Although, the proton exchange membrane fuel cell is a promising clean and efficient energy converter that can be used to power an entire building in electricity and heat in a combined manner, it suffers from a limited lifespan due to degradation mechanisms. As a consequence, in the past years, researches have been conducted to estimate the state of health and now the remaining useful life (RUL) in order to extend the life of such devices. However, the developed methods are unable to perform prognostics with an online uncertainty quantification due to the computational cost. This paper aims at tackling this issue by proposing an observer-based prognostic algorithm. An extended Kalman filter estimates the actual state of health and the dynamic of the degradation with the associated uncertainty. An inverse first-order reliability method is used to extrapolate the state of health until a threshold is reached, for which the RUL is given with a 90% confidence interval. The global method is validated using a simulation model built from degradation data. Finally, the algorithm is tested on a dataset coming from a long-term experimental test on an eight-cell fuel cell stack subjected to a variable power profile.