Sleep is associated with important changes in respiratory rate and ventilation. Currently, breathing rate (BR) is measured during sleep using an array of contact and wearable sensors, including airflow sensors and respiratory belts; there is need for a simplified and more comfortable approach to monitor respiration. Here, we present a new method for BR evaluation during sleep using a non-contact microphone. The basic idea behind this approach is that during sleep the upper airway becomes narrower due to muscle relaxation, which leads to louder breathing sounds that can be captured via ambient microphone. In this study we developed a signal processing algorithm that emphasizes breathing sounds, extracts breathing-related features, and estimates BR during sleep. A comparison between audio-based BR estimation and BR calculated using the traditional (gold-standard) respiratory belts during in-laboratory polysomnography (PSG) study was performed on 204 subjects. Pearson's correlation between subjects' averaged BR of the two approaches was R=0.97. Epoch-by-epoch (30 s) BR comparison revealed a mean relative error of 2.44% and Pearson's correlation of 0.68. This study shows reliable and promising results for non-contact BR estimation.