We present results for $\beta$-decay half-lives based on a new recipe for calculation of phase space factors recently introduced. Our study includes $fp$-shell and heavier nuclei of experimental and astrophysical interests. The investigation of the kinematics of some $\beta$-decay half-lives is presented, and new phase space factor values are compared with those obtained with previous theoretical approximations. Accurate calculation of nuclear matrix elements is a pre-requisite for reliable computation of $\beta$-decay half-lives and is not the subject of this paper. This paper explores if improvements in calculating the $\beta$-decay half-lives can be obtained when using a given set of nuclear matrix elements and employing the new values of the phase space factors. Although the largest uncertainty in half-lives computations come from the nuclear matrix elements, introduction of the new values of the phase space factors may improve the comparison with experiment. The new half-lives are systematically larger than previous calculations and may have interesting consequences for calculation of stellar rates.