Internal variability comprises all processes that occur within the climate system without any natural or anthropogenic forcing. Climate driving variables like the surface solar radiation (SSR) are shown to exhibit unforced trends (i.e. trends due to internal variability) of magnitudes comparable to the magnitude of the forced signal even on decadal timescales. We use annual mean data from 50 models participating in the pre-industrial control experiment (piControl) of the Coupled Model Intercomparison Project – Phase 6 (CMIP6) to give quantitative grid-box specific estimates of the magnitudes of unforced trends. To characterise a trend distribution, symmetrical around 0, we use the 75th percentile of all possible values, which corresponds to a positive trend with 25% chance of occurrence. For 30-year periods and depending on geographical location, this trend has a magnitude between 0.15 and 2.1Wm^-2/decade for all-sky and between 0.04 and 0.38Wm^-2/decade for clear-sky SSR. The corresponding area-weighted medians are 0.69Wm^-2/decade for all-sky trends and 0.17Wm^-2/decade for clear-sky trends. The influence of internal variability is on average 6 times smaller in clear-sky, compared to all-sky SSR. The relative uncertainties of these estimates, derived from the CMIP6 inter-model spread, are ±32% for all-sky and ±43% for clear-sky SSR trends. Reasons for differences between models like horizontal resolution, aerosol handling and the representation of atmospheric and oceanic phenomena are investigated. The results can be used in the analysis of observational time series by attributing a probability for a trend to comprise a component due to internal variability, given its magnitude, length and location.