Abstract The O(M) system is aimed at formalizing reasoning with approximate relations among quantities—relations like “much smaller than” or “slightly larger than.” O(M) is based on seven primitive relations among quantities, and compound relations formed as implicit disjunctions of consecutive primitives. In the interpretation of the relations, strict interpretation allows exact conservative inferences, while heuristic interpretation allows inferences more aggressive and human-like, by permitting some slack at each inference step. Inference strategies within O(M) are based on propagation of order-of-magnitude relations through properties of the relations, solved or unsolved algebraic constraints and rules. Assumption-based truth-maintenance is used, and the physical dimensions of quantities efficiently constrain the inferences. Statement of goals allows more effective employment of the constraints and focuses the system's opportunistic forward reasoning. O(M) relations permit order-of-magnitude analysis in process engineering. The O(M) system is suitable for many process engineering activities, such as preliminary design of process flowsheets, planning of process operations, design of control structures for chemical plants, fault simulation and diagnosis, process trend analysis and analysis of biochemical pathways.