  We give an explicit estimate of the distance of a closed, connected, oriented
and immersed hypersurface of a space form to a geodesic sphere and show that
the spherical closeness can be controlled by a power of an integral norm of the
traceless second fundamental form, whenever the latter is sufficiently small.
Furthermore we use the inverse mean curvature flow in the hyperbolic space to
deduce the best possible order of decay in the class of $C^{\infty}$-bounded
hypersurfaces of the Euclidean space.
