This is the question everyone's afraid to ask out loud, so here's the honest, unglamorous answer.
The categories you're paying for: a new member fee (one-time, covers recruitment materials, badge, etc.), national dues (paid to the sorority's national organization, funds programming, insurance, resources), chapter dues (covers house operations, if there's a house: rent, meals, utilities), and social/event fees layered on top for formals, date parties, and sisterhood events.
The real range. New member fees commonly run a few hundred dollars. Ongoing semester dues vary enormously by school and by whether the chapter has a physical house, anywhere from a few hundred dollars a semester at a non-housed chapter to well over a thousand at a large housed chapter that includes room and board. There is no single number, anyone who gives you one flat figure for "sorority cost" is guessing.
Where to get real numbers. Every chapter is required to disclose dues during recruitment if you ask, and most Panhellenic councils post a dues comparison chart before recruitment starts specifically so this isn't a surprise mid-process. Ask directly, "what are your dues," it's a completely normal and expected question, not an awkward one.
If cost is a real constraint: ask about payment plans (most chapters offer them), scholarships (many chapters and nationals have need-based or merit funds specifically for this), and whether living in the house is required or optional, since housing is usually the single biggest cost driver. Some campuses also have chapters known to run leaner, your Panhellenic VP of recruitment can point you toward them without judgment, they get this question constantly.
Cost is a completely legitimate factor in your decision. Don't let anyone, including your own nerves, make you feel like asking about it upfront is tacky.