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<!DOCTYPE html><html lang="en-US"><meta name="keywords" content="Chinese calendar, frequently asked questions, caleendar calculation"><meta charset="UTF-8"><meta name="viewport" content="width=device-width,initial-scale=1"><head><title>FAQ</title><link rel="stylesheet" href="calendar_min.css"><script src="header_min.js"></script><base href="https://ytliu0.github.io/ChineseCalendar/"><script async src="https://www.googletagmanager.com/gtag/js?id=G-SN0QJRDXXT"></script><script>function gtag(){dataLayer.push(arguments)}window.dataLayer=window.dataLayer||[],gtag("js",new Date),gtag("config","G-SN0QJRDXXT")</script></head><body><div id="wrap" style="max-width:800px;margin:auto"><div id="menu"></div><div id="language"></div><h1>Frequently Asked Questions</h1><ol><input type="checkbox" class="accordion" id="conversion_program"> <label class="accordion" for="conversion_program"><li>I want to develop an app for conversion between Western and Chinese calendars. What is the best way to do it?</li></label><div class="content"><p>The simplest method is to get a conversion table/tables (such as the ones <a href="table.html">here</a>) between Western and Chinese calendar and then do a table look-up.</p></div><input type="checkbox" class="accordion" id="conversion_tables"> <label class="accordion" for="conversion_tables"><li>Where do you get the calendar data on the <a href="table.html">conversion table page</a>?</li></label><div class="content"><p>This is explained in detail on the <a href="computation.html">Calendar Calculation page</a>. In a nutshell...</p><p>The data for the <a href="computation.html#modern">modern period (1912-2200)</a> are computed according to the rules stated by the GB/T 33661-2017 document, but several dates before 1929 are corrected according to the <i>New Edition of Perpetual Calendar (revised edition)</i> (《《新编万年历（修定本）》) edited by the Purple Mountain Observatory (紫金山天文台).</p><p>The data for the <a href="computation.html#qing">Qing period (1645-1911)</a> are based on <i>New Edition of Perpetual Calendar (revised edition)</i> and <i>3500 Years of Calendars and Astronomical Phenomena</i> (《三千五百年历日天象》) by Zhāng Péiyú (張培瑜).</p><p>The data for the <a href="SouthernMingCalendar.html">Southern Ming and Zheng Period (1645 – 1683)</a> are largely based on <i>Cán Míng Dà Tǒng Lì</i> (殘明大統曆 or <i>Datong Calendar of the Waning Ming Dynasty</i>) by Fu Yili (傅以禮) compiled in the 19th century.</p><p>The data for the <a href="computation.html#imperial">Middle Han to Ming Period (104 BCE – 1644 CE)</a> are largely based on <i>3500 Years of Calendars and Astronomical Phenomena</i>, but several dates are corrected based on various reliable sources.</p><p>The data for <a href="QinHanCalendars.html">Qin and Early Han period (221 BCE – 104 BCE)</a> are calculated according to the article "Qín zhì Hàn chū (qián 246 zhì qián 104) lì fǎ yán jiū — yǐ chū tǔ lì jiǎn wéi zhōng xīn" (秦至汉初(前246至前104)历法研究—以出土历简为中心 or "Researches on Calendars from Qin to early Han (246 B.C to 104 B.C.) — centering on excavated calendrical bamboo slips") by Lǐ Zhōnglín (李忠林) in 2012.</p><p>The data for the Warring States period (480 BCE – 222 BCE) are based on the <a href="guliuli.html">ancient six calendars</a>, using the information in Section 3.6 of the book <i>Zhōng Guó Gǔ Dài Lì Fǎ</i> (《中国古代历法》 or <i>Ancient Chinese Calendars and Almanacs)</i> by Zhāng Péiyú (張培瑜), Chén Měidōng (陳美東), Bó Shùrén (薄樹人), and Hú Tiězhū (胡鐵珠).</p><p>The <a href="chunqiu.html">calendar data for the Lu State in the Spring and Autumn Period (722 BCE – 481 BCE)</a> are calculated based on the information in Section 3.5 of <i>Ancient Chinese Calendars and Almanacs</i>.</p></div><input type="checkbox" class="accordion" id="conversion_formula"> <label class="accordion" for="conversion_formula"><li>Is there a simple formula to calculate the Chinese calendar?</li></label><div class="content"><p>For the modern Chinese calendar, the short answer is no.</p><p>As explained on the <a href="rules.html">Chinese Calendar rule page</a>, modern Chinese calendar is calculated according to the GB/T 33661-2017 document. The rules are strict (especially the one-second accuracy requirement for the computation of moon phases and solar terms) and there is no shortcut. Whether something is simple or not also depends on one's experience. For those who are familiar with astronomical computation, the calculation required by GB/T 33661-2017 document is not that difficult, although not simple.</p><p>Since the 7th century, the topics involved in calendrical astronomy in China were close to those covered in the modern astronomical almanac. Making calendar was just one funcion of calendrical astronomy. The calculations in calendrical astronomy were based on the most accurate observation data and most advanced theory available at the time. The calculations were also not simple relative to the calculation tools available at the time. So the requirements stated in the GB/T 33661-2017 document are in accord with the Chinese tradition of calendrical astronomy.