adobe photoshop - How to compute the radii (radiuses) of corners for concentric rounded rects

I have a roundrect button that I want to contain within another roundrect. The containing roundrect should always be 1px away from the button.

If I make the radius on the container too small then the corners have a larger gap around them.

Is there a good "rule of thumb" that I can use to figure out what the radius should be for the larger roundrect?