Carbon balances of croplands are often assessed using models that depend critically on accurate estimates of soil carbon inputs such as crop residues, dead roots, and root exudates. Here, we develop a method to estimate soil carbon inputs by combining satellite-based gross primary productivity (GPP) estimates with harvest yields extracted from agricultural statistics. We model the daily GPP as a statistical regression on photosynthetically active radiation and the red edge chlorophyll index measured by the Sentinel-2 satellites and train the model using data from five eddy covariance flux measurement sites. When tested with leave-one-site-out cross validation, the model predicted the yearly GPP with a root mean squared error equal to about 10 % of the mean. We furthermore show that the predicted cumulative GPP explains 60-70 % of the observed variability within a set of 135 aboveground biomass measurements collected on 40 agricultural fields. Finally, we apply the method to three Finnish regions and estimate the soil carbon inputs as the difference between the net primary productivity (NPP), assumed 50 % of the GPP, and the carbon removed in harvest. Compared to the allometric method used in the current national greenhouse gas inventory, our annual carbon inputs are within 5-30 % for wheat but 50-100 % higher for barley, 40-50 % higher for green fallows, and 100-160 % higher for forage grasses. These results highlight a discrepancy between the current national greenhouse gas inventory and carbon budgets derived from flux measurements at eddy covariance sites.