</p><p>However, there are simple approximate formulae to calculate solar terms and moon phases. You can find them in <i>Astronomical Algorithms</i> by Jean Meeus. The book only provides formulae for the equinoxes and solstices, but it should not be difficult to generalize them to calculate the other solar terms. While the accuracy of those approximate formulae do not meet the requirement of GB/T 33661-2017, they can still be used to calculate the Chinese calendar. The error of the computed Chinese calendar dates may be ~0.1% or even less. One can first use those approximate formulae to calculate the Chinese calendar, compare the calculated dates with the official Chinese calendar promulgated by the Purple Mountain Observatory, and then correct the ~0.1% error. This could be an alternative method to do the Western-Chinese calendar conversion.</p></div><input type="checkbox" class="accordion" id="sexagenary_calculation"> <label class="accordion" for="sexagenary_calculation"><li>How do you calculate the sexagenary cycles?</li></label><div class="content"><p>This is explained in detail on the <a href="sexagenary.html">sexagenary cycle page</a>. The sexagenary cycle can be used to count years, months, days, and (double) hours. The sexagenary years, days and hours are easy to compute. The sexagenary month on a particular Gregorian date is more complicated to compute. However, sexagenary months were rarely used even in ancient official Chinese documents, and hours were simply indicated by the branch numbers only.</p></div><input type="checkbox" class="accordion" id="conjunction"> <label class="accordion" for="conjunction"><li>Why were there discrepancies between the start of Chinese months and the times of new moons in the ancient time?</li></label><div class="content"><p>The question refers to the occasional mismatches between the times of new moons indicated on the <a href="index.html">calendar page</a> and the start of Chinese months in the ancient time. For example, a new moon occurred at 19:54 on March 6 in 813, but the start date of the second Chinese month was on March 7, 813.</p><p>As explained on the <a href="rules.html">Chinese calendar rules page</a>, a new moon (conjunction) must fall on the first day of a Chinese month. This rule was established since ancient times. The mismatches are caused by at least the following three reasons.</p><ol><li><p>The times of moon phases listed on the calendar page are calculated using modern ephemerides and following modern definition. The calculation of moon phases in the ancient time could deviate significantly from modern calculation. For example, the conjunctions were calculated by taking into account only the mean motion of the Moon and Sun (mean conjunction) before the 7th century. Modern calculations also take into account the non-uniform motion of the Sun and Moon (true conjunction). The times of mean conjunctions can deviate from the true conjunctions by one day. It is also well-known that the conjunction times determined by calendars in the Qin and Early Han dynasties (221 BCE – 104 BCE) were later than the astronomical conjunction times. The average of the time differences was about one day (see the discussion <a href="QinHanCalendars.html#conjDiff">here</a>). This explains why the recorded solar eclipses in the early Han dynasty often occurred one day (and sometimes two days) before the calendrical conjunction days. True conjunctions were used in the calendar calculation since the mid 7th century. However, the calculated times were not very accurate.</p></li><li><p>The times of moon phases listed on the calendar page are the local mean time of 120°E (UT+8). Here UT refers to UT1 (before 1972) or UTC (1972 and later). The ancient people didn't use mean solar time. Their times were based on the local apparent solar time. For example, the capital of China was at the present day Xi'an (longitude = 108.9°E) in the Tang dynasty (618 – 907). The difference between the apparent solar time of Xi'an and UT+8 is 44 minutes + the equation of time.</p></li><li><p>The Chinese calendars between 665 and 1280 sometimes imposed the <i>jinshuo rule</i> (進朔法), which stipulated that the conjunction day would be moved to one day later if the conjunction time fell on later than ~18:00 (the exact time slightly depended on seasons) if no solar eclipse was visible on that day.</p></li></ol><p>The discrepancy in the second Chinese month of 813 mentioned above was likely casued by the jinshuo rule. Since 1914, moon phases and solar terms have been computed using modern method. However, time was based on the mean solar time of the Beijing meridian (116°25' E), which has a time difference of about 14 minutes with respect to UT+8. For example, the new moon associated with the Chinese new year in 1916 occurred on February 4 at 00:05 (UT+8), but the Chinese new year was celebrated on February 3 because the new moon was on February 3 at 23:51 in Beijing's local mean time. The current China standard time (UT+8) was adopted in 1929.</p></div><input type="checkbox" class="accordion" id="leap_months_1_12"> <label class="accordion" for="leap_months_1_12"><li>Why are leap months after the first and 12th months extremely rare?</li></label><div class="content"><p>This question is explained in detail on the page <a href="leap_month_1_12.html">on the rarity of leap months after the first and 12th month</a>. The following is an abridged version of that page.