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What physical quantity gives a good sense of $1/\sqrt{\pi}$?

An example of a "physical quantity that gives a good sense" of $\pi$ would be the area of a disk with unit radius.

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closed as off-topic by mrf, punctured dusk, Daniel W. Farlow, graydad, Tim Raczkowski Nov 12 '15 at 0:59

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is not about mathematics, within the scope defined in the help center." – mrf, Daniel W. Farlow, graydad
If this question can be reworded to fit the rules in the help center, please edit the question.

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The radius of a disk with unit area.

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