iOS App Icon Rounded Corner Radius

Apple starts with the 57px icon and a radius of 10px, then scales up and down from there.

Calculate the radius for the corners of any size icon by multiplying the width by 10/57.

Examples:

• Icon512.png: 512*(10/57) = 89.825
• Icon.png: 57*(10/57) = 10
• Icon@2x.png: 114*(10/57) = 20
  Icon-72.png: 72*(10/57) = 12.632
• Icon-72@2x.png: 144*(10/57) = 25.263
• Icon-Small.png: 29*(10/57) = 5.088
• Icon-Small@2x.png: 58*(10/57) = 10.175

For more details, see drbarnard's answer on stackoverflow.