What is the relationship between the arc length and the radius of a circle when the central angle is defined in radians?

There are two formulae for this: 

angle/360 X (pi) X (radius squared) = Area of a sector 

angle/360 X (pi) X (diameter) = Arc Length of sector 
or 
angle/360 X (2) X (pi) X (radius) = Arc Length of sector 

If you want to work out the perimeter of a sector, use this formula: 

Arc Length + (2 X radius) = Perimeter of sector.