We know that it is important to maintain tires with close to the same circumference on AWD cars, and pay a lot of attention to keeping identical tires with similar tread depths on the car. I have often seen it mentioned on the forum that maintaining proper tire pressures is also important as tire pressures affect tire circumference. I have not noticed any numbers regarding how much a drop in tire pressure in a tire affects circumference... so I did a little experiment.
I attached a bar clamp to a tire with a long nail taped to the end to act as a pointer. I taped a ruler to a board and positioned the board vertically next to the point of the nail. I inflated the tire (a cold 225/55 17 Geolander G95) to 36 psi and noted the pointer position on the ruler. Then I dropped the pressure in 2 psi increments down to 20 psi...noting the change in position every 2 psi. Then I reinflated back up to 36 psi in the same 2 psi increments.
The pointer dropped 1/32" every 2 psi from 36 psi to 26 psi, then dropped about 2/32" every 2 psi from 26 psi to 20 psi. The measurements were the same while reinflating.
So.... a 2 psi change in tire pressure (above 26 psi) results in a 1/32" change in radius... and therefore a 2/32" change in diameter. 3.14 X 2/32" (pi x d) = a little over 3/16" change in circumference. Double that for pressures between 26 psi and 20 psi.