What the calculator does
It converts the entered local clock reading to one UTC instant with the offset you supply. Astronomy Engine gives sidereal time and the true equator/ecliptic orientation at that instant. We add the east-positive geographic longitude to find the local meridian, solve for its upper ecliptic intersection, and put the IC exactly opposite it. The five-row table recalculates the same longitude at times 60 and 10 minutes earlier or later.
This calculation uses the tropical zodiac and true ecliptic/equinox of date. It does not calculate the Ascendant, houses, an entire birth chart, or a place’s historical time-zone rules. For those, see the birth-chart tool and birthplace atlas. House systems differ over whether the MC is exactly the tenth cusp.