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Overlapping Polygons

I have two polygons that are overlapping each other. I need to calculate the area that's created in between these overlapping polygons. I used the "intersect" tool but it's not giving me the exact area. I used the field calculator function in the attribute table to manually subtract the areas between those two polygons. Is there a way to calculate the area between the overlapping polygons and represent it in a new polygon?

The area of the outer polygon is (red): 9.319671 The area of the inner polygon is (grey): 5.070906 The difference is: 4.248765 (need to represent this area in a new polygon)

The highlighted field in the attribute shows the value I manually calculated using the field calculator function.

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    Just about every one of the overlay tools will give you access to the result you want... Union, Difference, Intersect. You just need to pay attention to the order in which you provide parameters with some of them. – Vince Apr 5 '16 at 1:08
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To do this I would use Union which:

Computes a geometric union of the input features. All features and their attributes will be written to the output feature class.

Its Usage says:

The output feature class will contain a FID_ attribute for each of the input feature classes. For example, if one of the input feature classes is named Soils, there will be a FID_Soils attribute on the output feature class. FID_ values will be -1 for any input feature (or any part of an input feature) that does not intersect another input feature.

If your feature classes were called FC1 and FC2 then any polygon(s) where FID_FC1 = -1 or FID_FC2 = -1 represents the area that you are after i.e. where one or other feature class exists but not both.

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Erase tool in Analysis tools > Overlay will do the job. Then add a new field to the attribute table of the result and calculate the area.

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Also, using the intersect tool, intersect the smaller into the larger; you'll get a two-part feature. One of those will be the one that you want, complete with area measurements.

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