The American Academy of Pediatrics Guide to Your Child's Sleep provides some helpful guidelines regarding just how much sleep children need at different stages in their development. Keep in mind that these numbers reflect total sleep hours in a 24-hour period. So if your child still naps, you'll need to take that into account when you add up sleep hours.
Between Birth-Six Months, children need 16-20 hours
Between Six-Twelve Months, children need 14-15 hours
Between Ages 1-3, children need 10-13 hours
Between Ages 3-10, children need 10-12 hours
Between Ages 11-12, children need about 10 hours
Teenagers need about 9 hours of sleep per night
If those numbers are surprising, you're not alone. As adults, we're accustomed to needing 7-9 hours of sleep, and we're often forced to get by with far less. As a result, it might be tempting to think that our kids have similar sleep requirements, or that they should be able to cope fairly well with a few skipped hours here and there. However, kids who are regularly sleep deprived may exhibit some difficult behaviors. They may display frequent irritability, overreact emotionally, have difficulty concentrating, forget easily, wake often during the night, and may even display hyperactive behaviors.
The best thing you can do is simply move your child's bedtime up. This may sound impossible at first, but by moving the entire bedtime routine up half an hour, you'll help your child associate bedtime with an earlier time. In fact, you may be surprised to find that your child goes to sleep easily and sleeps through the night more regularly when well-rested.
1Cohen, George J., M.D., F.A.A.P. (Ed.). (1999). American Academy of Pediatrics Guide to Your Child’s Sleep.