Agriculture has sustained human civilisation for centuries, yet it remains a sector in critical need of technological advancement. Existing crop-growth and yield-prediction methods lack a simple and generic framework that relies on climate data with minimal parameters, particularly for leguminous crops. Addressing this gap, this study develops a Crop Growth Rate Computation Model (CGRCM) to simulate crop growth with a focus on soil nitrogen utilisation. The CGRCM integrates climate variables and nine parameters to predict cowpea growth in terms of above-ground biomass and final yield, derived from biomass at maturity and harvest index. Climatic input data and soil parameters were obtained through remote sensing for Makurdi and Mokwa in North Central Nigeria, covering 32 growing seasons (1990-2021). The model was calibrated for the FUAMPEA cultivar and implemented using a Python-based neural network post-processor. Training was conducted on data from 1990--2017 and testing on data from 2018--2021. Results show that the CGRCM effectively captures biomass responses to drought, temperature and heat stress. The model achieved strong agreement with observed yields, with an MAE of 134.2, an RMSE of 153.6 and a prediction accuracy of 91.4% for Makurdi, and an MAE of 109.4, an RMSE of 113.7 and a prediction accuracy of 93.5% for Mokwa. Bootstrap confidence interval, paired t-test and Diebold-Mariano tests confirmed that the CGRCM performed better, demonstrating its reliability as a scalable and data-efficient tool for crop-growth prediction.