Analysis and applications of vision correction via accommodating intraocular lens (AIOL) are presented. By Gaussian optics, analytic formulas for the accommodation rate function (M) for two-optics and three-optics systems are derived and compared with the exact numerical results. In a single-optics AIOL, typical value of M is (0.5–1.5) D/mm, for an IOL power of (10–20) diopter. For a given IOL power, higher M is achieved in positive-IOL than negative-IOL. In the dual-optics AIOL, maximum accommodation is predicted when the front positive-optics moves toward the corneal plan and the back negative-optics moves backward. Our analytic formulas predict that greater accommodative rate may be achieved by using a positive-powered front optics, a general feature when either front or back optics is mobile. The M function is used to find the piggy-back IOL power for customized design based on the individual ocular parameters. Many of the new features demonstrated in this study can be easily realized by our analytic formulas, but not by raytracing method.