Automatic vessel tortuosity measures are crucial for many applications related to retinal diseases such as those due to retinopathy of prematurity (ROP), hypertension, stroke, diabetes and cardiovascular diseases. An automatic evaluation and quantification of retinal vascular tortuosity would help in the early detection of such retinopathies and other systemic diseases. In this paper, we propose a novel tortuosity index based on principal component analysis. The index is compared with three existant indices using simulated curves and real retinal images to demonstrate that it is a valid indicator of tortuosity. The proposed index satisfies all the tortuosity properties such as invariance to translation, rotation and scaling and also the modulation properties. It is capable of differentiating the tortuosity of structures that visually appear to be different in tortuosity and shapes. The proposed index can automatically classify the image as tortuous or non tortuous. For an optimal set of training parameters, the prediction accuracy is as high as 82.94% and 86.6% on 45 retinal images at segment level and image level, respectively. The test results are verified against the judgement of two expert Ophthalmologists. The proposed index is marked by its inherent simplicity and computational attractiveness, and produces the expected estimate, irrespective of the segmentation approach. Examples and experimental results demonstrate the fitness and effectiveness of the proposed technique for both simulated curves and retinal images.