Water trees occurring in polyethylene (PE) insulated power cables at defects exist on the inner or outer semiconductor layers or in PE insulation medium. Water trees start with the existence of water source and penetration under the action of high electric fields. The inevitable micro air voids (1µm radius) in PE medium with an internal pressure 4450 Torr, and 2.3 dielectric constant, will lead to an electric field (E) of 1.08 MV/cm which can be called tree inception field (E_i). For a protrusion defect of 200 µm tip radius and 2.5 mm insulation thickness, the minimum required breakdown field in PE is 0.417 MV/cm at 2.5 per unit (pu) over voltages. In this paper a new breakdown equation has been introduced related to the injected energy (U), electric field (E) and air void radius (r) with the so called breakdown index (n) under two cases: First case, for n<25, the air void radius increases till 5µm diameter (water bouquet value). But for the second case, n≥ 25, the air void will crack to many branches in free space and these assume 25 cracks at n=25. The crack length (L_cr) differs according to the mechanical strength (P_m) of PE insulation. According to the new introduced equations L_cr equal 197 µm, 248 µm, and 332 µm for P_m 12 N⁄〖mm〗^2 low density polyethylene (LDPE), 15 N⁄〖mm〗^2 high density polyethylene (HDPE), and 20 N⁄〖mm〗^2 cross-linked polyethylene (XLPE) respectively. The water will penetrate these cracks and the progress of water trees starts.