Quantitative knowledge of external climate forcing is required for accurately attributing past climatic changes. Information on volcanic activity over the past millennium has primarily been drawn from high-latitude ice cores. A few large events with distinct signatures in the ice are well known and they are commonly used as marker events to synchronize time scales in individual ice cores. Over the past decade different efforts have been undertaken to systematically identify lesser known eruptions and to develop time series of past volcanic forcing. Here we mathematically quantify the distribution of the magnitude of volcanic events that have a climatic relevance during the past millennium. Volcanic sulfate magnitudes of such events clearly exhibit a heavy tailed extreme value distribution. Indeed, the climatically relevant eruptions are only the extremes of global volcanic activity. This characterization of volcanic amplitude is a fundamental step in detection and attribution studies of past natural forcing and of its effects on climate.