I am curious to see how many stars I can see with my binoculars. I saw online you can see on perfect conditions ~5,000 stars, which includes all stars mag 6+

My binoculars should be able to pickup mag 10 stars.

Approx how many stars are mag 10 or brighter in the night sky.

Is there a chart somewhere that just shows a list of magnitudes and an approximate number of stars that fall into that magnitude?

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Here ya go, but I'm not vouching for its reliability, just yet.

Most of the sky map programs available have a settings function that invites you to enter what magnitude you wish to go down to. The logic here is so as to reduce clutter of fainter objects while making the familiar patterns a little more visible. You will need to be away from the lights of city and businesses to enhance what you can see.. A dark sky site is of greater value than the size of your telescope. Binoculars are an excellent tool for star viewing and globular identifications,. good luck.

Many factors will affect the number of stars you can see. For example, there may be some 9000 stars stars brighter than 7.0 but will never see them unless you travel to both hemispheres. Your local conditions have a huge impact as well. I think all-in-all the chart posted by hhEb09'1 is a good estimate.

You can do an experiment yourself. First determine the field of view of your binoculars. You can do this by looking at the full moon and estimating how many moons it would take to span your field of view. Let's say for example that you can fit 5 full moons across your field of view. This means that your field of view is 5^2 times the the area of the full moon. And the area of a full moon is pi*.25^2, which equals about 0.2 square degrees. So your field of view in this example would be about 5 square degrees. The full sky is about 41000 square degrees. Divided by 5 square degrees gives you 8200 square degrees. So the full sky is 8200 binocular field of views.

Now aim the binoculars at a random spot in the sky, and count how many stars you can see. Do this 10-20 times and take an average. Multiply this average by 8200. This gives the total stars you can see with binoculars. Compare this to the chart provided by hhEb09'1.

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Or you can do it by reading this and crunching the numbers printed on most binoculars.