In the literature, many studies are conducted to obtain the mathematical models of semiconductor elements such as diodes, transistors, etc. These elements are commonly used in the circuits and systems. Main objective in this subject is to establish a mathematical model (or expression) to describe all the features of the semiconductor circuit elements. One of the most popular circuit elements is a diode. A general diode equation, which is commonly used in the solid-state physics literature, uses the diode leakage current, temperature values and material dependant coefficients other than the diode voltage. Major factor to get results as close as possible to actual results using this equation is to obtain the leakage current accurately. Otherwise, error in the results will be unacceptable. Therefore, in this study, a work has been carried out to obtain acceptable reverse saturation currents (or leakage currents) of a diode using three different methods, which are least squares, neural network and genetic algorithm. In addition, a new mathematical model of a semiconductor diode has been also proposed. This model is created using the actual measured diode current-voltage values. The new model is not using the diode leakage current, ambient temperature or coefficients of the diode construction materials. To obtain the diode characteristics using the above mentioned methods, a graphical user interface program has been also designed. The simulation/experimental results are obtained and compared using this program. By this way, validity of the proposed approximate model and other methods are proved.