One of the important parameters that affects the performance of a solar collector is its tilt angle with the horizontal. This is due to the fact that the variation of tilt angle changes the amount of solar radiation reaching the collector surface. A mathematical model was used for estimating the total (global) solar radiation on a tilted surface, and to determine the optimum tilt angle and orientation (surface azimuth angle) for the solar collector in Brunei Darussalam on a daily basis, as well as for a specific period. The optimum angle was computed by searching for the values for which the total radiation on the collector surface is a maximum for a particular day or a specific period. The results reveal that changing the tilt angle 12 times in a year (i.e. using the monthly-averaged optimum tilt angle) maintains approximately the total amount of solar radiation near the maximum value that is found by changing the tilt angle daily to its optimum value. This achieves a yearly gain in solar radiation of 5% more than the case of a solar collector fixed on a horizontal surface.