 20 katún 144,000 394.3
pictún 20 baktún 2,880,000 7,885
calabtún 20 piktún 57,600,000 157,704
kinchiltún 20 calabtún 1,152,000,000 3,154,071
alautún 20 kinchiltún 23,040,000,000 63,081,429

Los mayas creían que al término de cada ciclo pictún de circa 7,885 años el universo se destruye y se recrea. Los con inclinaciones apocalípticas estarán aliviados a observar que el ciclo actual no se terminará hasta el Día de la Raza, 12 de octubre de 4772 en el calendario gregoriano. Hablando de acontecimientos apocalípticos, es interesante observar que el ciclo más largo del calendario maya, el alautún, circa 63 millón años, es comparable a los 65 millón años desde el impacto que destruyó los dinosaurios—un impacto que ocurrió cerca de la península de Yucatán donde, casi un alautún más tarde, la civilización maya florecía. Si el universo va a ser destruido al término del pictún actual, escribir fechas con los ciclos más grande no tiene sentido, así que no los usamos aquí.

Por convención, se escriban fechas en el calendario de la cuenta larga como:

baktún . katún . tun . uinal . kin

¡y así parecen a direcciones IP actuales del internet!

Para propósitos civiles los mayas usaban el calendario haab en que el año era dividido en 18 periodos con nombres, cada de 20 días, seguido de cinco días de wayeb que no eran considerado parte de ningún periodo. Se escriban fechas en este calendario como un nombre del día (0 a 19 para periodos normales y 0 a 4 para los días de wayeb) seguido por el nombre del periodo. Este calendario no tiene ningún concepto de números de años; sencillamente repite al término del ciclo completo de 365 días. Por consiguiente, dado una fecha en el calendario haab, no es posible determinar la cuenta larga o el año en otros calendarios. El ciclo de 365 días provee alineación mejor con el año solar que el tun de 360 días de la cuenta larga, pero sin mecanismo de años bisiestos, el calendario haab se movaba un día en relación con las estaciones aproximadamente cada cuatro años.

La religión maya usaba el calendario tzolkin, compuesto de 20 periodos con nombres, cada de 13 días. A diferencia del calendario haab, en que los números del día se aumenta hasta el fin del periodo, cuando el nombre del próximo perodo es usado y la cuenta del día se reajuste a 0, los nombres y números en el calendario tzolkin avanzan en paralelo. Cada día sucesivo, el número del día aumenta por 1, siendo reajustado a 1 después de llegar a 13, y se pone el siguiente en el ciclo de veinte nombres. Ya que 13 no divide 20 en partes iguales, hay un total de 260 combinaciones de número del día y nombre del periodo antes de que el calendario repita. Como con el calendario haab, ciclos no se cuentan y por lo tanto no se puede convertir un fecha de tzolkin en una fecha única en otros calendarios. El ciclo de 260 días formaba la base de eventos religiosos de los mayas y no tiene ninguna relación al año solar ni al mes lunar.

Los mayas especificaban fechas a menudo usando el calendario haab y el calendario tzolkin; fechas de esta forma solo repiten cada 52 años solares.

Los aztecas usaban un calendario muy similar al calendario maya. Les faltaba una cuenta larga y usaban palabras diferentes para días y meses. Fechas mayas de haab no corresponden a su equivalente azteca, llamado xiuhpōhualli en náhuatl, aunque los dos tienen 365 días. Los dos tenían un ciclo religioso de 260 días y un ciclo civil de 365 días. Aquí se puede elegir entre los calendarios maya y azteca.

Julian Calendar

The Julian calendar was proclaimed by Julius Cæsar in 46 B.C. and underwent several modifications before reaching its final form in 8 A.D. The Julian calendar differs from the Gregorian only in the determination of leap years, lacking the correction for years divisible by 100 and 400 in the Gregorian calendar. In the Julian calendar, any positive year is a leap year if divisible by 4. (Negative years are leap years if the absolute value divided by 4 yields a remainder of 1). Days are considered to begin at midnight.

In the Julian calendar the average year has a length of 365.25 days. compared to the actual solar tropical year of 365.24219878 days. The calendar thus accumulates one day of error with respect to the solar year every 128 years. Being a purely solar calendar, no attempt is made to synchronise the start of months to the phases of the Moon.

ISO-8601 Week and Day, and Day of Year

Day of week of year

Day of year

Martian Mangli Calendar

Solar longitude Ls:
Time :
Mars Sol Date (MSD)

The Mangli calendar is designed to be used on Mars (Sanskrit: मंगल mangala). Rather than counting Earth days, it counts sols, or the time for Mars to rotate on its axis. One Martian sol is equal to slightly more than an Earth day at 1.02749125170 Earth days (24 hours, 40 minutes). A year on Mars is 668.5991 sols, or about 687 Earth days—almost twice an Earth year. Because of this, the Mangli calendar has 24 months rather than the 12 in most Earth calendars.

