Micro-light emitting diodes (µ-LEDs) suffer from a drastic drop in internal quantum efficiency that emerges with the miniaturization of pixels down to the single micrometer size regime. In addition, the light extraction efficiency (LEE) and far field characteristics change significantly as the pixel size approaches the wavelength of the emitted light. In this work, we systematically investigate the fundamental optical properties of nitride-based µ-LEDs with the focus on pixel sizes from 1 µm to 5 µm and various pixel sidewall angles from 0∘ to 60∘ using finite-difference time-domain simulations. We find that the LEE strictly increases with decreasing pixel size, resulting in a LEE improvement of up to 45% for a 1 µm pixel compared to a 20 µm pixel. The ideal pixel sidewall angle varies between 35∘ and 40∘, leading to a factor of 1.4 enhancement with respect to vertical pixel sidewalls. For pixel sizes in the order of 2 µm and smaller, a substantial transition of far field properties can be observed. Here, the far field shape depends severely on the pixel sidewall angle and affects the LEE within a solid angle of ±15∘. Moreover, we investigate the impact of emission wavelength and observe major differences in optical characteristics for blue, green and red emitting pixels, which is relevant for real-world applications. Finally, we discuss the implications of the assumptions we made and their significance for the design of µ-LEDs.