This tool can help you determine the size of an optic needed for a given beam angle and LED chip including:
This calculator provides a rough estimate based on a etendue calculation. Enter the size of your LED chip (or select from one of the defaults we have entered) and the desired lens size to calculate the achievable beam angle. Please note that the estimate works for LEDs with a Lambertian beam angular profile; most LEDs produce a Lambertian beam.
If you need help developing a custom LED optic design, please let us know!