A Fermi estimate (or back-of-the-envelope calculation, often abbreviated BOTEC) is a rough calculation that aims to be right within about an order of magnitude, prioritizing getting an answer good enough to be useful without putting the large amounts of thought and research needed to attain greater accuracy. Fermi estimates typically approximate an answer by making various simplifying assumptions and decomposing the problem into smaller tractable units. Open Philanthropy and other organizations in the effective altruism community routinely use BOTECs for impact assessment and cause prioritization.
Berger, Alexander (2014) Alexander’s back of the envelope “importance” calculations, GiveWell.
Muehlhauser, Luke (2013) Fermi estimates, LessWrong, April 11.
von Baeyer, Hans Christian (1988) How Fermi would have fixed it, The Sciences, vol. 28, pp. 2-4.