How to evaluate three dimensional angle error from plain radiographs

Evaluating three-dimensional angle error is necessary because we cannot get every patient's CT or MRI at all times. Creating a method that can calculate angle error from plain radiographs is therefore important. Using vector and trigonometric mathematics, we gradually deduct our formula which can calculate angle error from goal angles (the angles we plan to achieve before operation) to result angles (the angles we get after operation) by two perpendicular radiographs. We also encode it into Micorsoft Excel (Redmond Campus, Redmond, Washington, U.S.) so that it becomes more user-friendly. We hope this tool can be used when evaluating TKR, corrective osteotomy, fracture fixation, and so on.