  The tidal acceleration experienced by an object at the event horizon of a
black hole decreases as one over the square of the black hole's mass. As such
there is a maximum mass at which a black hole can tidally disrupt an object
outside of its event horizon and potentially produce observable emission. This
maximum mass is known as the ``Hills mass'', and in full general relativity is
a function of both the black hole's spin $a_\bullet$ and the inclination angle
of the incoming object's orbit with respect to the black hole's spin axis
$\psi$. In this paper we demonstrate that the Hills mass can be represented by
a simple analytical function of $a_\bullet$ and $\psi$, the first general
solution of this problem. This general solution is found by utilising the
symmetries of a class of critical Kerr metric orbits known as the innermost
bound spherical orbits. Interestingly, at fixed black hole spin the maximum
Hills mass can lie at incoming orbital inclinations outside of the black hole's
equatorial plane $\psi \neq \pi/2$. When compared to previous results in the
literature this effect can lead to an increase in the maximum Hills mass (at
fixed spin) by as much as a factor of $\sqrt{11/5} \simeq 1.48$ for a maximally
rotating black hole. We then demonstrate how Bayesian inference, coupled with
an estimate of the mass of a black hole in a tidal disruption event, can be
used to place conservative constraints on that black hole's spin. We provide a
publicly available code tidalspin which computes these spin distributions.
