How many hours should my newborn be sleeping?

16-22 hours. Newborns sleep a lot, but not for long stretches at a time. Newborns need to eat every 3 hours or so (and sometimes more frequently) so between eating, changing their diapers and putting them down it doesn't allow for a long continuous stretch of sleep. By 3 months most babies can go 6 hours (at night) and some may even sleep through the night by 4 months!
18-20 hours. Most newborns are only awake for feedings, diaper changes and, on average, a few hours of crying time per day. Remember that this is an average. Some babies, just like some adults, need less sleep. If your baby is happy, healthy and growing properly, she is probably getting enough sleep. Also, most newborns are more awake at night, so try to nap when she is napping.