Calculating the inflation pressure when up sizing is a fairly simple calculation, but it requires the load tables, which are difficult to find. But there are several simple things:
1) The proper pressure for the original tire size is what is written on the plcarard.
2) If you are using the same Load index and have changed from SL to XL or vice versa, then the pressure is the same.
3) For every change in Load Index of 1, the pressure changes 1 psi in the opposite direction. Go from 93 to 96 and the pressure can be dropped 3 psi.
4) I don't recommend lower than 26 psi for passenger car tires, and 35 for LT tires. This is for bead retention during cornering
5) For passenger car tires, if the calculation indicates the need for more than 35 psi, then you need an XL. If the calculation indicates more than 41 psi, then you need a bigger tire size. For LT tires, don't exceed what is written on the sidewall.
6) For aspect ratios lower than 60, I think 3 more psi is needed to protect the rim from impact damage.
I am not a fan of the "Chalk Method". This assumes that a tire driving straight down the road will have a proper footprint. Maybe, maybe not!. Most tire wear occurs in cornering. Some tires don't have good footprints. The load on a tire has a lot to do with the footprint and this method only measures one condition - usually the most empty one, and what you really want is the worst case for durability. Plus I think more pressure gives you better wear than a good footprint does.
But the big ticket item is that inflation pressure is the key to tire durability, and too little can be dangerous. Underinflated tire failures can sometimes have tragic results.