University school fee in US is charge by the percentage of household income?

That's not exactly how it works.

Every school has a "sticker price." That's how much tuition, fees, and room and board cost at the school. Most prestigious colleges have a sticker price of between $40,000 and $60,000 a year right now.

Many top schools also offer financial aid, so that only some people have to pay the full cost of attendance. But it's not a fixed percentage; it's a complicated formula. You have to fill out two forms - the Free Application for Federal Student Aid (although international students may not have to fill that out) and the CSS PROFILE. The school takes into account not only your parents' income, but also your parents' assets held. Then they come up with an Expected Family Contribution for you. The most prestigious schools in the nation will only require you to pay that out of your pocket, and will cover the rest with financial aid. So for example, if your EFC is $10,000, they will meet the rest of the costs with other aid.

But beware - many schools include repayable forms of aid in that "financial aid." So at a school that costs $60,000, you will be required to pay $10,000 out of pocket (or your parents may borrow loans). But in the $50,000 package the school gives you, there will probably be small student loans and a work-study/student employment requirement.

However, there are many top schools that don't meet 100% of need. There, your financial aid is still dependent on school formulae, but even once they determine that you need $50,000 to attend their school - they may only give you $20,000.