The Sun and the Moon about the same size in the sky
The full moon in the sky appears to have almost the same size as the Sun by day, because the Sun is approx. 400 times as large as the Moon, but also 400 times further away. So it balances itself out and this is how these two very different sized orbs appear to be of the same magnitude to us.
The Moon varies in distance and size
Due to the shape and the position of the Moon’s orbit around the Earth, the Moon gets closer to the Earth in some months during the year and hence appears to be slightly larger. The astronomical term for this is »perigee«. This is also popularly called »supermoon«, even though, this is slightly exaggerated, because the Moon is only 7% larger than on average. Is the Moon further away (»apogee«), it is up to 7% smaller than on average. This would be, so to speak, the »minimoon«.
The Moon appears larger on the horizon
In general, the Moon appears larger to us when it is within close proximity to the horizon (at moonrise or moonset). This optical illusion is called Moon illusion.
The Moon smaller than the thumb (»thumb rule«)
To switch off the Moon illusion, you can create a small frame with your hands around the Moon. Or you stretch your arm, hold up the thumb and cover the Moon with it. The Moon is then about half the size of the tip of your thumb, so it can always be covered by the thumb, regardless how large or small it was at the time. This »thumb rule« is often passed on incorrectly, if it claims that the Moon has the same size as the thumb. In reality, the Moon is only half the size. The thumb rule is shown in the movie »Dear John«, whereby here too, cheating was involved. The Moon is depicted too big in the movie!
It is interesting how the size of the Moon keeps people occupied on many levels. The reality is of course: the Moon has always the same size. Only for us it varies.