The Jewish Calendar - Section 2: Detailed Molad Tables

REGULAR (NON-LEAP) YEAR TABLE
THIS Rosh Hashanah					NEXT Rosh Hashanah				THIS Year's Result Length
Detailed New Moon Time		Result Day	Shift Reason(s)	Day Phase Shift	New Moon Time	Result Day	Shift Reason(s)	Day Phase Shift	THIS Year's Result Length
Sunday am	pre 3:11:20am	Mon	S/W/F	+1	Thu am	Thu	-	[4]+0	353
Sunday am	later am	Mon	S/W/F	+1	Thu pm	Sat	PM, S/W/F	[4]+2	355
Sunday pm	pre 3:11:20pm	Mon	S/W/F, PM	+1	Thu pm	Sat	PM, S/W/F	[4]+2	355
Sunday pm	later pm	Mon	S/W/F, PM	+1	Fri am	Sat	S/W/F	[5]+1	355
Monday am	pre 3:11:20am	Mon	-	0	Fri am	Sat	S/W/F	[4]+1	355
	3:11:20am, up to but excluding 9:32:43+1/3am	Mon	-	0	Fri pm	Sat	S/W/F, PM	[4]+1	355
	later am with previous year non-leap	Mon	-	0	Fri pm	Sat	S/W/F, PM	[4]+1	355
	later am with previous year leap	Tue	382DAYS	+1	Fri pm	Sat	S/W/F, PM	[4]+1	354
Monday pm	pre 3:11:20pm	Tue	PM	+1	Fri pm	Sat	S/W/F, PM	[4]+1	354
Monday pm	later pm	Tue	PM	+1	Sat am	Sat	-	[5]+0	354
Tuesday am	pre 3:11:20am	Tue	-	0	Sat am	Sat	-	[4]+0	354
Tuesday am	later am	Thu	356DAYS	+2	Sat pm	Mon	PM, S/W/F	[4]+2	354
Tuesday pm	pre 3:11:20pm	Thu	PM, S/W/F	+2	Sat pm	Mon	PM, S/W/F	[4]+2	354
Tuesday pm	later pm	Thu	PM, S/W/F	+2	Sun am	Mon	S/W/F	[5]+1	354
Wednesday am	pre 3:11:20am	Thu	S/W/F	+1	Sun am	Mon	S/W/F	[4]+1	354
Wednesday am	later am	Thu	S/W/F	+1	Sun pm	Mon	S/W/F, PM	[4]+1	354
Wednesday pm	pre 3:11:20pm	Thu	S/W/F, PM	+1	Sun pm	Mon	S/W/F, PM	[4]+1	354
Wednesday pm	later pm	Thu	S/W/F, PM	+1	Mon am	Mon	-	[5]+0	354
Thursday am	pre 3:11:20am	Thu	-	0	Mon am	Mon	-	[4]+0	354
Thursday am	later am	Thu	-	0	Mon pm	Tue	PM	[4]+1	355
Thursday pm	pre 3:11:20pm	Sat	PM, S/W/F	+2	Mon pm	Tue	PM	[4]+1	353
	3:11:20pm, up to but excluding 6:22:40pm	Sat	PM, S/W/F	+2	Tue am	Tue	-	[5]+0	353
	later pm with next year leap	Sat	PM, S/W/F	+2	Tue am	Tue	-	[5]+0	353
	later pm with next year non-leap	Sat	PM, S/W/F	+2	Tue am	Thu	356DAYS	[5]+2	355
Friday am	pre 3:11:20am with next year leap	Sat	S/W/F	+1	Tue am	Tue	-	[4]+0	353
	pre 3:11:20am with next year non-leap	Sat	S/W/F	+1	Tue am	Thu	356DAYS	[4]+2	355
	later am	Sat	S/W/F	+1	Tue pm	Thu	PM, S/W/F	[4]+2	355
Friday pm	pre 3:11:20pm	Sat	S/W/F, PM	+1	Tue pm	Thu	PM, S/W/F	[4]+2	355
Friday pm	later pm	Sat	S/W/F, PM	+1	Wed am	Thu	S/W/F	[5]+1	355
Saturday am	pre 3:11:20am	Sat	-	0	Wed am	Thu	S/W/F	[4]+1	355
Saturday am	later am	Sat	-	0	Wed pm	Thu	S/W/F, PM	[4]+1	355
Saturday pm	pre 3:11:20pm	Mon	PM, S/W/F	+2	Wed pm	Thu	S/W/F, PM	[4]+1	353
Saturday pm	later pm	Mon	PM, S/W/F	+2	Thu am	Thu	-	[5]+0	353

TABLE 2a. Detailed molad table for regular years.

