The calculation of DoF for any given mechanism is essential for its kinematic and dynamic analysis, and hence, a reliable and fast method to determine the DoF is of paramount importance. The conventional methods for DoF calculation are found to be inaccurate when dealing with various useful mechanisms. Therefore in this work, a novel matrix-based method is proposed that accurately calculates the DoF of every possible planar mechanism. A strong foundation is provided in the physical derivation of the method, and the mathematical premise is explained by the idea of vector space and linear transformation using the Fundamental Theorem of Linear Algebra. Several postulates have been formulated for a clear stepwise approach to apply this method. A few well-studied examples are elaborated as case studies to demonstrate the effectiveness and advantages of this proposed matrix-based method. A comprehensive analysis of the four-bar mechanism is undertaken to elucidate the profound implications of this method and its capacity to expand the horizons of mechanism analysis through this matrix-based technique. This endeavor serves to highlight the practical significance and broader applicability of this approach.