The cycling of <sup>14</sup>CH<sub>4</sub> (''radiomethane'') through the atmosphere has been strongly perturbed in the industrial era by the release of <sup>14</sup>C-free methane from geologic reservoirs (''fossil methane'' emissions), and in the nuclear era, especially since ca 1970, by the direct release of nucleogenic radiomethane from nuclear power facilities. Contemporary measurements of atmospheric radiomethane have been used to estimate the proportion of fossil methane in the global methane source (the ''fossil fraction''), but such estimates carry high uncertainty due to the ill-determined nuclear-power source. We exploit an analysis in a companion paper of the global radiomethane budget through the nuclear era, using contemporary measurements of atmospheric radiomethane since 1986 to quantify both the fossil fraction and the strength of the nuclear power source. We deduce that 28.6±1.9% (1 s.d.) of the global methane source has fossil origin, a fraction which may include some <sup>14</sup>C-depleted refractory carbon fraction such as in aged peat deposits. The co-estimated strength of the global nuclear-power source of radiomethane is consistent with values inferred independently from local nuclear facilities.