Abstract 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 Third Cambridge Catalogue of Radio Sources (3C) 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 5σ 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.