The article has grounded the necessity to develop an empirical power dependence of cutting modes influence on part surface roughness obtained during thread grinding. The calculations were carried out for grinding of parts made of steel and hard alloy. There have been developed a relation of part material properties, grinding wheel options, lubricating and cooling liquid (constant for concrete conditions of thread grinding), depth of cutting (thickness of a grinded layer per path), revolutions of a part and a wheel, longitudinal feed refer to obtained roughness. It has been stated that components of the grinding mode contribute in roughness values in different way, in particular they are arranged in the ascending order as follows: grinding depth, rotation speed, and detail’s diameter.