</p><p>Since the adoption of true solar terms in 1645, leap months after the first and 12th months have not occurred yet. I used the rules of modern Chinese calendar GB/T 33661-2017 to find all leap months from now to 3500. I find that the leap months after the first month only occur 6 times, and the leap months after the 12th month only occur twice. The first leap month after the first month will occur in 2262, and the first leap month after the 12th month will occur in 3359 (Chinese year 3358).</p><p>The following explanation assumes the readers already know about the rules of Chinese calendar explained on the <a href="rules.html">Chinese calendar rule page</a>. The complete rules and their associated concepts will not be repeated here.</p><p>The necessary condition for a leap month after the 12th month is having a lunar month without a major solar term (aka the no Zhongqi month) between Z12 (around Jan 20) and Z1 (around Feb 19), and the necessary condition for a leap month after the first month is having a no Zhongqi month between Z1 (around Feb 19) and Z2 (around March 21). The usual explanation for the rarity of leap months after the first and 12th months is that the Earth passes perihelion in early January in recent centuries and hence Earth's motion is relatively fast from December to February. The time interval between Z12 and Z1 and the time interval between Z1 and Z2 are relatively short, and it's relatively rare to have a no Zhongqi month occurring between these major solar terms. However, this is only part of the reason.</p><p>Earth moving fast near perihelion not only makes no Zhongqi months around that time rare, but also increases the frequency of lunar months with two major solar terms. Since the time interval between two major solar terms at times when Earth is near perihelion can be smaller than 30 days, it's possible to squeeze two major solar terms within a lunar month. In fact, the average number of days between Z11 and Z12 is so short that it's more likely to have Z11 and Z12 within a lunar month than having a no Zhongqi month between Z11 and Z12. Calculation shows that there are 17 lunar months with both Z11 and Z12 in 1921-3500 and 10 no Zhongqi months between Z11 and Z12 in the same period. This is also true for the Z12-Z1 pair: it's more likely to have Z12 and Z1 within a lunar month than having a no Zhongqi month between Z12 and Z1. Calculation shows that there are 14 lunar months with both Z12 and Z1 in 1921-3500 and 9 no Zhongqi months between Z12 and Z1.</p><p>The intercalation rule of modern Chinese calendar is applied to the lunar months in a sui, which is the period from the lunar month containing Z11 (winter solstice) to the month before the following month containing Z11. There can be either 12 or 13 lunar months in a sui. I call the sui with 12 lunar months as a regular sui and the sui with 13 lunar months a leap sui. The intercalation rule stipulates that a leap month is the first no Zhongqi month after Z11 in a leap sui. That's why having a no Zhongqi month is only a <i>necessary</i> condition for a leap month. If a no Zhongqi month appears in a regular sui, it's not a leap month. If there are two no Zhongqi months in a leap sui, only the first one is a leap month. A no Zhongqi month that is not a leap month is called a <i>fake leap month</i>.</p><p>There are 12 major solar terms in a sui: Z11, Z12, Z1, Z2, ..., Z10. If a lunar month with two major solar terms occurs in a regular sui. The remaining 10 major solar terms will have to be placed in the remaining 11 months. It follows that there will be a month without a major solar term. Since there is no leap month in a regular sui, this no Zhongqi month is a fake leap month. If a lunar month with two major solar terms occurs in a leap sui. The remaining 10 major solar terms will have to be placed in the remaining 12 months. It follows that there will be two no Zhongqi months in this sui. One of them will be a leap month and the other will be a fake leap month. Hence lunar months with two major solar terms and fake leap months occur in pairs.</p><p>We see that the occurrence of lunar months with two major solar terms create more no Zhongqi months than the leap months required for intercalation. The extra no Zhongqi months become fake leap months. In 1921-3500, there are 22 no Zhongqi months between Z1 and Z2 (candidates for leap months after the first month) and 9 no Zhongqi months between Z12 and Z1 (candidates of leap months after the 12th month). They are indeed very rare. However, of the 22 no Zhongqi months between Z1 and Z2, 16 of them are fake leap months thanks to the occurrence of lunar months with two major solar terms prior to these no Zhongqi months, leaving 6 to become the leap months after the first month. Of the 9 no Zhongqi months between Z12 and Z1, 7 of them are fake leap months thanks to the occurrence of lunar months with two major solar terms prior to these no Zhongqi months, leaving only 2 to become the leap months after the 12th month. The occurrence of lunar months with two major solar terms effectively suppresses the occurrence of the leap months after the first and 12th month.</p><p>Hence it's the combination of the rarity of no Zhongqi months between Z1-Z2 and between Z12-Z1 and the occurrence of lunar months with two major solar terms that makes the leap months after the first and 12th month extremely rare.</p></div></ol></div><br><br><script>header(0,"","faq")</script></body></html>