Hand preference and degree of handedness (DoH) are two different aspects of human behavior which are often confused to be one. DoH is a person's inherent capability of the brain; affected by nature and nurture. In this study, we used dominant and non-dominant handwriting traits to assess DoH for the first time, on 43 subjects of three categories- Unidextrous, Partially Unidextrous, and Ambidextrous. Features extracted from the segmented handwriting signals called strokes were used for DoH quantification. Davies Bouldin Index, Multilayer perceptron, and Convolutional Neural Network (CNN) were used for automated grading of DoH. The outcomes of these methods were compared with the widely used DoH assessment questionnaires from Edinburgh Inventory (EI). The CNN based automated grading outperformed other computational methods with an average classification accuracy of 95.06% under stratified 10-fold cross-validation. The leave-one-subject-out strategy on this CNN resulted in a test individual's DoH score which was converted into a 4-point score. Around 90% of the obtained scores from all the implemented computational methods were found to be in accordance with the EI scores under 95% confidence interval. Automated grading of degree of handedness using handwriting signals can provide more resolution to the Edinburgh Inventory scores. This could be used in multiple applications concerned with neuroscience, rehabilitation, physiology, psychometry, behavioral sciences, and forensics.