University of Auckland specialists investigated sleep patterns among 519 seven-year-olds, monitoring them with a gadget attached to their waist that can tell from a child's movements whether it is asleep, awake but inactive, or active.
After hitting the sack, the children fell asleep 26 minutes later on average, in a range of 13 to 42 minutes, and slept for an average of 10.1 hours.
Those who had been inactive during the day took longer to nod off. Every sedentary hour during daytime added 3.1 minutes to the time it took to fall asleep.
The study, published in a specialist British journal, Archives of Disease in Childhood, also found that children who fall asleep faster also sleep for longer.
The findings are important because children who sleep badly or for short periods are likelier to do poorly at school or become obese.
Going to bed after 9:00 p.m., and the amount of television a child watched, did not make a difference to the time it took to fall asleep.
The researchers say the results provide statistical backing to what many parents already know instinctively -- that tiring a child out before he or she goes to bed will help it to sleep.
"These findings emphasise the importance of physical activity for children, not only for fitness, cardiovascular health and weight control, but also for promoting good sleep," they say.