How to arrange selected vertices in a perfect circle [duplicate]

So how do I get the surrounding vertices to make a circle (centered) without needing to manually move every single one to the right spot? Also I need the outer shape to stay as a square.

• SHIFT + "A" > Choose Mesh from the drop down menu > Choose "Circle" – Dontwalk Sep 21 '17 at 14:47

I think the easiest method is to use the handy LoopTools addon which is already included in Blender. Just enable it in User Preferences -> Add-ons.