I had a very American moment of excitement where I first interpreted this question to mean that Austria had, unbeknownst to me, fallen into anarchy and was now trying to re-establish rule of law de novo. But it turns out that in parliamentary systems "form a government" means to establish a viable coalition government after an election.

Since this is a routine event and not an unprecedented collapse of democratic order, we can look at previous election-to-swearing-in spans:

2019: 100 days

2017: 64 days

2013: 78 days

2008: 65 days

2006: 102 days

2002: 96 days

1999: 124 days

So that's a mean of ~90 days, with a standard deviation of ~20. This election was held on 29 September 2024, 108 days ago. It's about time for a swearing-in, so what's unusual about this election that could cause a delay?

Well, until a week ago, the party that won the election wasn't actually leading the coalition talks. The president chose to give the center-conservative party the first chance to form a government alliance even though the far-right party actually won the election, which is apparently a thing that you can do in Austria. As far as I can tell this kind of switcheroo hasn't happened in any other elections from 1999 onward (though in 1999 the same far right party won but a guy from a centrist party got to be chancellor instead), so I'm going to guess that these negotiations will make the process run longer than 123 days.

@cherrvak Nice! How did you get the election-to-swearing-in spans? It doesn't seem obvious to me from the wikipedia table? That said, if this party actually forms a party, it's a disaster.

@ScipioFabius The date of the elections are given on the individual pages for each election, i.e 2019. The swearing-in date is usually also given on the individual pages, but in cases where it wasn't I got it from the start date in the "Duration of Government" column on the Government of Austria page chart. Then I plugged those two dates into https://www.calculator.net/date-calculator.html to get the span.