I wouldn't say calculations, as that implies, to me, a mathematical kernel. I can't think of any low-level calculations that are easier with concurrency. But some problems are most naturally solved with concurrency - that is, it's easier to architect the software with threads. Applications with GUIs are sometimes like this: it may be easier to have a main application thread that does the real computations, and a separate thread that handles all GUI work.

The pattern is that instead of one monolithic process that must know about and do everything, sometimes it's easier to think about several independent processes that only know about one domain, and make requests or give answers to other processes that know about other domains.

Some of the calculations I did for my PhD were inherently parallel - some branches could be cut as others found certain features in the structures. There was no obvious way to order things, it was natural to just set them all off at once and let things trim and prune concurrently.

Various image processing algorithms I use also work concurrently over the image, agents working in different places, and then deciding who is doing best and letting each other know so resources can be concentrated and refocused.

Unless you've worked for a long time in an inherently parallel environment it's hard to see things as anything other than serial processes. For me it can sometimes be hard to see how to serialize things, as many things are naturally parallel. I've worked for nearly 20 years on systems with at least 100 processors and limited communications, so parallel algorithms tend to be what I see first.

Sorting, for example. Merge sort is inherently a parallel algorithm. Why sort that part, then this part? Why not do them both at once, and then start merging while the remainder of the sort is still going on? Or quick sort. Once you have divided your vector into two pieces, why sort them serially?

Sieve of Eratosthenes can be thought of as inherently parallel, as can many factoring algorithms. Why factor this small number, then that one, then that one, and so on, when you can factor them all together?

These are all things that are naturally expressed as concurrent algorithms, processes, or calculations.