The formula is:

1 / (φ(x+w/2) − φ(x−w/2))

where *x* is your IQ, *w* is the chosen window
size^{1}, and *φ(x)* is the
percentile of *x* (*φ* being the cumulative
distribution function). Both *x* and *w* are given in
standard deviations (σ).

*φ(x)* calculates the area under the normal distribution curve
from −∞ to *x*. So
*φ(x+w/2) − φ(x−w/2)* calculates
the area under the curve spanning the window
of comprehension corresponding to *x* and *w*.

In the diagram, the orange area is the area under the curve correpsonding to an IQ of 1.5σ (about 123) and a window of 1σ (15 points).

The number of people you have to meet to find one in your window is then the quotient of the population (1) and the the size of the area associated with the window (about 1 / 0.25 = 4 in the example).

^{1} It's actually *w−1* due to a
fencepost issue.

Here you can go back to the calculator, but use the "back" button if you want to preserve your entries.