Hah! I wrote a unit converter for Android recently and that is one of the criticism I get. "Why does my conversion end up in becquerel?" It is usually because people forgot to divide by time, where they write something like "(31l/m2)/1min in mm" when they should have have written something like "(31l/m2)/1min in mm/h". Anyway, check it out here:
https://github.com/bjoli/Umits
I am about 6 days away from publishing and open beta (currently in mandatory closed testing). If you want to join the closed test, you can do so by mailing me at the email at the top of the readme.
I think your interface is a bit inconsistent, this is why people ask that question.
If you have
65mi in 12mi/h -> 19500s
then instead of
12h in s -> 43200s
you should have
12h in s -> 43200
Then a unit at the end should mean that not all dimensions have been reduced.
In the same vein, in the README, the "weird results" section should come after the "dimension removal" section. The way it is now, the apparent "bug" comes before the feature.