1. The problem statement, all variables and given/known data I have to determine the radius at which 50% of energy is in a Gaussian profile. 2. Relevant equations The intensity is given by I=Ioe^(-r/2c)^2. This is just a gaussian function ofcourse. 3. The attempt at a solution I know c is the standard deviation. I searched through charts that 50% of the data set is contained within about 0.67 standard deviations. So can i set I/i0 to 0.5 and set c=0.67? I feel like this is not the correct method though. What I need is the area under the gaussian curve that is 50%. So I need to integrate between values of -r and r that will give me an answer of 50 % but I dont know what values those are.