  Large scale neutrino detectors and muon tomography rely on the muon direction
in the detector to infer the muon's or parent neutrino's origin. However, muons
accumulate deflections along their propagation path prior to entering the
detector, which may need to be accounted for as an additional source of
uncertainty. In this paper, the deflection of muons is studied with the
simulation tool PROPOSAL, which accounts for multiple scattering and deflection
on stochastic interactions. Deflections along individual interactions depend on
the muon energy and the interaction type, and can reach up to the order of
degrees -- even at TeV to PeV energies. The accumulated deflection angle can be
parametrized in dependence of the final muon energy, independent of the initial
muon energy. The median accumulated deflection of a propagated muon with a
final energy of 500 GeV is $\theta_{\text{acc}} = 0.10{\deg}$ with a 99 %
central interval of $[0.01{\deg}, 0.39{\deg}]$. This is on the order of
magnitude of the directional resolution of present neutrino detectors.
Furthermore, comparisons with the simulation tools MUSIC and Geant4 as well as
two different muon deflection measurements are performed.
