  The Tucana-Horologium association is one of the closest young stellar groups
to the Sun and despite the close proximity its age is still debated in the
literature. We take advantage of the state-of-the-art astrometry delivered by
the third data release of the Gaia space mission combined with precise radial
velocity measurements obtained from high-resolution spectroscopy to investigate
the dynamical age of the association. We perform an extensive traceback
analysis using a combination of different samples of cluster members, metrics
to evaluate the minimum size of the association in the past and models for the
galactic potential to integrate the stellar orbits back in time. The dynamical
age of $38.5^{+1.6}_{-8.0}$ Myr that we derive in this paper is consistent with
the various age estimates obtained from isochrone fitting in the literature
(30-50 Myr) and reconciles, for the first time, the dynamical age of the
Tucana-Horologium association with the age obtained from lithium depletion
($\sim40$ Myr). Our results are independent from stellar models and represent
one more step towards constructing a self-consistent age scale for the young
stellar groups of the Solar neighbourhood based on the 3D space motion of the
stars.
