Let's say some average person was doing bodybuilding for a year or so. He gained some muscles, increased his weights in all exercises from 1.5 to 3 times. Then he had to do a break for a half a year. After this period, he sees that his muscles are mostly gone and probably the exercise weights are also lower. How long after this break will it take him to get back to the previously achieved results? Another year or less? May be there is some formula to calculate this or may be someone had this kind of experience that he can share?
It shouldn't take as long as the first time getting into it. The benefit you have now is that muscle memory is there. In essence, your muscles have adapted and can now "remember" the movement to perform the exercises you once performed. So when you go back to it, that whole element of learning the movement is gone. This will hasten your results.
However, intensity is important and is solely up to the individual. If you're going back into weightlifting, and your intensity is not there, you're not going to reap the rewards of the muscle memory.
I'm sure some people will debate this, but keeping your diet in check is also going to be a huge attribute to your success. Depending on your goals, to lose weight for example, start with a 500 calorie deficit. Use a tracker like myfitnesspal - this will ensure that you don't go overboard on your caloric intake. Calorie tracking + intense workouts + muscle memory = results.
Previously achieved results are subjective, I noticed after a 6 month break, I came back to the gym doing 2 compound lifts (i.e. bench + deadlift, or squat + pull up) per workout with accessory exercises....I got my results back and was stronger within 1 month of 3 workouts per week. Again, it's about intensity.
Hope this helps! Best of luck!