205/50/16 Diameter
[205mm x (.50 x 2)] / 25.4 = 8.071" + 16" = 24.071"

195/55/15 Diameter
[195mm x (.55*2)] / 25.4 = 8.445" + 15" = 23.445"

Difference - [24.071 / 23.445] * 100 = 2.67%

This is how you calculate it without the tire size calc that Ken provided.

Take the width, times by twice the aspect ratio (50 = 0.50 or 50% of the width of the tire), change to inches, add the diameter of the rim. Compare/divide with the stock diameter... there you go.

At ANY speed, with 205/50/16 tires, you will be 2.67% SLOWER on the speedo than you would with 195/55/15 due to the increased diameter of the tire. (therefore less rotations per minute, so it appears you are going to slower to the speed sensor)

Diameter comparisons.
205/50/15 is 1.7% smaller than 195/55/15. (speedo reads higher)
195/50/15 is 3.3% smaller than 195/55/15. (see above)
215/45/16 is 0.7% LARGER than 195/55/15. (speedo reads SLOWER)

While the differences are minor (195/50/15 is only off 3.3mph at 100mph, half that at 50mph), these tires change your effective final drive ratio.

A tire like a 195/50/15 is so much smaller that you can feel the car moving through the gears quicker, similar to a higher final drive.