You can use Cad2Stl (a data conversion tool) - free with Flow 3D
This is normal as the .stl file format turns your solid model into a collection of triangles, this process is called tesselation and produces a mesh. The coarseness of this can be controlled by going to File > Save As and choosing the .stl format, then before clicking save you should have an Options... button.
Simply take the deviation and angle sliders and push them all the way towards the right. Then click OK and save.
The resultant .stl will be larger in filesize and will have better fidelity and should be much closer to the true 60 value but it will never get there all the way, as it is still an approximation. You should see a preview of the mesh right after you clicked Save.
Experiment with some different values using those two sliders and you will quickly see what is going on here and how the cylinder is being approximated by straight line segments resulting in the discrepency error.