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The cone relation $\cos \theta =1/(n\beta )$ determines speed. Together with a measured kinetic energy $T$, the rest mass is $m=T/[(\gamma -1)c^2]$. The inference requires the radiation to be identified as Cherenkov radiation, and the frequency-dependent phase refractive index must be known.

Interpreting the cone as Cherenkov radiation, its angle gives the speed, not directly the mass:Combining this with the relativistic kinetic energy $T=(\gamma -1)m{c}^2$ gives the Cherenkov mass inferenceThe material must be transparent at the observed frequency, $n$ is its phase refractive index there, and $n\cos \theta >1$. For $T>0$ this requires $0<\theta <\arccos (1/n)$ for a massive particle above threshold. Radiation of an unspecified other origin would not determine the mass from these data alone.