This paper is the fourth in a series of four papers aiming to describe the (almost integral) Chow ring of M I 3 \overline{\mathcal{M}}_{3}, the moduli stack of stable curves of genus 3. In this paper, we finally compute the Chow ring of M I 3 \overline{\mathcal{M}}_{3} with Z [ 1 / 6 ] \mathbb{Z}[1/6] -coefficients.