According to this article:
Different animals have different fields of view, depending on the
placement of the eyes. Humans have an almost 180-degree forward-facing
horizontal field of view, while some birds have a complete or
nearly-complete 360-degree field of view. In addition, the vertical
range of the field of view in humans is typically around 100 degrees.
The range of visual abilities is not uniform across a field of view,
and varies from animal to animal. For example, binocular vision, which
is important for depth perception, only covers 120 degrees
(horizontally) of the field of vision in humans; the
remaining peripheral 60 degrees have no binocular vision (because of
the lack of overlap in the images from either eye for those parts of
the field of view). Some birds have a scant 10 or 20 degrees of
Similarly, color vision and the ability to perceive shape and motion
vary across the field of view; in humans the former is concentrated in
the center of the visual field, while the latter tends to be much
stronger in the periphery. This is due to the much higher
concentration of color-sensitive cone cells in the fovea, the central
region of the retina, in comparison to the higher concentration of
motion-sensitive rod cells in the periphery. Since cone cells require
considerably brighter light sources to be activated, the result of
this distribution is that peripheral vision is much stronger at night
relative to binocular vision.
So a human observer should be able to see roughly half of the visible sky, or a quarter of a full sphere. If you look about 50° above the horizon, you should be able to see an area of the sky extending from directly to your left to directly to your right horizontally, and from the horizon to about 10° past the zenith.
You won't be able to see as well around the edges of your field of view. Depth perception isn't relevant when looking at the sky, but being able to see with both eyes is probably better than seeing with just one.
This can vary from person to person; some people have much better peripheral vision than others.