The automotive industry is seeking new concepts for a continuously variable transmission (CVT) in the driveline. One possible solution for a CVT design is half toroidal traction drive, providing a high torque capacity with quick ratio change. An analytical study on the contact points of the half toroidal CVT has been detailed. The shapes of the contact areas among the input disk, power roller and output disk are considered ellipses. Mathematical equations for estimating the torque capacity, power loss due to spin action, and contact efficiency of the elliptical contacts of the half toroidal CVT are formulated and expressed in the form of integrals which can be readily evaluated by numerical scheme. The contact efficiency calculations of the half toroidal CVT have been developed for the proper spin point locations under the effect of system parameters. Numerical results are presented in graphical forms for considered parameters, which can help the designer to select the proper system parameters to minimi The automotive industry is seeking new concepts for a continuously variable transmission (CVT) in the driveline. One possible solution for a CVT design is half toroidal traction drive, providing a high torque capacity with quick ratio change. An analytical study on the contact points of the shapes of the contact areas among the input disk, power roller and output disk are considered ellipses. Mathematical equations for estimating the torque capacity, power loss due to spin action, and contact efficiency of the elliptical contacts of the half toroidal CVT are formulated and expressed in the form of integrals which can be sought evaluated by numerical schemes. The contact efficiency calculations of the half toroidal CVT have been developed for the proper spin point locations under the effect of system parameters. are presented in graphical forms for considered parameters, which can help the designer to select the proper system pa rameters to minimi