The bottom number, called the diastolic pressure, is the measurement as the heart relaxes between beats. Normal blood pressure is a systolic pressure of less than 120 millimeters of mercury (mm Hg) and a diastolic pressure of less than 80 mm Hg, or 120/80 mm Hg, according to the American Heart Association (AHA).Having a blood pressure greater than 140/90 mm Hg is considered high blood pressure or hypertension.A blood pressure level between normal and hypertension, is called prehypertension, meaning it is higher than normal, but not high enough to be considered hypertension.aving a blood pressure greater than 140/90 mm Hg is considered high blood pressure or hypertension. A blood pressure level between normal and hypertension, is called prehypertension, meaning it is higher than normal, but not high enough to be considered hypertension.