Calculation of Zmanim

The zmanim here were adapted from the calculations in the excellent PalmOS program, luach from Penticon. The following discussion is based on the zmanim.txt file from that program.

The halacha involved in determining zmanim is quite complicated and there are many different opinions regarding these calculations. Luach is by no means a halachic authority on this subject, and if there is ever any doubt, you should consult the rabbi.


Zmanim Calculations

The accuracy of the Zmanim calculations cannot be completely validated. The current tests indicate an accuracy within plus/minus one minute when compared to other Jewish Calendar and Sunrise/Sunset programs. If there is ever a question as to the accuracy of Zmanim calculations, consult the rabbi.

The program uses the PHP functions date_sunrise and date_sunset to calculate all the other times.

Official sunrise is when the sun just touches the horizon, and the center of the sun is 50/60 of a degree below the horizon (for the interested, the apparent diameter of the sun is 32 arc-minutes, so the center is 16 minutes from the top, and refraction pulls the image up another 34 minutes. In all, 50 arc-minutes or 50/60 degrees). In PHP, this would be date_sunrise (timestamp, format, latitude , longitude, 90+50/60, gmt_offset). Official sunrise is when the last of the sun drops below the horizon, and the center of the sun is 50/60 of a degree below the horizon. In PHP, this is date_sunset (timestamp, format, latitude , longitude, 90+50/60, gmt_offset). In the following notes, sunrise(x) is short for date_sunrise (timestamp, SUNFUNCS_RET_DOUBLE, latitude , longitude, 90+x, gmt_offset) and sunset(x) is short for date_sunset (timestamp, SUNFUNCS_RET_DOUBLE, latitude , longitude, 90+x, gmt_offset); i.e. the top of sun is x degrees below the horizon and the functions return hours from midnight.

Zman Definition PHP code
Sha'a Zmanis/Sha'a Zmanit 1/12 of the time between Sunrise and Sunset (sunset (50/60)-sunrise(50/60))/12
Alos HaShachar/Alot HaShachar According to the Rambam, when the sun is 16.1 degrees below the horizon sunrise(16.1)
Netz Sunrise sunrise(50/60)
Earliest Tallis/Tallit The earliest time for putting on Tallis/Tallit and Tefillin. The common value used is when the sun is 11 degrees below the horizon sunrise(11)
Latest Sh'ma The latest time that Sh'ma may be recited according to the GR"O; 3 sha'os zmanios/sha'ot zmaniot from netz sunrise(50/60) + (sunset(50/60)-sunrise(50/60))/4
Hatzos/Hatzot Hayom Midday; halfway between sunrise and sunset sunrise(50/60) + (sunset(50/60)-sunrise(50/60))/2
Mincha Gedola This is the earliest that Mincha may be recited. This is half an hour after hatzos/hatzot hayom, with an "hour" defined as the larger of a clock hour and a sha'a zmanis/sha'a zmanit sunrise(50/60) + (sunset(50/60)-sunrise(50/60))/2 + max((sunset (50/60)-sunrise(50/60))/12, 1)/2
Plag Hamincha 1.25 sha'os zmanios/sha'ot zmaniot before sunset sunset(50/60)-(sunset(50/60)-sunrise(50/60))*5/48
Tzeis/Tzeit HaKochavim There are many standards for "3 small stars visible". More stringent standards include when the sun is 6 or 8.5 degrees below the horizon. Rabbi Bienenfeld has paskened that Young Israel uses the standard of 42 minutes after sunset sunset(50/50)+42/60
Light Candles 18 minutes before sunset sunset(50/60)-18/60