In the case you have a pure Gaussian beam then things are well defined. The thing that is still open from your question is what do you mean you have the "intensity in  a crystal"? Do you have an intensity measuring method / tool within the crystal? usually power meters tell you the power at a point in space where you can later place the crystal.

Anyway, Gaussian profile is simple and relation between peak / average / half height are completely defined in books / web.

Recall: the Intensity in the center is twice the average, if you obtain the Gaussian waist (86% and 4-Sigma yield the same in Gaussian).... 

Already discussion was carried out in the research gate and the corresponding link I have given below it may useful for you

https://www.researchgate.net/post/Is_laser_spot_size_beam_diameter_at_the_waist_depends_on_the_laser_intensity

Unfortunetelly not. For a given beam waist intensity is just entirely independent parameter. But if you can measure intensity profile, there you go... Just use a camera 

you can use a power meter and a knife edge.