Back-of-Envelope Calculations

• Premise: It is possible to get an approximate answer, to a useful degree of accuracy, using only the space available on the back of an envelope.
• Procedure: This is the list of steps for a more or less "universal" Back-of-Envelope procedure.
  1. What parameter are you interested in?
  2. What is the simplest generally applicable conceptual model describes the physics controlling this parameter?
  3. Express your parameter of interest as a function of all the variables in your conceptual model.
  4. Algebraically rearrange your expression into a form that can be easily interpreted in terms of the conceptual model. This step often involves expanding your function in terms of power series of the input variables.
  5. Evaluate each term to see which are important. Use of typical values for the input variables is very helpful in this step.


• Application:
  1. Locate or derive the full theory only for the important terms to your parameter of interest.
  2. Don't bother implementing higher order terms which your back-of-envelope calculation says make insignificant contributions.
  3. Implementing the resulting theory lets you calculate the desired parameter as efficiently as possible.

This page was last updated by George Young on December 1, 2004