Back-of-the-envelope

Doing some quick back-of-the-envelope calculations, he reckoned that the raw materials actually cost less than one-thirtieth of the selling price.

We can do some back-of-the-envelope calculations before all the facts come in.

[T]he original estimates are frequently back-of-the-envelope-type estimates made internally without detailed engineering studies, if you go all the way back to Day 1.

We joke about having to make back-of-the-envelope calculations, while in the university environment we might spend 2 or 3 weeks computerizing the calculations. I might say, however, that making back-of-the-envelope calculations and later checking them out on computers has impressed me that we have developed a considerable skill in back-of-the-envelope calculations.

On one defense item, somebody kept referring to it as a back-of-an-envelope cost estimate. Do you have a back-of-an-envelope cost estimate?

Apart from those manuscripts which were intended as more or less complete, self-contained works, [William] Petty left a huge body of papers, much of which amounts to fragments and hastily written private notes – many the seventeenth-century equipvament of back-of-the-envelope calculations and comments. These papers constitute a further testament to his sustained investigation of economic and political subjects.

The reader will not need to be warned that the calculations involved are of the back of an envelope type and statements of the form ‘a equals b’ should be read ‘a equals b approximately’ or even ‘with a bit of luck, a and b will be of the same order of magnitude’.

Misapplying a basic feature of diffusion theory, [Werner] Heisenberg arrived at an impossibly high figure for a critical mass of pure U235. This was done by means of a seductively simple "back of an envelope" calculation in 1940, […]

Back of the envelope calculation: I've traveled roughly 17 million miles since we left the crew quarters at Cape Kennedy, not including the van ride to the pad … in fact, Earth seems a bit dreamlike these days, as we are connected only by crackling voices on the radio and the photographs brought along and our memories.

I remember very distinctly in October 1995, after I completed my paper design, I had an epiphany. This back-of-the-envelope design was five years ahead of its time.

[I]t quickly became apparent that the natural mapping we had thought of—and which seemed to make perfect sense back when we were doing our back-of-the-envelope estimates—turned out not to be acceptable at all.

Now, those Treasury mandarins unfamiliar with the railway might assume on the back of an envelope that if only 80% of trains are running, then that will cost 20% less. If only it were that simple.