# How to show barometer height is independent of area

I have seen this question asked before (https://forums.studentdoctor.net/threads/please-help-explain-this-concept.724066/) however, I don’t fully understand the explanation given. I am trying to understand why a mercury barometer will always rise to the same height irregardless of the surface area of the tube or container. I have seen it explained as P = F/A so F = ρhgA and P = ρhg. But I don’t understand why the last step is allowed. It seems that on the left side of the equation you are dividing by the area of the whole barometer dish but on the right hand side you are only dividing by the area of the tube.