Working memory (WM) is thought to have a fixed and limited capacity. However, the origins of these capacity limitations are debated, and generally attributed to active, attentional processes. Here, we show that the existence of interference among items in memory mathematically guarantees fixed and limited capacity limits under very general conditions, irrespective of any processing assumptions. Assuming that interference (i) increases with the number of interfering items and (ii) brings memory performance to chance levels for large numbers of interfering items, capacity limits are a simple function of the relative influence of memorization and interference. In contrast, we show that time-based memory limitations do not lead to fixed memory ...