  Kinetic jet power estimates based exclusively on observed monochromatic radio
luminosities are highly uncertain due to confounding variables and a lack of
knowledge about some aspects of the physics of active galactic nuclei (AGNs).
We propose a new methodology to calculate the jet powers of the largest, most
powerful radio sources based on combinations of their size, lobe luminosity and
shape of their radio spectrum; this approach avoids the uncertainties
encountered by previous relationships. The outputs of our model are calibrated
using hydrodynamical simulations and tested against independent X-ray
inverse-Compton measurements. The jet powers and lobe magnetic field strengths
of radio sources are found to be recovered using solely the lobe luminosity and
spectral curvature, enabling the intrinsic properties of unresolved
high-redshift sources to be inferred. By contrast, the radio source ages cannot
be estimated without knowledge of the lobe volumes. The monochromatic lobe
luminosity alone is incapable of accurately estimating the jet power or source
age without knowledge of the lobe magnetic field strength and size
respectively. We find that, on average, the lobes of the 3C radio sources have
magnetic field strengths approximately a factor three lower than the
equipartition value, inconsistent with equal energy in the particles and the
fields at the 5$\sigma$ level. The particle content of 3C radio lobes is
discussed in the context of complementary observations; we do not find evidence
favouring an energetically-dominant proton population.
