# Airway Resistance Calculation Formula

Airway resistance is the change in trans-pulmonary pressure needed to produce a unit flow of gas through the airways of the lung. More simply, it is the pressure difference between the mouth and alveoli of the lung (Î”P), divided by airflow (Q).

Airway resistance (R) = (Î”P) / Q

It can also be described by Ohm’s law:

Airflow = Î”P ÷ R

Airflow through the airways is proportional to the gradient between atmospheric pressure and alveolar pressure (DP) and inversely proportional to the airway resistance (R).

Factors determining resistance to airflow are also analogous to those determining the resistance to blood flow and include viscosity, length of the airway, and airway radius. Under normal conditions, the viscosity of the air is fairly constant and the length of the airway is fixed. Therefore, airway radius is the critically important physiological factor determining airway resistance:

R ∝ 1 ÷ r^4

Airway resistance is inversely proportional to the radius (r) of the airway to the fourth power. In other words, when the radius is reduced by a factor of two (50%), the airway resistance increases 16-fold. Several factors determine airway resistance, including:

• Lung volume
• Airway obstruction
• Bronchial smooth muscle tone