For successful calculating undercut radius from hobbed machining of involute spur gear with small tooth number. Firstly,the application scope of the conventional calculation method is analyzed by two examples. Secondly,because of the special feature of gear hobbed machining with small tooth number,the tangent continuity condition of gear profile on undercut point must be neglected,and from center transposed angle of arc blade of undercut point,an developed method for calculating undercut radius is derived. Finally,all parameterized tooth profile equations of the gear is created. All results indicated that the conventional calculation method is applicable only the condition of upper radius coefficient limit determined by rack cutter geometry greater than its lower limit determined by successful gear hobbed machining,unfortunately,for the involute spur gear with small tooth number,its upper limit usually is less than its lower limit,so the conventional calculation method isn’t applicable for calculating undercut radius. The center transposed angle of arc blade really is greater than the pressure angle with 20° of straight blade,the hobbed machining is successful from optimized normative radius coefficient of arc blade for the gear with small tooth number. The created 3D gear model is reliability and fully parameterized,etc. It is concluded that the developed calculation method as an theoretical basis is provided for other followed calculating of involute spur gear with small tooth number.