What is the origin of the idiom "back-of-the-envelope calculation" and when to use it?

The idiom "back-of-the-envelope calculation" originates from a common practice in which people perform quick calculations or estimations on the back of an envelope or a scrap of paper when they don't have access to a calculator or formal tools. This practice is often associated with simplicity, informality, and rough estimations. This idiomatic phrase is used to describe a rough, simplified, or quick estimation or calculation, typically done without using precise data or detailed analysis.