Find the horizontal, vertical and diagonal angle of view from your focal length and sensor, plus how wide the frame is at a given subject distance.
Angle of view is how much of the scene the lens takes in, set by the focal length and the sensor dimensions. A longer lens or a smaller sensor narrows it. The frame width is how wide the scene is at the chosen subject distance.
Angle of view = 2 times arctan(sensor dimension / (2 times focal length)). The horizontal, vertical and diagonal values use the sensor width, height and diagonal respectively, so a 50mm lens on full frame gives about 40 degrees horizontally and 47 degrees diagonally.
The same lens projects the same image, but a smaller sensor crops into it, so it sees a narrower angle of view. That is the crop factor effect: a 50mm lens on APS-C frames like a 75-80mm lens on full frame.
It tells you how wide a slice of the scene fits in the frame at a given distance, which is handy for group photos, real-estate and product shots where you need to know if the subject fits.