This paper proposes a new interval observer aiming at the estimation of the specific growth rate in a bioreactor. The observer is based on a high gain bounded error observer, which is able to estimate the unknown input. This observer is useful when an accurate model and noise-free measurements are available. An interval observer can be derived from this high gain observer, guarantying bounds on the prediction error. This observer is then applied when reaction rate is considered as an unknown input. We nevertheless use the knowledge of the (uncertain) growth rate to bound the growth rate derivative using the available state interval. Then, we run in parallel various observers and we take the best estimates. The method is applied to the specific growth rate estimation of a simple bioreactor model.