Aircraft black carbon (BC) emissions contribute to climate forcing, but few estimates of BC emitted by aircraft at cruise exist. For the majority of aircraft engines the only BC-related measurement available is smoke number (SN) - a filter based optical method designed to measure near-ground plume visibility, not mass. While the first order approximation (FOA3) technique has been developed to estimate BC mass emissions normalized by fuel burn [EI(BC)] from SN, it is shown that it underestimates EI(BC) by >90% in 35% of directly measured cases (R2 = -0.10). As there are no plans to measure BC emissions from all existing certified engines - which will be in service for several decades - it is necessary to estimate EI(BC) for existing aircraft on the ground and at cruise. An alternative method, called FOX, that is independent of the SN is developed to estimate BC emissions. Estimates of EI(BC) at ground level are significantly improved (R2 = 0.68), whereas estimates at cruise are within 30% of measurements. Implementing this approach for global civil aviation estimated aircraft BC emissions are revised upward by a factor of ∼3. Direct radiative forcing (RF) due to aviation BC emissions is estimated to be ∼9.5 mW/m2, equivalent to ∼1/3 of the current RF due to aviation CO2 emissions.