An analytical and numerical analysis of light extraction from light pipes using total internal reflection grooves with linear and elliptical profiles is presented. We performed the study considering light sources with different aperture angles, such as sunlight delivered by optical fibers and LEDs. With this analysis, we propose an analytical model based on the edge ray concept that allows selecting the most convenient profile, size, and orientation of the groove to extract light with a desired illumination area according to the source aperture angle employed in the light pipe system. We also have numerically found that for sources with high aperture angles, the light extracted by the linear and elliptical grooves produces similar irradiance and angular distributions, whereas for sources with low aperture angles, the elliptical groove focuses the extracted light and produces a higher angular distribution in comparison to this obtained with the linear groove. Our results are scalable to different light pipe dimensions and provide a systematic way to obtain preliminary designs of grooves for lighting systems that employ optical sources with different aperture angles.