Two new X-ray timing observations of the 44.7 ms pulsar in G12.82-0.02/HESS J1813-178 were obtained with Chandra and XMM-Newton to determine its precise spin-down rate. With a period derivative of dP/dt = 1.265E-13, PSR J1813-1749 is the third most energetic pulsar in the Galaxy, having spin-down luminosity dE/dt = 5.6E37 erg/s. Lack of pulsed detection in a deep radio search from the Green Bank Telescope, and in gamma-rays from Fermi, are reported. We reconsider the distance to PSR J1813-1749/G12.82-0.02 in view of its large X-ray measured column density, N(H) = 10.E22 cm^-2, which exceeds the visual extinction A(V) = 9.1 to a young stellar cluster at d = 4.8 kpc that has been associated with it. Although the distance may well be larger, existing data do not constrain it further. The small radiative output of PSR J1813-1749/G12.82-0.02 in all bands would not exceed its spin-down power at any distance in the Galactic disk.