LEAP YEAR TABLE
THIS Rosh Hashanah					NEXT Rosh Hashanah				THIS Year's Result Length
Detailed New Moon Time		Result Day	Shift Reason(s)	Day Phase Shift	New Moon Time	Result Day	Shift Reason(s)	Day Phase Shift	THIS Year's Result Length
Sunday am	pre 2:27:16+2/3am	Mon	S/W/F	+1	Fri pm	Sat	S/W/F, PM	[5]+1	383
Sunday am	later am	Mon	S/W/F	+1	Sat am	Sat	-	[6]+0	383
Sunday pm	pre 2:27:16+2/3pm	Mon	S/W/F, PM	+1	Sat am	Sat	-	[6]+0	383
Sunday pm	later pm	Mon	S/W/F, PM	+1	Sat pm	Mon	PM, S/W/F	[6]+2	385
Monday am	pre 2:27:16+2/3am	Mon	-	0	Sat pm	Mon	PM, S/W/F	[5]+2	385
Monday am	later am	Mon	-	0	Sun am	Mon	S/W/F	[6]+1	385
Monday pm	pre 2:27:16+2/3pm	Tue	PM	+1	Sun am	Mon	S/W/F	[6]+1	384
Monday pm	later pm	Tue	PM	+1	Sun pm	Mon	S/W/F, PM	[6]+1	384
Tuesday am	pre 2:27:16+2/3am	Tue	-	0	Sun pm	Mon	S/W/F, PM	[5]+1	384
Tuesday am	later am	Tue	-	0	Mon am	Mon	-	[6]+0	384
Tuesday pm	pre 2:27:16+2/3pm	Thu	PM, S/W/F	+2	Mon am	Tue	382DAYS	[6]+1	383
Tuesday pm	later pm	Thu	PM, S/W/F	+2	Mon pm	Tue	PM	[6]+1	383
Wednesday am	pre 2:27:16+2/3am	Thu	S/W/F	+1	Mon pm	Tue	PM	[5]+1	383
	2:27:16+2/3am, up to but excluding 5:38:36+2/3am	Thu	S/W/F	+1	Tue am	Tue	-	[6]+0	383
	later am	Thu	S/W/F	+1	Tue am	Thu	356DAYS	[6]+2	385
Wednesday pm	pre 2:27:16+2/3pm	Thu	S/W/F, PM	+1	Tue am	Thu	356DAYS	[6]+2	385
Wednesday pm	later pm	Thu	S/W/F, PM	+1	Tue pm	Thu	PM, S/W/F	[6]+2	385
Thursday am	pre 2:27:16+2/3am	Thu	-	0	Tue pm	Thu	PM, S/W/F	[5]+2	385
Thursday am	later am	Thu	-	0	Wed am	Thu	S/W/F	[6]+1	385
Thursday pm	pre 2:27:16+2/3pm	Sat	PM, S/W/F	+2	Wed am	Thu	S/W/F	[6]+1	383
Thursday pm	later pm	Sat	PM, S/W/F	+2	Wed pm	Thu	S/W/F, PM	[6]+1	383
Friday am	pre 2:27:16+2/3am	Sat	S/W/F	+1	Wed pm	Thu	S/W/F, PM	[5]+1	383
Friday am	later am	Sat	S/W/F	+1	Thu am	Thu	-	[6]+0	383
Friday pm	pre 2:27:16+2/3pm	Sat	S/W/F, PM	+1	Thu am	Thu	-	[6]+0	383
Friday pm	later pm	Sat	S/W/F, PM	+1	Thu pm	Sat	PM, S/W/F	[6]+2	385
Saturday am	pre 2:27:16+2/3am	Sat	-	0	Thu pm	Sat	PM, S/W/F	[5]+2	385
Saturday am	later am	Sat	-	0	Fri am	Sat	S/W/F	[6]+1	385
Saturday pm	pre 2:27:16+2/3pm	Mon	PM, S/W/F	+2	Fri am	Sat	S/W/F	[6]+1	383
Saturday pm	later pm	Mon	PM, S/W/F	+2	Fri pm	Sat	S/W/F, PM	[6]+1	383

TABLE 2b. Detailed molad table for leap years.

Please keep in mind that the times in these tables are shown in Western day format. For example, "6:22:40pm" of "Thursday pm" refers to a time that occurs during the last quarter of the Western day of Thursday (with that day ending at midnight), not during the first few hours of a Jewish Thursday (with that day ending at the following sunset or 6 p.m.—roughly 24 hours later)! The corresponding modern Jewish day time is, of course, within the first hour of a modern Jewish Friday. Depending on exactly when the sun sets, the corresponding traditional Jewish day here could be either Thursday (late in the day) or Friday (early).

These two tables should, for the most part, be easy to understand. But here is some additional information on some of the entries. The "Result Day" is the day that Rosh Hashanah is actually observed. The "Shift Reason(s)" can show any of the four shift-causing conditions ("dechiyyot"). "Day Phase Shift", under "THIS Rosh Hashanah", indicates the number of days in the week that this year's Rosh Hashanah is shifted forward, from the day containing its corresponding new moon. The number after the plus sign in each "Day Phase Shift" entry under "NEXT Rosh Hashanah" refers to the number of days in the week that next year's Rosh Hashanah is shifted forward, from the day containing that corresponding new moon. But the bracketed number in this column shows the day-of-the-week difference between the corresponding new moon days of the two Rosh Hashanahs (i.e., how many days forward along the week that next year's new moon day occurs, relative to this year's). If you add such a bracketed number in a given row to its number after the plus sign, then from this sum subtract this row's "Day Phase Shift" number under "THIS Rosh Hashanah", you come up with the day-of-the-week difference between the two Rosh Hashanah holidays (i.e., next Rosh Hashanah minus this Rosh Hashanah). This is illustrated below:

where NM = New Moon, and RH = Rosh Hashanah. The Rosh Hashanah difference (nextRH - thisRH) is useful in helping to determine the number of days in the year ("THIS Year's Result Length") for the given row.