The American Academy of Sleep Medicine, which are also endorsed by the American Academy of Pediatrics has several recommedations when it comes to the amount of SLEEP a child needs...
Infants 4 months to 12 months should sleep 12 to 16 hours per 24 hours (including naps) on a regular basis to promote optimal health.
Children 1 to 2 years of age should sleep 11 to 14 hours per 24 hours (including naps) on a regular basis to promote optimal health.
Children 3 to 5 years of age should sleep 10 to 13 hours per 24 hours (including naps) on a regular basis to promote optimal health.
Children 6 to 12 years of age should sleep 9 to 12 hours per 24 hours on a regular basis to promote optimal health.
Teenagers 13 to 18 years of age should sleep 8 to 10 hours per 24 hours on a regular basis to promote optimal health.
Because the amount of sleep a child needs is cumulative over a total 24 hour day, this chart tells us what we instinctually already knew—when our kids sleep more during the day, they can stay up a little later at nighttime and be okay. When they start dropping naps, you might need to inch bedtime up earlier to make up for those lost hours.