The Steer-by-Wire (SbW) system is a system that eliminates the physical connection structure of the steering system. Instead, it steers the tires through electrical communication that transmits the driver’s intention to the motor. However, the SbW system poses a significant risk in the event of a system failure. This highlights the need for effective failure backup strategies.In our study, we propose a new estimation technique. This technique accurately predicts the magnitude of the front wheel steering angle, which is determined by the vehicle motion. This prediction is particularly useful when rear wheel steering and differential braking are applied to facilitate vehicle steering in the event of a fatal SbW system failure. The estimation model is derived based on the single track model. To construct the prediction model using only measurable states, we replaced the side slip angle with the lateral acceleration signal. Additionally, we incorporated compensation for changes in cornering stiffness due to differential braking. This enhances the accuracy of the model. We validated the proposed steer angle estimation model in a virtual environment using CarSim SW and MATLAB/Simulink.