.

Handwaving arguments often include order-of-magnitude estimates and dimensional analysis. Competent well-intentioned researchers and professors rely on handwaving when, given a limited time, a large result must be shown and minor technical details cannot be given much attention—e.g., "It can be shown that z is even."

Back-of-the-envelope calculations are approximate ways to get an answer by over-simplification and are compatible with handwaving.