I strongly recommend that you read "The Promise of Sleep" by William Dement. It's pretty much the best layperson's guide to sleep science that you'll find anywhere.

As far as your specific question goes, your basic intuition is right, but unfortunately, it's not quite that simple. The average sleep cycle length is 90 minutes, but for different people, it can be as low as 80 or as high as 120. And often, sleep cycles increase in length during the night.

However, there's a much more important concept, which is sleep debt. For every two hours (approximately) that you're awake, you incur an hour (approximately) of sleep debt. Normally, you repay your sleep debt each night, but in our chronically underslept society, there's a good chance that you're carrying around weeks/months/years of debt.

So my real recommendation is this: Give yourself time for 9 hours of sleep each night. For a while, you'll probably sleep the full 9 hours, because you need it. Gradually, you may find yourself waking up after 7.5 or 8 or 8.5 hours and not feeling tired at all... in which case, congratulations, you've found out how much sleep you need!

Another note: If you snore, or ever feel tired during the day, get yourself to a sleep medicine clinic. Sleep apnea affects between 5-20% of American adults. Treatment is simple, but untreated apnea can shave 10-20 years off your life. If you're feeling groggy in the mornings -- especially if you have a dry mouth, sore throat, or headache -- you should investigate this ASAP.