This is a great question, unfathomlessconstellations! Thanks for asking.
Yale is committed to meeting every student’s demonstrated financial need with aid awards that do not include loans. Nearly 52% of students this past school year received aid from Yale’s generous financial aid program. The average Yale financial aid package was $41,781, or about 70% of the cost of attendance (including room and board). There was a great news article on all of this recently that you can check out here. In calculating financial need, factors beyond tuition—such as room, board, books, personal expenses, and travel—are also weighted and many aid packages well help support these additional non-tuition costs.
Admissions is need-blind, so applying for aid will not affect your application for admission. You can find everything you need to know about financial aid on our website: http://admissions.yale.edu/financial-aid. If you want to calculate an estimate for how much your family would pay for you to attend Yale, check out the net price calculator here: http://admissions.yale.edu/yale-net-price-calculator