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Want to find the degree of rotation based on forward and side rotations.

I have an xbox controller and I want to find the equation that will tell me the amount of rotation when I push the thumbstick on it in any direction. To be a bit more clear: When the thumbstick is at rest and pointing straight up, the x and y values are 0. When I push the thumbstick forward all the way, the Y value is 1.0. When I push the thumbstick all the way to the left, the X value is 1.0.
I want to know what the value is, between 0 and 1, of the thumbstick's rotation if I push it in any diagonal direction.
Example: If I push the thumbstick so that Y = 0.25 and X = 0.35, what is the value of the rotation between the resting point and the current thumbstick location. And specifically, what is the equation that brings you to this answer?
Thank you for your time.

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