The main idea of a back of the envelope calculation is to make a very quick and dirty model that captures the main factors that will affect the outcome of a situation and be able to quickly and easily write down an approximate solution on the space of a paper napkin or on the back of an envelope.

There is a possibly apocryphal story about the an atomic bomb test where Enrico Fermi tossed some scraps of paper into the air and then based on how far they were pushed by the atomic blast, estimated the amount of energy released in the blast. According to some, this is the original source of the back of the envelope calculation. These calculations are also known as fermi questions.