Great answer by David Barnard on a question over at Stackoverflow:

Apple starts with the 57px icon and a radius of 10 then scales up or down from there. Thus you can calculate the radius for any icon size using 10/57 x new size (for example 10/57 x 114 gives 20, which is the proper radius for a 114px icon).

And for the lazy ones, he listed the calculations for the most common icons:

• Icon512.png - 512px - 89.825
• Icon.png - 57px - 10
• Icon@2x.png - 114px - 20
• Icon-72.png - 72px - 12.632
• Icon-72@2x.png - 144px - 25.263
• Icon-Small.png - 29px - 5.088
• Icon-Small@2x.png - 58px - 10.175