Student resident permit in Finland stay duration in Germany for travel

This depends on what kind of visa/permit you had in Germany until January 31.

Assuming that it was either a German residence permit or a German type D visa, then the time you spent in Germany under it does not count for the Schengen clock.

Similarly, I understand that you already have a valid residence permit for Finland. Then the Schengen clock stops ticking again once you have arrived in Finland. In the mean time the Finnish residence permit gives you rights to travel in Schengen-outside-Finland closely similar to a multiple-entry short-stay visa.

Assuming that you haven't been in any Schengen country other than Germany or Finland in the 180 days leading up to January 31, you can be present in Schengen-outside-Finland for 90 days in total in the period between February 1 and May 11 (since this period in less than 180 days).

Februrary 1 to April 20 is 79 days, so after you leave on April 20 you will have 11 days left.

If you re-enter Schengen on May 11, those 11 days will start being used, and you need to be either outside Schengen or in Finland (where the Schengen clock doesn't reach thanks to your residence permit) by the end of May 21.

The 90-day period does not restart just because you leave the Schengen area. The rule is that you get 90 days in any 180-day period. You're in violation on a given day whenever more than 90 of [that day plus the 179 preceding days] are days where you have set foot in a Schengen country (except for the issuer of a valid residence permit or type D visa).