Filet mignon that is 1-inch thick should be cooked between 2 minutes per side and 8 minutes per side, depending on the chef's preferences. It should always be cooked on medium heat. It takes 2-2.5 minutes for rare, 5-6 minutes for medium rare and 6-8 minutes for well done.
If the filet mignon is 1-1/2 inches thick, it takes a little longer. These cooking times are per side as it is flipped once on the pan. For rare, cook it 3.5-4 minutes on medium heat on each side. Medium rare is 4-5 minutes, medium is 5-7.5 minutes, medium well is 7.5-9.5 minutes and well done is 9.5-11 minutes per side. Most people don't cook it past medium rare since it can become dry and lose its flavor.