See the definition of hydrostatic pressure.
The pressure is just the weight of the column of air spread over the area at the base of the column.
There is however one small problem, the density of the air is not constant because air is not incompressible.
However If we make h very small we can calculate the weight of thin slivers of air each of different density and sum the up the weight of all the tiny slivers of air which make up a column and calculate its total weight.
So how do we know the density ?