Spirometry test, a measure of the patient's lung function, is the gold standard for diagnosis and monitoring of chronic pulmonary diseases. Spirometry is currently being done in hospital settings by having the patients blow the air out of their lungs forcefully and into the spirometer's tubes under the supervision and constant guidance of clinicians. This test is expensive, cumbersome and not easily applicable to every-day monitoring of these patients. The lung mechanism when performing a cough is very similar to when spirometry test is done. That includes a big inhalation, air compression and forceful exhalation. Therefore, it is reasonable to assume that obstruction of lung airways should have a similar effect on both cough features and spirometry measures. This paper explores the estimation of lung obstruction using cough acoustic features. A total number of 3695 coughs were collected from patients from 4 different conditions and 4 different severity categories along with their lung function measures in a clinical setting using a smartphone's microphone and a hospital-grade spirometry lab. After feature-set optimization and model hyperparameter tuning, the lung obstruction was estimated with MAE (Mean Absolute Error) of 8% for COPD and 9% for asthma populations. In addition to lung obstruction estimation, we were able to classify patients' disease state with 91% accuracy and patients' severity within each disease state with 95% accuracy.Clinical Relevance- This enables effort-independent estimation of lung function spirometry parameters which could potentially lead to passive monitoring of pulmonary patients.