Significance: Clean groundwater is essential for water supply in many regions of the world. Fast flow to the groundwater through enlarged cracks and fissures, which is known to transmit short-lived pollutants into the groundwater, is often neglected in large-scale studies. We quantify the rapid transport of pollutants by fast flow into the carbonate rock groundwater storage in Europe, North Africa, and the Middle East. We show that, through rapid transport, up to 50% of infiltrating pollutants may still reach the groundwater table, which is substantially more than estimated when fast transport is neglected. These results imply that the contamination risk of usable groundwater storages is much larger than expected where fast flow to the groundwater occurs.