Abnormal vital signs often predict a serious condition of acutely ill hospital patients in 24 hours. The notable fluctuations of respiratory rate (RR) are highly predictive of deteriorations among the vital signs measured. Traditional methods of detecting RR are performed by directly measuring the air flow in or out of the lungs or indirectly measuring the changes of the chest volume. These methods require the use of cumbersome devices, which may interfere with natural breathing, are uncomfortable, have frequently moving artifacts, and are extremely expensive. This study aims to estimate the RR from electrocardiogram (ECG) and photoplethysmogram (PPG) signals, which consist of passive and non-invasive acquisition modules. Algorithms have been validated by using PhysioNet’s Multiparameter Intelligent Monitoring in Intensive Care II (MIMIC-II)’s patient datasets. RR estimation provides the value of mean absolute error (MAE) for ECG as 1.25 bpm (MIMIC-II) and 1.05 bpm for the acquired data. MAE for PPG is 1.15 bpm (MIMIC-II) and 0.90 bpm for the acquired data. By using 1-minute windows, this method reveals that the filtering method efficiently extracted respiratory information from the ECG and PPG signals. Smaller MAE for PPG signals results from fewer artifacts due to easy sensor attachment for the PPG because PPG recording requires only one-finger pulse oximeter sensor placement. However, ECG recording requires at least three electrode placements at three positions on the subject’s body surface for a single lead (lead II), thereby increasing the artifacts. A reliable technique has been proposed for RR estimation.