Electromagnetic field behaviours in free space are defined by Maxwell’s Equations, which couple the temporal and spatial variations of electric and magnetic fields through partial derivatives. These derivatives quantify the rate of change of each field’s vector component with respect to position and time in 3D lattice, forming the basis for numerical field analysis. This research will develop a mathematical and computational framework using multivariable calculus to model, simulate, and visualize electromagnetic wave propagation in free space using MATLAB. Gradient, divergence, and curl operations are implemented to compute local field variations and energy transfer. The resulting data are used to generate 3D plots that represent the propagation of electromagnetic waves and the coupling between electric and magnetic components. By integrating partial differentiation into simulation, this study demonstrates how calculus enables precise modelling and visualisation of dynamic field interactions, supporting validation of Maxwell’s equations and providing insights applicable to spacecraft communication, sensor optimization, and electromagnetic system design.