We determine the relationship between the turnaround radius, Rt, and mass, Mt, in Λ CDM , and in dark energy scenarios, using an extended spherical collapse model taking into account the effects of shear and vorticity. We find a more general formula than that usually described in literature, showing a dependence of Rt from shear, and vorticity. The Rt− M t relation differs from that obtained not taking into account shear, and rotation, especially at galactic scales, differing ≃ 30 % from the result given in literature. This has effects on the constraint of the w parameter of the equation of state. We compare the Rt− M t relationship obtained for the Λ CDM , and different dark energy models to that obtained in the f(R) modified gravity (MG) scenario. The Rt− M t relationship in Λ CDM , and dark energy scenarios are tantamount to the prediction of the f(R) theories. Then, the Rt− M t relationship is not a good probe to test gravity theories beyond Einstein’s general relativity.