So, I understand that in general one should use coalesce() when:
the number of partitions decreases due to a
filteror some
As others have answered, there is no formula which calculates what you ask for. That said, You can make an educated guess on the first part and then fine tune it over time.
The first step is to make sure you have enough partitions. If you have NO_OF_EXECUTOR_INSTANCES executors and NO_OF_EXECUTOR_CORES cores per executor then you can process NO_OF_EXECUTOR_INSTANCES*NO_OF_EXECUTOR_CORES partitions at the same time (each would go to a specific core of a specific instance). That said this assumes everything is divided equally between the cores and everything takes exactly the same time to process. This is rarely the case. There is a good chance that some of them would be finished before others either because of locallity (e.g. the data needs to come from a different node) or simply because they are not balanced (e.g. if you have data partitioned by root domain then partitions including google would probably be quite big). This is where the REPARTITION_FACTOR comes into play. The idea is that we "overbook" each core and therefore if one finishes very quickly and one finishes slowly we have the option of dividing the tasks between them. A factor of 2-3 is generally a good idea.
Now lets take a look at the size of a single partition. Lets say your entire data is X MB in size and you have N partitions. Each partition would be on average X/N MBs. If N is large relative to X then you might have very small average partition size (e.g. a few KB). In this case it is usually a good idea to lower N because the overhead of managing each partition becomes too high. On the other hand if the size is very large (e.g. a few GB) then you need to hold a lot of data at the same time which would cause issues such as garbage collection, high memory usage etc.
The optimal size is a good question but generally people seem to prefer partitions of 100-1000MB but in truth tens of MB probably would also be good.
Another thing you should note is when you do the calculation how your partitions change. For example, lets say you start with 1000 partitions of 100MB each but then filter the data so each partition becomes 1K then you should probably coalesce. Similar issues can happen when you do a groupby or join. In such cases both the size of the partition and the number of partitions change and might reach an undesirable size.