As described in Stellarium Wiki, section Handy Angles, your hand at arm’s length provides a few useful estimates for angular size. It’s useful to know if your handy angles are typical, and if not, what they are. The method here below is just one way to do it – feel free to use another method of your own construction!
Hold your hand at arm’s length with your hand open – the tips of your thumb and little finger as far apart as you can comfortably hold them. Get a friend to measure the distance between your thumb and your eye, we’ll call this D. There is a tendency to over-stretch the arm when someone is measuring it – try to keep the thumb-eye distance as it would be if you were looking at some distant object.
Without changing the shape of your hand, measure the distance between the tips of your thumb and little finger. It’s probably easiest to mark their positions on a piece of paper and measure the distance between the marks, we’ll call this d. Using some simple trigonometry, you can estimate the angular distance θ:
For me: D=87 cm, d=18 cm, so: