The zi hour and the day boundary

Where a day is taken to begin

The day column is read from a calendar day, and a calendar day has to begin somewhere. Nothing in a birth record settles where. A date and a clock time say when a birth happened; they do not say whether the hour before midnight belongs to the day that is ending or to the one that is starting.

This calculator carries three settings for that, in a list on the same screen as the date fields. One takes the day to change at midnight. One takes it to change at 23:00, when the zi hour begins. The third is a late zi hour treatment, which on this screen is also described as changing the day at midnight. The list shows the site default first and labels it as the default, and any of the three can be selected before a chart is produced.

The default here is the first of them. It was picked as the least weakly supported of the three, and that is a different thing from having been checked against a source. The screen carries that statement beside every result, and this page carries it rather than a firmer one.

One hour of the clock, and the branch that does not move

The setting reaches one hour and no further: from 23:00 to 23:59 on the clock of the place of birth, and only when a time of birth was entered. A birth at 00:30 comes out the same under all three settings, and so does a birth at 22:30. With no time of birth the setting does not engage at all, because the hour column is not produced either.

The branch of the hour column does not move under any of them. In this calculation the zi branch covers 23:00 through 00:59, so a birth in either half of that stretch carries the same branch whichever setting is in force. What is open is not which branch the hour gets. It is which calendar day the 23:00 hour is counted into, and that question has no answer inside the birth record.

What moves in a chart when the setting moves

Under the 23:00 setting a birth in that hour is counted into the following day, so the day column becomes the following day's pair: one step along the cycle of sixty. The hour column keeps its branch and takes a different stem, because the hour stem is derived from the day stem. The element counts across the eight characters shift with them.

The year and month columns stay where they were. They are settled from the solar term the birth moment falls in, before the day boundary is applied at all. Three inputs were run here against both settings — one in June 1990, one on February 3, 2026 close to a solar term, and one at 23:30 on December 31, 1990, where the following day is in the next calendar year. In all three the year and month columns came out identical while the day column advanced by one.

Two of the three settings return the same day column here. The late zi hour treatment returns what the midnight setting returns. That is not a finding that the two are the same thing. The rule that would separate them was looked for and not found, and no branch was written in to stand where it would go, so selecting that option leaves the chart as it was.

What the screen records, and what it leaves out

Under a chart the calculator prints a row for this setting: the wording of the option that was in force, with the machine value beneath it. If a reader selected something other than the default, the screen records beside the result that the choice came from the reader and names what the site default was.

What the screen does not print is which of the two outcomes the setting reached for that particular input. The calculation holds a value for whether the day was kept or moved, and that value is not one of the rows. Whether it moved is read off the birth time and the setting rather than off the screen.

Which of the three a tradition settles on is outside what this page states. What it states is where the three part company, how wide that window is, which columns move when the setting does, and which of them do not.