Is 124 beats per minute high for a 4 year-old?

In pediatrics, it is generall recognized that younger (and thus smaller) patients can have higher heart rates than adults. In the extreme, the example of the hummingbird is often alluded to (hummingbirds are tiny and thus have extremely rapid heartbeats). Newborns have heart rates that can range from 110-160 and be totally normal.

Average or Normal heart rates for a 4- year old (or any healthy preschooler aged 3-5) can range from 80-120.

Heart rates outside of this range or right at the extremes of this range should be contemplated further and evaluated by a physician or nurse practitioner. Thus, a heart rate of 120 in a 4-5 year old could possibly be associated with a higher level of emotional stress or lower physical fitness in a sedentary or overweight child. It could also be completely normal and attributable to that child's unique physiology.

If your child can tolerate greater or more frequent exercise, you can try taking their pulse over time to see if this improves their heart rate, though the most obvious changes may be to their blood pressure.

Sources:

http://www.rnceus.com/psvt/psvtvs.html

http://www.emedicinehealth.com/pediatric_vital_signs/article_em.htm