Work on basement ceiling insulation with stone wool

You can use PUR/PIR, then you need less. You weren't given any stone wool for free - were you? If you win the lottery you can use vacuum insulation panels. then 2cm is enough.

You can use PUR/PIR, then you need less. You haven't received any mineral wool as a gift - right? If you win the lottery, you can use vacuum insulation panels. Then 2cm is enough.

If rigid foam boards are twice as expensive as mineral wool, the calculation is simple. Provided I don't have to insulate twice as thick as with rigid foam boards. So 10cm rigid foam boards are equivalent to 14cm mineral wool, is that correct?

10cm PUR (WLG 025, alukaschiert) has 0.235 W/(m²K). Vlieskaschiert (WLG 028) would have 0.261. 14cm stone wool (WLG 040) has 0.266 W/(m²K).

So 10 cm rigid foam boards act like 14 cm mineral wool, is that correct?

Yes, 10 cm mineral wool with WLG035 has about the same thermal resistance as 14 cm 024 PUR. 10 cm mineral wool also provides some effect – the first centimeters are the most important. Ideally, 14 cm mineral wool would be best; if only 10 cm is possible, that's also good. Whether you save the additional costs for PUR depends on the energy price and material cost. PUR is easier to work with because it is very light and can be glued without thermal bridges using foam adhesive, and you can foam-fill holes. With mineral wool, you need something to hold it in place, like construction supports or similar, and the mortar mess is a bit more.

If rigid foam boards are twice as expensive as stone wool,

Therefore, I always recommend PUR second choice for such applications. Almost no difference to first choice - the price is about €16 per sqm for 10cm (+ shipping or free pickup). Much easier to work with than stone wool (saves time and money).
And if you want it to look really nice, you simply glue the thin drywall (Renoboard) underneath with the same foam adhesive, fill the joints, and paint. Then it looks like a "real" ceiling.

That’s why I always recommend PUR second choice for such applications. Almost no difference to first choice - it costs about €16 per sqm for 10cm (+ shipping or free pickup). Much easier to work with than stone wool (saves time and money).
And if you want it to look really nice, just glue the thin drywall (Renoboard) underneath with the same foam adhesive, fill and paint it. Then it looks like a “real” ceiling.

Where can you get second choice stuff?