This paper documents the derivation of the data reduction equations for the calibration of the six-component thrust stand located in the CE-22 Advanced Nozzle Test Facility. The purpose of the calibration is to determine the first-order interactions between the axial, lateral, and vertical load cells (second-order interactions are assumed to be negligible). In an ideal system, the measurements made by the thrust stand along the three coordinate axes should be independent. For example, when a test article applies an axial force on the thrust stand, the axial load cells should measure the full magnitude of the force, while the off-axis load cells (lateral and vertical) should read zero. Likewise, if a lateral force is applied, the lateral load cells should measure the entire force, while the axial and vertical load cells should read zero. However, in real-world systems, there may be interactions between the load cells. Through proper design of the thrust stand, these interactions can be minimized, but are hard to eliminate entirely. Therefore, the purpose of the thrust stand calibration is to account for these interactions, so that necessary corrections can be made during testing. These corrections can be expressed in the form of an interaction matrix, and this paper shows the derivation of the equations used to obtain the coefficients in this matrix.Wong, Kin C.Glenn Research CenterAXIAL LOADS; DATA REDUCTION; TEST FACILITIES; THRUST MEASUREMENT; EXHAUST NOZZLES; NOZZLE GEOMETRY; CALIBRATING; PITCHING MOMENTS; YAW; THRUST VECTOR CONTROL; COORDINATES; MATRICES (MATHEMATICS); ROLLING MOMENTS; COEFFICIENTS...