It’s probably an approximation, but I guess it’s a good one: If you look at the toilet paper roll from the side, you will see that it forms a roughly circular ring. The surface area of that ring can be calculated as (R-r)²*pi, where r is the radius of the cardboard spool in the centre and R that of the overall roll (cardboard spool plus toilet paper wrapped around it). So the surface area is proportional to the square of the thickness of the rolled-up paper. I would therefore assume that the thickness of the rolled-up paper, if only half of the initial roll is left, would be 1/(sq rt 2) of the thickness of the initial roll.