What are the radii and sizes for the new iOS 7 icons?
If this is the correct icon, looks like the border radius is 12px.
The overall size is 60 x 60px.
Image taken from DesignBoom
It's not a radius. The iOS icon grid, including the corner curve can be easily put together using two ratios. These ratios are the golden section and the square root of two. Determining the points through which the curved corner passes is surprisingly simple. The grid as it is presented by Apple shows how to establish three points of the curve: 1) the point where the curve departs from the horizontal 2) the point where it departs from the vertical, and 3) the point where it intersects the 45 degree line drawn from the centre.
Extending the grid using the ratios mentioned above perfectly establishes two more points through which a line of best fit can be drawn, e.g., a Bézier curve.