What is the formula for calculating the FWHM of a gaussian function?

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SUMMARY

The formula for calculating the Full Width at Half Maximum (FWHM) of a Gaussian function defined as exp[-(π*x²/A²)] is established as FWHM = 0.939A. The derivation involves setting the Gaussian function equal to 0.5 to find the half-maximum point, followed by taking the natural logarithm to eliminate the exponential term. The variable substitution x = kA leads to the calculation of k as k = (-ln(0.5)/π)^(1/2), which is essential for determining the full width.

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

Your Gaussian looks funny.
 

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