In this work, a computational study on the dendritic solidification of delta ferrite in 1.4031 stainless steel is carried out. A multi-component and multi-phase-field formulation is employed and grand chemical potential-based phase-field simulations are performed. For better quantitative analysis of the simulation results of this commercial alloy, the parameters of Gibbs energy functions at all compositions and temperatures are fitted with the CALPHAD (CALculation of PHAse Diagrams) database. The fitted results for liquid and delta-ferrite phases show a good agreement with the experimental database with a maximum error of 0.009% and 0.02% respectively. Computationally efficient simulations for various isothermal cases in 2D and 3D were carried out to understand the dendrite growth parameters and concentration profiles of the alloy during solidification. The simulation results reveal a good understanding of microstructure, offering valuable insight into the solidification process for such an alloy with low carbon content. The quantitative results of the solidification under controlled conditions serve as reference data for further simulation studies of the microstructure evolution, the morphologies, and material properties under conditions of Laser Beam Welding (LBW).