Accurate scale estimation of a target is a challenging research problem in visual object tracking. Most state-of-the-art methods employ an exhaustive scale search to estimate the target size. The exhaustive search strategy is computationally expensive and struggles when encountered with large scale variations. This paper investigates the problem of accurate and robust scale estimation in a tracking-by-detection framework. We propose a novel scale adaptive tracking approach by learning separate discriminative correlation filters for translation and scale estimation. The explicit scale filter is learned online using the target appearance sampled at a set of different scales. Contrary to standard approaches, our method directly learns the appearance change induced by variations in the target scale. Additionally, we investigate strategies to reduce the computational cost of our approach. Extensive experiments are performed on the OTB and the VOT2014 datasets. Compared to the standard exhaustive scale search, our approach achieves a gain of 2.5% in average overlap precision on the OTB dataset. Additionally, our method is computationally efficient, operating at a 50% higher frame rate compared to the exhaustive scale search. Our method obtains the top rank in performance by outperforming 19 state-of-the-art trackers on OTB and 37 state-of-the-art trackers on VOT2014.