How can you calculate the vertical speed of an helicopter during auto-rotation?
It would depend on the pilot's inputs, since autorotation is still controlled flight and the pilot could choose to descend faster or slower. Depending on the helicopter, there may be a trade off between the amount of time it takes to descend and the distance covered. For example, the sink rate of the best ratio of forward distance covered to vertical distance covered (equivalent to glide ratio in a fixed wing aircraft--the engine failed over water and the pilot wants to go as far as possible toward land) could be different than the minimum possible sink rate (the engine failed over a safe place to land and the pilot wants to buy time while trying to restart the engine).

The most important quantity that affects minimum sink rate in either case is disk loading, which is the equivalent of wing loading in fixed wing aircraft. Page 4 of this pdf (heading: "Basic Physics of Autorotation") has the information you need to calculate minimum sink rate during autorotation based on an assortment of parameters.