Why do our dates differ from the Hebrew Calculated Date (HCD)?

The modern rabbinical calendar (HCD), fixed by Hillel II around 359 CE, bakes Saturday into the system as a fixed weekly Sabbath. Because of this, it introduces postponement rules (dehiyyot) that shift the start of months to prevent holy days from falling on certain weekdays. Month lengths for Cheshvan and Kislev are adjusted, and Rosh Hashanah is moved if it would land on Sunday, Wednesday, or Friday, all to protect the Saturday Sabbath cycle from conflicts.

This calendar does not honor Saturday as the Sabbath. Instead, the Sabbath cycle resets with each new moon, as Isaiah described: from new moon to new moon and Sabbath to Sabbath. With no fixed weekday Sabbath to protect, there is no need for postponements. The full moon opposition on the evening of day 14, when the sun and moon appear on opposite horizons at sunset, confirms the month is in sync. The result is a calendar that can differ from the HCD by one to two days in any given month.

How month lengths are set. The moon's month is not 29 and a half days. It runs from 29 days 7 hours to 29 days 20 hours in a wave that repeats about every 14 months. Months keep the 30/29 rhythm. A month never loses a day, but a 29-day month takes an extra day when the next new moon would otherwise begin while the old moon can still be seen at dawn. Aviv is always 30 days and Iyyar 29, so the Omer count always reaches 50 on Sivan 7. Every month shows its moon's length and marks where an extra day was added. The months already kept stay as they were kept.

A lunar year of 12 months totals roughly 354 days, about 11 days short of a solar year. The 19-year Metonic cycle solves this: 235 lunar months fit almost exactly into 19 solar years. In years 3, 6, 8, 11, 14, 17 and 19 of each cycle a leap month, Adar I, is inserted before Adar (which becomes Adar II). This keeps Aviv (Passover) in the spring.

Gregorian date offset: Each Hebrew day begins at evening (sunset), not midnight, so every lunar day overlaps two Gregorian dates. The Gregorian date shown on each day is its daytime portion. The actual overlap shifts throughout the year with sunset times and daylight saving, but we estimate roughly 30% of the lunar day falls on the previous Gregorian date, and the weekday row is set off by that much. Sky events that happen after sunset are shown on the next day, because that lunar day has already begun. All times are Detroit time, and the calendar reads the same wherever you view it from.