Recognizing and classifying gait activities, such as stair ascending and descending, using smartphones' inertial sensors has significant potential in various applications. However, accurately identifying stairs and inclined surface activities has long been a challenge in this study, the feasibility of employing both machine learning and deep learning models to identify stair ascending and descending activities based on collected datasets is explored. The datasets were utilized to train both machine learning and deep learning models. Notably, an impressive accuracy rate of 99.39% was achieved by the convolutional neural network (CNN). By leveraging the trained model, an online streaming system capable of predicting five different activities, including stair ascending, descending, level ground walking, and ramp up and down, was successfully developed. The system utilizes accelerometer data obtained in real-time. The system's prediction accuracy and reliability were evaluated and found to be satisfactory. Though real-time prediction method does not have guaranteed immediate responses and depends on the reliability and speed of the remote connection, which could be considered a limitation when aiming for real-time applications. This research demonstrates the promising feasibility of utilizing smartphone inertial sensors, coupled with advanced machine learning deep learning techniques, to accurately identify and classify various gait activities, particularly those associated with stair ambulation. The potential applications of this technology extend to areas such as health monitoring, rehabilitation, and activity tracking. By leveraging smartphones' widespread availability, this approach offers a cost-effective and accessible solution for gait activity recognition without the need for external sensors or complex circuitry.