edVirtus Reference

What Are Stock-and-Flow Diagrams?

Stock-and-Flow Diagrams: Representing Accumulation and Rates of Change

A stock-and-flow diagram represents the accumulations that describe a system's state and the rates that increase or decrease them. Stocks may include inventory, population, money, knowledge, capacity, pollutants, or work awaiting completion. Flows describe change per unit time.

A stock changes only through its inflows and outflows. The underlying relationship is integration: the present stock equals its initial value plus the accumulated net flow. This simple rule gives dynamic systems memory because past flows remain embodied in current stock levels.

Standard diagrams show stocks as boxes, flows as pipes with valves, and sources or sinks as clouds outside the model boundary. Auxiliary variables and information links specify how current conditions, goals, parameters, and policies influence flow rates.

Stock-and-flow thinking prevents common errors. A stock is measured at a point in time, while a flow is measured over an interval. A deficit is not the same thing as debt, annual emissions are not the same thing as atmospheric concentration, and hiring is not the same thing as workforce size.

Unlike a causal-loop diagram, a complete stock-and-flow model can be translated into equations and simulated. Units must remain consistent: a flow into a stock of people must have units such as people per month, and multiplying it by a time interval must produce people.

The diagram is therefore both a communication device and a formal model specification. By making accumulation explicit, it reveals inertia, delayed responses, capacity constraints, and the reasons a system may continue moving after the initiating condition has changed.