Accurate distance estimation is a fundamental challenge in robotic perception, particularly in omnidirectional imaging, where traditional geometric methods struggle with lens distortions and environmental variability. In this work, we propose a neural network-based approach for monocular distance estimation using a single 360° fisheye lens camera. Unlike classical trigonometric techniques that rely on precise lens calibration, our method directly learns and infers the distance of objects from raw omnidirectional inputs, offering greater robustness and adaptability across diverse conditions. We evaluate our approach on three 360° datasets (LOAF, ULM360, and a newly captured dataset Boat360), each representing distinct environmental and sensor setups. Our experimental results demonstrate that the proposed learning-based model outperforms traditional geometry-based methods and other learning baselines in both accuracy and robustness. These findings highlight the potential of deep learning for real-time omnidirectional distance estimation, making our approach particularly well-suited for low-cost applications in robotics, autonomous navigation, and surveillance.