Persistent contrails and contrail cirrus are estimated to have a larger impact on climate than all CO2 emissions from global aviation since the introduction of jet engines. However, the measure for this impact, the effective radiative forcing (ERF) or radiative forcing (RF), suffers from uncertainties that are much larger than those for CO2. Despite ongoing research, the so called level of scientific understanding has not improved since the 1999 IPCC Special Report on Aviation and the Global Atmosphere. In this paper, the role of weather variability as a major component of the uncertainty range of contrail cirrus RF is examined. Using 10 years of MOZAIC flights and ERA-5 reanalysis data, we show that natural weather variability causes large variations in the instantaneous radiative forcing (iRF) of persistent contrails, which is a major source for uncertainty. Most contrails (about 80%) have a small positive iRF of up to 20 W m−2. IRF exceeds 20 W m−2 in about 10% of all cases but these have a disproportionally large climate impact, the remaining 10% have a negative iRF. The distribution of iRF values is heavily skewed towards large positive values that show an exponential decay. Monte Carlo experiments reveal the difficulty of determining a precise long-term mean from measurement or campaign data alone. Depending on the chosen sample size, calculated means scatter considerably, which is caused exclusively by weather variability. Considering that many additional natural sources of variation have been deliberately neglected in the present examination, the results suggest that there is a fundamental limit to the precision with which the RF and ERF of contrail cirrus can be determined. In our opinion, this does not imply a low level of scientific understanding; rather the scientific understanding of contrails and contrail cirrus has grown considerably over recent decades. Only the determination of global and annual mean RF and ERF values is still difficult and will probably be so for the coming decades, if not forever. The little precise knowledge of the RF and ERF values is, therefore, no argument to postpone actions to mitigate contrail’s warming impact.