The critical surface for random-cluster model with cluster-weight q ≥ 4 on iso-radial graphs is identified using parafermionic observables. Correlations are also shown to decay exponentially fast in the subcritical regime. While this result is restricted to random-cluster models with q ≥ 4, it extends the recent theorem of [6] to a large class of planar graphs. In particular, the anisotropic random-cluster model on the square lattice is shown to be critical if pvp h (1−pv)(1−p h) = q, where p v and p h denote the horizontal and vertical edge-weights respectively. We also provide consequences for Potts models.