We use N-body simulations to quantify how the escape velocity in cluster-sized halos maps to the gravitational potential in a ΛCDM universe. Using spherical density-potential pairs and the Poisson equation, we find that the matter density inferred gravitational potential profile predicts the escape velocity profile to within a few percent accuracy for group and cluster-sized halos (10 < < M 1013 200 15 M , with respect to the critical density). The accuracy holds from just outside the core to beyond the virial radius. We show the importance of explicitly incorporating a cosmological constant when inferring the potential from the Poisson equation. We consider three density models and find that the Einasto and Gamma profiles provide a better joint estimate of the density and potential profiles than the Navarro, Frenk, and White profile, which fails to accurately represent the escape velocity. For individual halos, the 1σ scatter between the measured escape velocity and the density-inferred potential profile is small (<5%). Finally, while the sub-halos show 15% biases in their representation of the particle velocity dispersion profile, the sub-halo escape velocity profile matches the dark matter escape velocity profile to high accuracy with no evidence of velocity bias outside 0.4r 200 .