A standard tier is 4". You want your cake, before filling & covering to be pretty close if not 4". My finished height is usually just about 5", but it really depends on how thick you fill and ice. I use 2 – 2" layers of cake typically for a 4" tier, unless otherwise requested.
An easy way to get your layers to reach at least 2" in a 2" pan is to use a collar. The way I use the collar is to cut 4” strips of parchment paper. Prepare the bottom of your pan how you normally would and then place the strips around the sides of the cake pan allowing them to stick up past top of the pan 2 inches. I use little dabs of butter to help the paper stick to the sides of the pan. If one strip is not long enough, you can use 2 strips, just be sure that the two strips overlap and are tight up against each other when you pour in your batter. Then pour in your batter. I have made 3 1/2 layers this way in a 2" pan in order to achieve a tall tier.
Hope that answers some of your questions.