  The active galaxy NGC 4151 has a crucial role as one of only two active
galactic nuclei for which black hole mass measurements based on emission line
reverberation mapping can be calibrated against other dynamical methods.
Unfortunately, effective calibration requires an accurate distance to NGC 4151,
which is currently not available. Recently reported distances range from 4 to
29 megaparsecs (Mpc). Strong peculiar motions make a redshift-based distance
very uncertain, and the geometry of the galaxy and its nucleus prohibit
accurate measurements using other techniques. Here we report a dust-parallax
distance to NGC 4151 of $D_A = 19.0^{+2.4}_{-2.6}$ Mpc. The measurement is
based on an adaptation of a geometric method proposed previously using the
emission line regions of active galaxies. Since this region is too small for
current imaging capabilities, we use instead the ratio of the
physical-to-angular sizes of the more extended hot dust emission as determined
from time-delays and infrared interferometry. This new distance leads to an
approximately 1.4-fold increase in the dynamical black hole mass, implying a
corresponding correction to emission line reverberation masses of black holes
if they are calibrated against the two objects with additional dynamical
masses.
