## 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.
- What parameter are you interested in?
- What is the simplest generally applicable conceptual model describes
the physics controlling this parameter?
- Express your parameter of interest as a function of all the variables
in your conceptual model.
- 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.
- Evaluate each term to see which are important. Use of typical values
for the input variables is very helpful in this step.

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

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