Electrochemical ammonia production using catalysts offers a promising alternative to the conventional Haber-Bosch process, allowing for ambient temperature and pressure conditions, environmentally friendly operations, and high-purity ammonia production. In this study, we focus on the nitrogen reduction reactions occurring on the surfaces of ruthenium catalysts, employing first-principles calculations. By modeling reaction pathways for nitrogen reduction on the (0001) and (1000) surfaces of ruthenium, we optimized the reaction structures and predicted favorable pathways for each step. We found that the adsorption configuration of N2 on each surface significantly influenced subsequent reaction activities. On the (0001) surface of ruthenium, the end-on configuration, where nitrogen molecules adsorb perpendicularly to the surface, exhibited the most favorable N2 adsorption energy. Similarly, on the (1000) surface, the end-on configuration showed the most stable adsorption energy values. Subsequently, through optimized hydrogen adsorption in both distal and alternating configurations, we theoretically elucidated the complete reaction pathways required for the final desorption of NH3.