Often when people write me a very long sentence, they apologize for having created a run-on. In fact, a run-on sentence can be very short: This is a run-on sentence I don’t think it’s grammatical. Here’s another: This is a run-on sentence, I don’t think it’s grammatical.
A sentence is a run-on if it meets one of two conditions:
1. It is two or more complete sentences (which means each one has a subject, a verb and complete meaning) joined together with no punctuation between them (example #1 above).
2. It is those same sentences joined by only a comma (example #2 above).
What you need is either end punctuation between the sentences or else a conjunction after the comma: This is a run-on sentence, and I don’t think it’s grammatical. (Incidentally, it is grammatical.)
In theory, you could have an endless number of complete sentences strung together if they were punctuated correctly, and they would not constitute a run-on. It’s not the length of the sentences, it’s the punctuation that makes them either right or wrong.