Planarity of checkerboards is a widely used feature for extrinsic calibration of camera and LiDAR. In this study, we propose two analytically derived covariances of (i) plane parameters and (ii) plane measurement, for precise extrinsic calibration of camera and LiDAR. These covariances allow the graded approach in planar feature correspondences by exploiting the uncertainty of a set of given features in calibration. To construct plane parameter covariance, we employ the error model of 3D corner points and the analytically formulated plane parameter errors. Next, plane measurement covariance is directly derived from planar regions of point clouds using the out-of-plane errors. In simulation validation, our method is compared to an existing uncertainty-excluding method using the different number of target poses and the different levels of noise. In field experiment, we validated the applicability of the proposed analytic plane covariances for precise calibration using the basic planarity-based method and the latest planarity-and-linearity-based method.