ABSTRACT The dispersion measure (DM) of fast radio bursts (FRBs) provides a unique way to probe ionized baryons in the intergalactic medium (IGM). Cosmological models with different parameters lead to different DM–redshift (DM–z) relations. Additionally, the over/underdense regions in the IGM and the circumgalactic medium of intervening galaxies lead to scatter around the mean DM–z relations. We have used the Evolution and Assembly of GaLaxies and their Environments (EAGLE) simulations to measure the mean DM–z relation and the scatter around it using over 1 billion lines of sight at redshifts 0 < z < 3. We investigated two techniques to estimate line-of-sight DM: pixel scrambling and box transformations. We find that using box transformations (a technique from the literature) causes strong correlations due to repeated replication of structure. Comparing a linear and a non-linear model, we find that the non-linear model with a dependence on cosmological parameters provides a better fit to the DM–z relation. The differences between these models are the most significant at low redshifts (z < 0.5). The scatter around the DM–z relation is highly asymmetric, especially at low redshift (z < 0.5), and becomes more Gaussiana as redshift approaches z = 3, the limit of this study. The increase in Gaussianity with redshift is indicative of the large-scale structure that is better sampled with longer lines of sight. The DM–z relation measured in EAGLE is available with an easy-to-use python interface in the open-source FRB redshift estimation package fruitbat.