Stress can definitely trigger a fast heart rate, but some people have a condition called tachycardia, which is when you have a resting heart rate above 85 beats per minute. Most of the time, tachycardia is caused by an abnormal heart rhythm. If you experience this, definitely consult with your doctor.
Because the heart is a muscle, the more exercise it gets, the stronger it will be. The stronger it is, the more efficient it is, taking fewer beats to pump blood throughout the body. So, a heart with a resting heart rate under 60 (a condition known as bradycardia) may actually be more fit.
This is, indeed, the normal range, however numerous studies over the last few years have noted that if you're at the upper end of that range, you may be at risk for ischemic heart disease. A recent study out of Norway reported that for every 10-beat rise in resting heart rate, the risk of dying from a heart attack rose by 18 percent in women and by 10 percent in men.
Knowing your target heart rate will help you know whether you are over-exercising or not enough. To determine your target heart rate, take your pulse on the inside of your wrist, on the thumb side. Then, count your pulse for 10 seconds and multiply by six to find your beats per minute. You want to stay between 50 percent to 85 percent of your maximum heart rate.