The CTW number is quite an important factor because it will allow you to compare different rings and find which ring is of more carat weight. This way, if you divide the cost of each ring you chose by its total carat weight, you could see which ring is cheaper per carat.
Usually, a ring that has larger stones cost more per carat when compared to a ring with smaller diamonds. This is because bigger diamonds are very rare. Another reason why two rings may have a different price per carat is due to the quality difference. A stone of low color and clarity grade will be cheaper than the one with the same size but better quality.