Summary Statement. We present a simple and useful geometrical equation system to carry out the pre-operative planning and intra-operative assessments for total knee arthroplasty. These methods are extremely helpful in severely deformed lower limbs. Introduction. Total knee arthroplasty is a highly successful surgery for most of the patients with knee osteoarthritis. With commercial instruments and jigs, most surgeons can correct the deformity and provided satisfactory results. However, in cases with severe extra-articular deformity, the instruments may mislead surgeons in making judgment of the true mechanical axis. We developed a geometrical equation system for pre-operative planning and intra-operative measurement to perform correct bony cuts and achieve good post-operative axis. Patients & Methods. From 2008 to 2012, twenty-four patients with severe extra-articular deformities of low limbs underwent total knee arthroplasties for osteoarthritis. The deformities included malunion of femoral or tibial shafts with angulation, non-union of femoral supracondylar fractures, failed high tibia osteotomies, severe bowing of femurs, and other post-traumatic sequelae. The intra-medullary or extra-medullary guide devices were not possible to provide correct axis in these cases. For pre-operative planning, we analyzed the deformities on triple-film scanography and standing anterior-posterior and lateral X-ray films. The angles needed to be corrected in coronal and sagittal planes were measured. A geometrical equation system was applied to calculate the thickness of the proximal tibia cut and distal femoral cut. If the flexion contracture was presented, the degree of necessary elevation of joint line was also calculated. Intra-operatively, the degree of rotation of anterior and posterior femoral cuts was assessed after proximal tibial and distal femoral cuts. The sizes of prosthesis were judged according to the balance between flexion and extension gaps. A 3-in-1 jig was used for chamfering of the femur. After fine-tuning of bony cuts and balancing of soft tissue, the prostheses were cemented. The conventional intra-medullary and extra-medullary guiding devices were not used during the whole procedure. Results. All of the patients achieved satisfactory results in the aspect of pain relief and functional outcomes. All patients had good post-operative axis in coronal plane (varus or valgus deformity < 3 degrees). Twenty-two patients (92%) achieved good sagittal alignments (deformity < 3 degrees). The results were compatible with those in the patient population without those severe deformities. There was no major complication among these patients. Discussion/Conclusion. In this series, we present a simple and useful geometrical equation system to carry out the pre-operative planning and intra-operative assessments for total knee arthroplasty. These methods are extremely helpful in severely deformed lower limbs. Optimal post-operative alignments were achieved in this series and no major complication was found