Pie is a ratio derived when you compare the circumference of a circle with the diameter of the same.
So regardless of the size of the circle , this ratio remains the same, for your know that a circle is defined as the locus of a point which is equidistant from the centre. So here the key determining factor is the radius of the circle , how the radius when is added twice to itself becomes the diameter .
For we know that
Diameter= 2 radius
Hence Pie= 2πr./ 2r.
= π