How late you start and still finish depends of course on your average pace. But, let me give you some things to think about.
First, Baxter State Park closes for camping in Mid October, around Columbus Day. Katahdin is frequently open for climbing after that, provided that it is safe to do so. The Rangers close the summits whenever there is ice on the upper elevations. So, if you pick your days, it’s usually possible to summit as late as the end of October. That’s your deadline.
Second, some people do a leap frog or flip flop in order to summit before Katahdin is closed for the season.
Third, the typical thru-hike takes 5 1/2 months. Now, according to a survey done by Roland Muesser of 1989 hikers, the typical thru-hiker also takes 24 days off. So, if you reduce the number of zero days, that’s one way to do a thru-hike in fewer days. According to the same survey, 90% of thru-hikers require at least 21 weeks to do the hike. So, you better allow at least 5 months.
Generally speaking, very early May is about the latest you would want to comfortably start a thru-hike. If you start in late May, then you will probably need to hope that the weather holds, or you go faster than the average hiker.
On the other hand, 90% of thru-hikers take less than 27 weeks to do the trail. But, do hikers that have more time take more days off? I don’t know.
Peaks