Mobile devices have the potential to continuously monitor health by collecting movement data including walking speed during natural walking. Natural walking is walking without artificial speed constraints present in both treadmill and nurse-assisted walking. Fitness trackers have become popular which record steps taken and distance, typically using a fixed stride length. While useful for everyday purposes, medical monitoring requires precise accuracy and testing on real patients with a scientifically valid measure. Walking speed is closely linked to morbidity in patients and widely used for medical assessment via measured walking. The 6-min walk test (6MWT) is a standard assessment for chronic obstructive pulmonary disease and congestive heart failure. Current generation smartphone hardware contains similar sensor chips as in medical devices and popular fitness devices. We developed a middleware software, MoveSense, which runs on standalone smartphones while providing comparable readings to medical accelerometers. We evaluate six machine learning methods to obtain gait speed during natural walking training models to predict natural walking speed and distance during a 6MWT with 28 pulmonary patients and ten subjects without pulmonary condition. We also compare our model's accuracy to popular fitness devices. Our universally trained support vector machine models produce 6MWT distance with 3.23% error during a controlled 6MWT and 11.2% during natural free walking. Furthermore, our model attains 7.9% error when tested on five subjects for distance estimation compared to the 50-400% error seen in fitness devices during natural walking.