The circumference of a circle (or wheel) is proportional to the diameter (Circumference = πD).
Therefore, taking your example, should the diameter of a wheel be reduced from 500mm to 480mm � then the registered speed (based on wheel rotation) will be in error by 20 in 500, or 4%.
However, tyres are designed to provide a major component of ride smoothness � and are pressurised such there is a considerable �flat� area in contact with the road surface. Thus incorrect tyre inflation is likely to have a much greater effect on speedo error than tyre wear.
A further point to bear in mind is that car speedos typically read up to 10% high � this can be verified by driving at a constant speed (over a flat/level distance) and comparing the speed from an onboard satnav device, which have a much better speed accuracy.