First construct the natal axis
Take two tropical zodiac longitudes from a birth chart and bisect their shorter circular arc. The opposite point, 180° away, is the second end of the same midpoint axis. For a Sun at 350° and Moon at 10°, the short arc crosses 0° Aries; its center is 0°, its opposite is 180°, and its 90° dial coordinate is 0°. A plain arithmetic average of 350° and 10° would misleadingly report only 180° as though the shorter center were in Libra.
At exact opposition the two arcs between planets are equally short, so there is no unique preferred center. The axis remains well defined. For bodies at 0° and 180°, the two candidate centers are 90° and 270°, giving a single axis at 90° modulo 180° and a 90° dial coordinate of 0°.
Why one pair has four transit targets
Reducing a longitude modulo 90° places conjunctions, squares and oppositions on one dial coordinate. If a midpoint axis folds to 15°, the transit targets are 15°, 105°, 195° and 285° tropical longitude. A moving planet crossing 105° is square to one end of the midpoint axis, not literally standing at its 15° location. The result table keeps the absolute zodiacal target alongside the folded coordinate so these are not confused.
How the date finder works
The date finder calculates apparent geocentric tropical longitude for the chosen moving Sun, Moon or planet, using its bundled Astronomy Engine. It samples the selected interval in one-hour steps. Whenever the signed angular distance to one of the four targets changes sign without a 180° wrap, it bisects the interval and rounds the root to the nearest minute. A retrograde planet may cross a target before and after a station; both crossings are listed and motion direction is labeled from the bracketing samples. The CSV includes every result even when the on-page list is shortened.
This is a crossing search, not an orb calendar. A planet can sit inside an orb for hours or days without an exact hit in the selected interval. Conversely, a crossing at one minute does not establish an effect throughout the surrounding days. A perfectly tangent station contact, or two crossings less than one hour apart, may escape the hourly brackets. Check fine station timing in an ephemeris when a boundary matters.
Birth time and local clocks
The Sun/Moon midpoint depends on the birth Moon, which moves enough during a day to shift an exact transit date. The all-pairs option also includes Ascendant and Midheaven pairs, whose locations require a reliable birth time and birthplace. This tool therefore asks for a recorded birth hour and coordinates rather than presenting noon as a precise answer when the hour is missing. The natal chart uses the historical UTC offset in force at birth; the calendar uses a separate fixed offset for displaying local dates. If daylight saving changes during the selected interval, divide the search into ranges with the appropriate offsets. UTC times in the CSV remain unambiguous.
Use the natal midpoint dial to inspect static triads and four-point structures, or the personal transit calendar to compare moving planets with natal planets. Open the midpoint transit calendar when the question is about the timing of a moving planet against a natal midpoint axis.