A new highly accurate closed-form capacitance calculation model has been developed to calculate the capacitance of capacitive micromachined ultrasonic transducers (CMUTs) built with square diaphragms. The model has been developed by using a two-dimensional polynomial function that more accurately predicts the deflection curve of a square diaphragm deformed under the influence of a uniform external pressure and also takes account of the fringing field capacitances. The model has been verified by comparing the model-predicted deflection profiles and capacitance values with experimental results published elsewhere and finite element analysis (FEA) carried out by the authors for different material properties, geometric specifications, and loading conditions. New model-calculated capacitance values are found to be in excellent agreement with published experimental results with a maximum deviation of 1.7%, and a maximum deviation of 1.5% has been observed when compared with FEA results. The model can help in improving the accuracy of the design methodology of CMUT devices and other MEMS-based capacitive type sensors built with square diaphragms.