Excess-path-length distribution of shower electrons at radially distant points from the shower axis is derived as the product of 1-dimensional excess-path-length distribution of shower electrons with their lateral distribution integrated and lateral distribution of shower electrons with their excess-path-lengths fixed, the former of which is derived analytically and the latter of which is derived by Monte Carlo analyses. The result will give a method to determine the shower size (the total number of shower electrons) from the arrival-time-distribution of shower electrons at radial distance of $r$ from the shower axis, another than the traditional method from the lateral distribution of those.