Suppose the width of your fist is 3.9 inches and the length of your arm is 30.6 inches. Based on these measurements, what will be the angular width (in degrees) of your fist held at arm’s length?

Answer 1

Angular width is measured using the following formula:

α=2arctan(D/2r)

where

α - Angular width

D- diameter or size of object, 3.9 inches

r - the distance to the object from the observer, 30.6 inches

If we plug everything in, we get:

α = 2 arctan (3.9 inches/(2*30.6 inches))

α = 2 arctan(0.06372549019 inches)

α = 7.2925 deg == 7.293 deg

For physical reference, your pinkie finger held at arms length is about half a degree, or the same size of the full moon.