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Carbon capture and storage (CCS) can help nations meet their Paris CO₂ reduction commitments cost-effectively. However, lack of confidence in geologic CO₂ storage security remains a barrier to CCS implementation. Here we present a numerical program that calculates CO₂ storage security and leakage to the atmosphere over 10,000 years. This combines quantitative estimates of geological subsurface CO₂ retention, and of surface CO₂ leakage. We calculate that realistically well-regulated storage in regions with moderate well densities has a 50% probability that leakage remains below 0.0008% per year, with over 98% of the injected CO₂ retained in the subsurface over 10,000 years. An unrealistic scenario, where CO₂ storage is inadequately regulated, estimates that more than 78% will be retained over 10,000 years. Our modelling results suggest that geological storage of CO₂ can be a secure climate …