The closest measurement we can get to in terms of putting a NUMBER on eye box is exit pupil. Exit pupil is the diameter of the shaft of light that comes out the back of the scope. Exit pupil can be calculated at a basic level by a simple math formula: take the diameter of the objective lens and divide it by the magnification. As magnification goes up, the size of the exit pupil goes down.
So lets take a 4-16x44 Patriot scope. The objective lens diameter is 44mm. Divide by 4 at the lowest magnification and you get a theoretical exit pupil of 11mm. Divide by 16 at the highest magnification and you get a theoretical exit pupil of 2.75mm. So theoretically you have to place your eye inside an 11mm wide shaft of light at minimum magnification, and inside a 2.75mm shaft of light at full magnification.
In reality we have exit pupil on that scope calculated out to 11.6mm at 4x and 2.92mm at 16x, using more complicated math. The basic calculation breaks down at very low magnifications-- for example our 1x25 Blade Prism has an exit pupil of 13.5mm, not 25mm (wouldn't that be cool though). The maximum diameter of the human eye's pupil is about 4mm in daylight, and 5-9mm in low light as the pupil opens to take in more light.
So when we look through a Blade 1x25 prism scope in daytime, we have a 4mm wide hole in our eyeball that has to line up somewhere inside a 13.5mm shaft of light in order to get a sight picture. That's super easy, super fast. When we look through a Patriot at 16x magnification, now we have a 4mm wide eyeball that has to find a shaft of light measuring just 2.92mm across. Not as easy! When you get to the crazy high magnifications the situation gets worse-- Our Warhawk 5-25x56 has a minimum exit pupil of 2.2 mm at full magnification.
That doesn't mean our scope sucks, it's simply mathematics. The Leupold Mk5HD 5-25x56 also has a minimum exit pupil of 2.2mm at full mag, and that's a $2300 optic. Math always wins no matter how much you pay. So, that's why precision rifles mounting high magnification optics always have fancy adjustable stocks--the adjustable stocks are needed to put your eye in the same exact place every time you use the rifle, so you'll be able to see through those big optics consistently and comfortably.
Exit pupil isn't the WHOLE story on eye box. You can have two scopes with a theoretically identical exit pupil, look through them side by side, and its obvious that one of them is just easier to look through. But it gives us at least a starting point for a basic understanding of how easy or difficult an optic will be to look through.
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