title: Making Gaussians Constrained by the FWHM
body: <p>Firstly my maths is limited, so this question may have a simple answer. So, I am using the following equation to make guassian distributions:</p>
  
  <pre><code>height * np.exp( - ((x-mean)/width)**2 )
  </code></pre>
  
  <p>When I make gussians with the above equation where is the width of the peak applied? Is it at full width half maximum? I made the following gaussian with the following values:</p>
  
  <pre><code>height = 5
  mean = 100
  width = 10
  </code></pre>
  
  <p><img src="https://i.stack.imgur.com/0vK3z.png" alt="enter image description here"></p>
  
  <p>When I then calculate the FWHM it is <code>16.6510941453</code> so the peak width cannot be applied at the FWHM. Where is it applied?</p>
  
  <p>I am trying to constrain the FWHM so the FWHM is 10x smaller than that of the mean. So in the above example I would of liked the gaussian to have a FWHM of 10 at the mean of 100 at a peak height of 5.</p>