By definition, pi is the ratio of the circumference of a circle to its diameter.
So how can others answer that this value is not best found from the most precise measurement we can make?
In the real world, a perfect circle has a definite value for radius. Pi is thought to be a never ending, non repeating decimal. This kind of value cannot truly represent a real perfect circle. This kind of value can only be used for approximations. The formulas found in the link of user4894's post do just that, approximations.
Atomic-force microscopy (AFM) or scanning-force Microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the optical diffraction limit.
AFM - wikipedia
We should really use this to measure a circle! But how would we make a perfect circle to measure?
Circles are abstract, it might not even be possible to make a perfect circle to measure. I cannot find instances of anyone trying to measure a circle with AFM. But C = Pi*D still stands as the definition for pi that all those fancy calculations attempt to approximate. Good question OP!
One good way to approximate the right dimensions for C and D is to fit a polygon inside a circle, and keep subdividing it until you reach an absurd amount of vertices. This polygons perimiter is a good approximation of the circumference of the circle, take the distance between two points that are straight across from one another for diameter. We can reach the highest levels of precision with this method, althrough there are more efficient ways to generate good pi values, it seems the most trustable to me. Very simple.