Performing finite element analysis of CFRP-confined concrete columns involves complex procedures, particularly in selecting an appropriate constitutive model to predict their confinement behaviour accurately. Previous research indicates that the concrete damage plasticity (CDP) model is commonly employed for the finite element analysis of CFRP-confined concrete within the ABAQUS commercial software framework. This model includes plasticity parameters such as dilation angle, eccentricity, biaxial-to-uniaxial compressive strength ratio (fb0/fc0), K value, and viscosity parameter. Among these, the dilation angle is a crucial parameter for accurately predicting the behaviour of CFRP-confined concrete. Previous studies have demonstrated that the dilation angle is not constant but varies with the lateral confining pressure induced in the CFRP-confined concrete. Therefore, using a constant dilation angle in the CDP model is inadequate for accurate predictions. Further, researchers have addressed this problem by modifying the dilation angle according to the confining pressure using the VUSDFLD subroutine within the ABAQUS framework. This subroutine employs solution-dependent field variables (SDFV) to calibrate the dilation angle at each analysis step. However, this process generates multiple stress-strain curves for various confining pressures, which can be cumbersome. Hence, to simplify this process, novel analytical equations from fundamental mechanics are developed and presented in this paper. These analytical equations explicitly calculate the appropriate dilation angle for a three-dimensional concrete element subjected to multi-axial stresses. Finally, the equations are integrated into the ABAQUS finite element package through the VUSDFLD subroutine. The finite element analysis results are in close agreement with the experimental data of CFRP-confined circular concrete columns.