# FWHM of a gaussian function

1. Apr 20, 2010

### peterjaybee

Hi,

I have a gaussian of the form
$$exp[-\frac{\pi*x^{2}}{A^2}]$$.

I know that the FWHM=0.939A, but I cannot prove it.

I Let $$exp[-\frac{\pi*x^{2}}{A^2}=0.5$$ (i.e. the half maximum part)

taking natural logs I get rid of the exponential, but then which bit represents the full width?

2. Apr 20, 2010

### mathman

Write x = kA and compute k=(-ln(.5)/π)1/2