Object detection on panoramic/spherical images has been developed rapidly in the past few years, where IoU-calculator is a fundamental part of various detector components, i.e. Label Assignment, Loss and NMS. Due to the low efficiency and non-differentiability of spherical Unbiased IoU, spherical approximate IoU methods have been proposed recently. We find that the key of these approximate methods is to map spherical boxes to planar boxes. However, there exists two problems in these methods: (1) they do not eliminate the influence of panoramic image distortion; (2) they break the original pose between bounding boxes. They lead to the low accuracy of these methods. Taking the two problems into account, we propose a new sphere-plane boxes transform, called Sph2Pob. Based on the Sph2Pob, we propose (1) an differentiable IoU, Sph2Pob-IoU, for spherical boxes with low time-cost and high accuracy and (2) an agent Loss, Sph2Pob-Loss, for spherical detection with high flexibility and expansibility. Extensive experiments verify the effectiveness and generality of our approaches, and Sph2Pob-IoU and Sph2Pob-Loss together boost the performance of spherical detectors. The source code is available at https://github.com/AntXinyuan/sph2pob.