NOTE 1: The Gregorian Calendar was introduced on the date which corresponds to 15 October 1582 in that calendar. So strictly speaking there is no date in that calendar prior to that day. But in the present converter, the Gregorian calendar leap year rules are applied backwards to deal with past dates until 1 January 1. This calendar was introduced in an attempt to reform the previously dominant Julian calendar that had gone out of synchrony with seasons.
NOTE 2. In the Hijri Lunar calendar, each month begins on the day following the evening on which the new crescent moon first becomes visible. The observed new crescent is not the same as what is defined in astronomy as new moon and whose time appears as the "new moon phase" in most almanacs, calendars, and newspapers. This is the time each month when the moon's position is almost between the sun and the earth. The moon is not visible at this time, and becomes visible at least about 18 hours later. Moreover, the new crescent doesn't become visible all over the earth at the same time, so the starting dates of Hijri months are strictly local, and usually the same date in other calendars corresponds to two different Hijri dates in different locations across the earth. The calculations in the present converter are for the location of Greenwich, UK. The arithmetic Hijri calendar approximates the astronomical Hijri calendar by making months successively of 30 and 29 days, except for the last month which has 29 days in “normal” years (consisting of 354 days) and 30 days in “leap” years (of 355 days). There are various schemes for classifying years into into normal and leap, the most common being to define a 30-year cycle of which the years 2,5,7,10,13,16,18,21,24,26, and 29 are leap and the remaining years are normal.
NOTE 3: The New Year of the Jalali calendar is the day on which the vernal equinox occurs at Isfahan before true noon there. Jalali is thus a truly astronomical calendar agreeing with the observed solar position. By contrast, the more commonly used Persian calendar approximates the astronomical calendar by an elaborate arithmetic scheme. The names Jalali and Persian both sometimes confusingly refer to the arithmetic calendar. The two calendars are very close but they do disagree occasionally. For example, it can be checked with the present converter that the New Year of 1243 Jalali occured (on March 20, 1864 Gregorian) a day before the New Year of 1243 Persian, and the New Year of 1404 Jalali will occur (on March 21, 2025) a day after the New Year of 1404 Persian.
NOTE 4: The “Julian Day Number” (JDN) is not a calendar in the familiar sense, but is a serial counting of dates with the zero date being January 1, 4713 BCE in the Julian Calendar. A slight complication arises from the convention that a JDN starts at noon while a new date in most modern calendars starts at midnight. Because of that, for example, the JDN at the (midnight) start of the Gregorian calendar date January 1, 2000 is 2451544.5.