The safety of freight trains motion that have empty cars in their composition is in many cases determined by the stability of the motion of these cars. The problem is that the intense horizontal non-stationary-periodic oscillations arise due to the conicity of the wheel treads with the weak connection of the wheelsets with the side frames of the three-piece bogie of the freight car at a certain (critical) speed of motion. These oscillations begin to threaten the safety of train motion when the car's speed exceeds its critical value by 20-25 km/h. Numerically, the conicity is determined by the angle between the generatrix of the conical surface and the axis of the cone. The results of experimental studies and theoretical calculations show that within creasing conicity of the wheel treads of freight cars, the value of the critical speed decreases substantially. The article describes a method of an estimation of an equivalent conicity of wheel treads of cars with the worn out surface of rolling. The method is based on calculating the coefficients of a polynomial over even grades of the lateral oscillations amplitude of a single freely moving wheelset in the tangent segment of the track. Coefficients of the polynomial contain factors determined by the function of the difference in the radii of the worn wheel in sections equidistant from the vertical axis passing through the middle position of the point of contact between the wheel and the rail on the wheel tread. This method will help to further clarify the timing of car's wheel-turning on the condition of ensuring the safety of empty freight trains, taking into account the actual condition of the rolling surfaces of the wheel treads.