Clock time against body time
Two different sums run on this site. One counts cycles inside a night. The other moves a whole night sideways. They share almost nothing.
The wake-time pages take a fixed alarm and count backwards in a unit. The travel pages take a fixed rhythm and move it to a different clock. The first is multiplication and subtraction; the second is arithmetic on a circle.
A dial has no ends
Twenty-four hours joined into a loop has no beginning, so a nine-hour move in one direction is also a fifteen-hour move in the other, and they arrive at the same place. Whenever the planner works out a shift it takes whichever of the two is shorter, so no move it asks for is ever longer than twelve hours.
That is also why the same trip reversed is not the same trip. Flying west, the bedtime walks later; flying east, earlier. The planner has a page for each direction on the busiest routes for that reason.
What the site will not tell you
How fast a person actually adjusts. An hour a night is a step size chosen because it divides neatly into the numbers involved, not a rate anybody has established for you, and the planner offers half an hour and ninety minutes precisely because the hour is not special.
Four cases the dial settles
Past twelve hours the other way round is shorter. Flying London to Auckland in January, when Auckland runs thirteen hours ahead of London, the planner moves a bedtime eleven hours later rather than thirteen earlier. In July the gap is eleven hours and the planner moves it eleven hours earlier. The same trip asks for eleven nights at an hour a night in both months, in opposite directions.
At exactly twelve there is no shorter way. Johannesburg and Honolulu are twelve hours apart all year, because neither changes its clocks, so the two ways round are the same length. The planner then moves the bedtime later, whichever of the two you fly from.
The date line is not on the dial. In January Auckland is twenty-three hours ahead of Honolulu by the calendar, which on the dial is Honolulu one hour ahead, so flying from Auckland to Honolulu asks for a bedtime one hour earlier: a single night of shifting.
A half-hour zone costs a whole night. Delhi keeps five and a half hours ahead of London's winter clock and four and a half ahead of its summer one. At an hour a night that is six nights in January and five in July, the last of them a half-hour step.
The travel pages are timetables. They make no claim about how anybody responds to a change of zone and offer nothing about light, meals or medication, all of which are subjects for somewhere other than a calculator.