Hoping is from hope — wishing something will happen: "I am hoping for good news." Hopping is from hop — jumping on one foot, or moving quickly between things: "hopping on one leg." The doubled p is what keeps the vowel short, which is the whole spelling rule at work here.
The core difference
Two unrelated verbs whose participles sit one letter apart. Hoping is hope + ing; hopping is hop + ing.
The rule behind the doubled letter
English doubles a final consonant before -ing when the vowel before it is short, and leaves it single when the vowel is long. The double consonant is a signal to the reader about how to say the vowel:
- hope → hoping — long o, silent e dropped, single p
- hop → hopping — short o, consonant doubled
The same pattern runs through taping/tapping, pining/pinning and staring/starring. Once you see it in one pair you have it in all of them.
Why it slips through
Both spellings are real words, so nothing flags the swap. "I am hopping you can make it" is grammatical and means something faintly absurd — you are jumping about at somebody.
