Mean arterial pressure (MAP) is a function of systolic and diastolic blood pressure.
The easiest way to calculate MAP is to get the pulse pressure (Systolic BP – Diastolic BP), then multiply the result with 1/3. The answer you get, add it to diastolic pressure and the result is the MAP.

Systole is the time when the ventricles are contracting and diastole is the relaxation time. In normal condition, the systole phase takes about half the time the diastole takes. In other words, diastole takes twice as longer as systole.
This explains why we cannot just add systolic blood pressure and diastolic blood pressure and divide it with 2. The time each takes is different. In-stead, if we divided the time in equal parts, we would have 3 equal parts, where the systole takes 1/3 and diastole takes 2/3 of total time.

To test if this is true, we can multiply systolic BP by 1/3 and diastolic BP by 2/3 and add the results together to come up with the mean arterial pressure.

Lets use real example using the known formula of 1/3(SBP-DBP)+DBP = MAP and control theoretical explanation and see if we will come up with the same results.
Lets say a patient BP = 120/60. Pulse pressure (SBP-DBP) would be 120-60 = 60.
Mean Arterial Formula: 1/3(SBP-DBP)+DBP = MAP
1/3 X 60 = 20
Add the result above to DBP (60)
20+60 = 80
Lets now use the theoretical way of testing if the formula above gives a true picture of how the heart works in normal conditions.
Our sample BP is 120/60

We will multiple SBP X 1/3 AND DBP X 2/3 and then add the total. We should get the same results as above
1/3×120 = 40 + 2/3×60 = 40. 40+40 = 80

Reference :

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