Causal reasoning and compositional reasoning are two core aspirations in AI. Measuring the extent of these behaviors requires principled evaluation methods. We explore a unified perspective that considers both behaviors simultaneously, termed compositional causal reasoning (CCR): the ability to infer how causal measures compose and, equivalently, how causal quantities propagate through graphs. We instantiate a framework for the systematic evaluation of CCR for the average treatment effect and the probability of necessity and sufficiency. As proof of concept, we demonstrate CCR evaluation for language models in the LLama, Phi, and GPT families. On a math word problem, our framework revealed a range of taxonomically distinct error patterns. CCR errors increased with the complexity of causal paths for all models except o1.