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How to approach a Fermi Problem



Tip #1

A problem's answer falls into the category of the following:

- too much

- too little

- just right

For example, before you go into a store, you know how much you are wiling to spend. You think it is reasonable to spend $100 on shoes. If the price is $30, you will buy it. If it is $300, you won't. Only if it is around $100, say $120 or even $150, you will think about this decision.

Similarly, our answers should fall within a factor of 10. A factor of 10 is good enough to make most decisions.

Note: “Factor” is a key word that indicates that either multiplication or division are involved.

If you increase “x” by a factor of 10, then you are talking about x*10.

If you decrease “x” by a factor of 10, then you are talking about x/10.

Tip #2

Break the problem to smaller pieces and estimate the answer for each one. Since you are breaking the problem into smaller parts, it is easier to establish the upper and lower boundaries than to estimate a number directly.

If, for example, we are trying to estimate how many circus clowns fit in a Volkswagen Beetle, it is easier to establish the upper and lower boundaries first. Obviously, the number will be more than 1 (lower boundary) and less then 100 (upper boundary).

It is then recommended to take the geometric average of these numbers. Why? A geometric mean is more conservative in nature. The Arithmetic Mean is more subject to skew from spurious outliers than the Geometric Mean. Look at the graph below to understand:

Source: webtortoise.com

Tip #3

It is easier to use the scientific notation for a Fermi problem than to manually write the string of pesky zeros. Further, using the coefficient in this form will allow for simpler calculation.

Learn more about scientific notation here.

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