We introduce SPAN, a cross-calendar temporal reasoning benchmark, which requires LLMs to perform intra-calendar temporal reasoning and inter-calendar temporal conversion. SPAN features ten cross-calendar temporal reasoning directions, two reasoning types, and two question formats across six calendars. To enable time-variant and contamination-free evaluation, we propose a template-driven protocol for dynamic instance generation that enables assessment on a user-specified Gregorian date. We conduct extensive experiments on both open- and closed-source state-of-the-art (SOTA) LLMs over a range of dates spanning 100 years from 1960 to 2060. Our evaluations show that these LLMs achieve an average accuracy of only 34.5%, with none exceeding 80%, indicating that this task remains challenging. Through in-depth analysis of reasoning types, question formats, and temporal reasoning directions, we identify two key obstacles for LLMs: Future-Date Degradation and Calendar Asymmetry Bias. To strengthen LLMs' cross-calendar temporal reasoning capability, we further develop an LLM-powered Time Agent that leverages tool-augmented code generation. Empirical results show that Time Agent achieves an average accuracy of 95.31%, outperforming several competitive baselines, highlighting the potential of tool-augmented code generation to advance cross-calendar temporal reasoning. We hope this work will inspire further efforts toward more temporally and culturally adaptive LLMs.