Monitoring apparatus for measuring the respiratory rate of a subject comprises an upper arm unit attached to a subject's upper arm in use and containing at least one movement sensor and a photoplethysmograph configured to monitor blood volume within the subject's upper arm while the upper arm unit is worn on the subjects upper arm. The output from the photoplethysmograph and movement sensor(s) are processed to calculate and output an estimate of the rate of respiration of the subject. Respiratory cycle induced variations in the photoplethysmograph signal and movement sensor signals can be independently determined and there is a greater confidence in the calculated respiratory rate when these independent calculations give consistent readings. If there is insufficient confidence, no rate of respiration is displayed.