This project envisages a Buck dc – dc converter mathematical analysis and simulation. This power regulator is made up of some vital circuit elements such as inductor, freewheeling diode, filter capacitor and electronics power switch. The circuit is analysed based on two modes of operation namely: continuous current conduction mode and discontinuous current mode. Ansoft Simplorer software is used to carry out the circuit simulation under the two modes of operation which aided in verifying the calculated results. Both calculated and simulated waveforms are displayed. The results obtained are very similar.