Mangli month Etymology Original name
Noroz Persian Nowruz نوروز
Ayorz Hebrew Iyyar אִיָּר
Paljen Sanskrit Phalguna फाल्गुन
Parmet Egyptian Parmouti
Prilum English April
Chetrum Sanskrit Chaitra चैत्र
Cansen Mayan K'ank'in
Dassem English December
Shebta Hebrew Shevat שְׁבָט
Setsa Mayan Sotz'
Sawvum Hindi Saavan सावन
Jeshtum Sanskrit Jyeshtha ज्येष्ठ
Onwin Igbo Ọnwa
Novin English November
Shivna Hebrew Sivan סִיוָן
Nisna Hebrew Nisan נִיסָן‬
Abro Persian Aban آبان
Azro Persian Azar آذر
Septid English September
Octid English October
Mawgun Sanskrit Maagha माघ
Yawshun Mayan Yaxk'in
Acacon Quechua Auqakuh
Arason Greek Ares Άρης

By default, in the Mangli calendar, all months are 28 days except the first four which are 27 days each. This gives a year length of 668 sols. However, in even numbered years, the fourth month (Parmet) has 28 days; and in years divisible by 10, the third month (Paljen) has 28 days as well. Finally, in years divisible by 1111, the last month (Arason) has only 27 days rather than 28. This gives an average year length of 668.5990999 sols, close to the 668.5991 of the Martian orbit.

Month names in the Mangli calendar are adapted from month names in various other calendars of the world, although the names are changed significantly. Only calendars that maintain approximate alignment with the seasons were used, as the Mangli calendar follows the orbit of Mars around the sun and seasons on Mars. Three month names are not from other month names but are from other cultural aspects. The first month, Noroz, is from نوروز Nowruz, a new year festival of Persian origin occuring during the spring equinox. The 23rd month, Acacon, is from Auqakuh, the Quechua word for Mars. The last month, Arason, is from the Greek god of war Ares, associated with the Roman Mars. Month names are in pairs with similar-sounding endings, although two months in a pair do not necessarily share an origin.

Like Earth, Mars has seasons, as it has a tilt of 25°. Since the Northern and Southern hemispheres of Mars have opposite seasons, month names can be inspired by the season of either hemisphere at that time of the year. A notable difference between Earth and Mars is that Mars has a much more elliptical orbit. Perihelion (when Mars is closest to the sun) occurs when it is winter in the North, summer in the South. Apehelion (when Mars is farthest from the sun) occurs when it is summer in the North, winter in the South. The effect of this is that seasons in the Southern hemisphere are more extreme than in the Northern hemisphere.

The Mangli calendar begins with the equinox on Mars on April 11, 1955 (on Mars, this was the spring equinox in the North and the autumn equinox in the South). Going by this calendar beginning, a major dust storm occured in year 1 of the Mangli calendar (1956 in the Gregorian calendar). This start date is not unique to the Mangli calendar but was proposed by Dr. R. Todd Clancy of the Space Science Institute and is commonly used by scientists for tracking time on Mars.

Times given are local times for the prime meridian of Mars.

Calendar Maker

Start of Week: 
Additional calendar:

 Gregorian (After 1582) or Julian (Before 1582) events
 Muslim events
 Hindu events
 Jewish events
 Julian events (After 1582)
 Astronomical events
 Include multiple-day periods



Meeus, Jean. Astronomical Algorithms 2nd ed. Richmond: Willmann-Bell, 1998. ISBN 0943396-61-1.
The essential reference for computational positional astronomy.
P. Kenneth Seidelmann (ed.) Explanatory Supplement to the Astronomical Almanac . Sausalito CA: University Science Books, [1992] 2005. ISBN 1-891389-45-9.
Authoritative reference on a wealth of topics related to computational geodesy and astronomy. Various calendars are described in depth, including techniques for interconversion.
The Institut de mécanique céleste et de calcul des éphémérides in Paris provides excellent on-line descriptions of a variety of calendars.
The Planetary Society: Mars' Calendar provides information on timekeeping and seasons on Mars used for the Mangli calendar.
Wikipedia: Mars and other pages provide essential information on the orbit of Mars.
Encyclopædia Britannica provides the historical background on King Cyaxares (Hevexştre) for the description of the Persian/Kurdish calendar.
R. Stöckli, E. Vermote, N. Saleous, R. Simmon and D. Herring (2005). The Blue Marble Next Generation - A true color earth dataset including seasonal dynamics from MODIS. Published by the NASA Earth Observatory. Corresponding author:
Maps from NASA for drawing the coordinate map
Moveable Type on the distance and bearing for great circle routes, used in the Qibla calculation
Alan Eliasen's Moon Locator for various algorithms for the position of the moon
Calendars through the Ages from webexhibits for information on various calendars
The original Fourmilab Calendar Converter
A huge thanks to this Fourmilab page and John Walker for basically making this site and for putting it into the public domain for me to build on.

Harys Dalvi
حارث دلوی
हारिस दळवी
December, MMXVIII – April, MMXXI
دسمبر ۲۰۱۸ء – اپریل ۲۰۲۱ء
اگہن سموت ۱۹۴۰ – چیت سموت ۱۹۴۳

दिसंबर २०१८ – अप्रैल २०२१
अगहन संवत १९४० – चैत संवत १९४३

by John Walker
September, MMXV

This document is in the public domain.
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