This applet is from the compact disk accompanies the book Calendrical
Calculations: The Millennium Edition by Edward M. Reingold and
Nachum Dershowitz (Cambridge University Press, second printing, 2002).
information, and any errata, see the site
have been careful to insure that our conversion functions work for at
least 10,000 years before/after the present, but the Chinese code, for
example, will not work for the 200th century.
astronomical code we use is not the best available. Hence,
positions and times of astronomical evenets are only approximate.
More precise code would be more time-consuming and complex and would
not necessarily yield in more accurate results for those calendars that
depended on observations, tables, or less accurate calculations. Thus,
the correctness of a date on any of the astronomical calendars
Islamic, French Revolutionary, Chinese, and Future
Bahá'í) is contingent on the physical and historical
accuracy of the astronomical code used in its calculation. For example,
when the equinox occurs close
to noon, our Persian calendar may be off a day. Likewise, historically,
the Chinese calendar for Gregorian year 1906, Month 4 began on April
24, not April 23 as shown; this disagreement occurs because our
calculations of times
of solar and lunar events are more accurate than the
seventeenth-century methods used by the Chinese until 1913.
- Checking the results of
conversions against the
historical record is sometimes misleading because the different
calendars begin their days at different times. Julian day numbers count
days from noon to noon;
modified Julian day numbers count days from midnight to midnight; fixed
day numbers count days from midnight to midnight. On the Hebrew
and Islamic calendars each day begins the prior evening at local
the Hindu calendars, each day begins at local sunrise. All of our
conversions are as of noon.
- All of our
"correct" (mathematically sensible) results for negative years and for
prior to the epoch of a calendar. However, these results may be
wrong. In particular,
year 0 is assumed to exist for all calendars except the Julian
and the Persian.
- The sequence of
Hindu months, their names, and the starting month of the new year all
differ regionally. We follow the conventions that the solar year
begins with Sowramana Ugadi (first of Vaiśākha), and the lunar year
with Chandaramana Ugadi (first of Chaitra). Our lunisolar calendar
follows the rules of the
Sūrya-Siddhānta, as amended by Gaṇesa Daivajna, except that the actual
time of sunrise in Ujjain is used. Months are from new moon to
new moon. The day numbers of the second ("dark") half of each
lunar month typically start over from 1. The solar
calendar follows the Orissa rule (one of four or five major variants)
and actual sunrise in Ujjain, which can differ by a day or two from the
rules used elsewhere.
- The astronomical
Islamic calendar is an approximation based on one simple way of
when the new cresent moon should become visible in Cairo; however, the
actual date may depend on reported observations of the crescent
moon. Thus, month beginnings and endings can be in error by a day
or so, and vary from country to country.
- The year in the French Revolutionary calendar date is not spelled
correctly; it should be "Année de la République".