The application of existing formulas to determine solar altitude and azimuth angles is inconvenient and inadequate. To improve the existing formulas, a new timing system named the Radiation Calendar was established. In this system the angles' ranges were redefined, making the angles calculated from the improved formulas singlevalued and varying with hour angle. Representative curves of solar altitude and azimuth angles varying with hour angle were plotted. The mathematical distinctions of these curves astronomically and geographically describe some rules of solar position varying with time, which proves the validity and generality of the improved formulas. The results calculated using the improved formulas show simply and clearly the daily and annual variation of solar altitude and azimuth angles, which are valuable in the work of sunlight distribution analysis related to the design of buildings, airconditioning systems and structures.