Stock and Flow Diagrams

Core Idea

Stock-and-flow diagrams (SFDs) are the formal modelling notation of system dynamics — a visual language that converts qualitative intuitions about feedback into quantifiable, simulatable models, by distinguishing what accumulates from what changes it.

Stock-and-flow diagrams extend Causal-Loop-Diagrams by forcing modellers to distinguish what accumulates from what changes it. Developed by Jay Forrester at MIT during the late 1950s.

Notation Elements

SFDs use a standardised set of symbols:

• Stocks (rectangles / “bathtubs”): Accumulations — inventory, population, debt, trust — the “state” of the system. See System-Stock.
• Flows (double-line arrows with a valve): Rates of change that fill or drain stocks. See System-Flow. Flows can change instantaneously; stocks cannot.
• Clouds: Sources or sinks outside the model boundary, acknowledging every model has limits.
• Auxiliary variables (circles): Intermediate calculations that determine flow rates.
• Connectors (thin arrows): Information links showing which variables influence which.

SFDs vs. Causal Loop Diagrams

Causal-Loop-Diagrams are fast and communication-friendly but have three limitations SFDs address:

• No stock-flow distinction: CLDs conflate accumulations with rates, producing misleading diagrams
• No simulation: CLDs cannot be run on a computer; SFDs map directly to differential equations
• No model boundary: Clouds in SFDs force explicit acknowledgement of scope

Use CLDs: Early hypothesis generation and stakeholder communication. Use SFDs: When precision matters, when System-Delays and accumulations drive behaviour, when you need to test policies quantitatively.

Origins and Tools

Forrester’s Industrial Dynamics (1961) introduced SFDs to model industrial supply chains — the same dynamics later popularised as The-Beer-Game.

Modern software tools: Vensim (most widely used in academic and policy research), STELLA/iThink (popular in education), AnyLogic (multiple modelling paradigms).

Related Concepts

• System-Stock
• System-Flow
• Causal-Loop-Diagrams
• Balancing-Feedback-Loops
• Reinforcing-Feedback-Loops
• System-Delays
• Thinking in Systems - Meadows - 2008

Sources

• Meadows, Donella H. (2008). Thinking in Systems: A Primer. Chelsea Green Publishing. ISBN: 978-1-60358-055-7.

  • Chapters 1–2 introduce SFD notation and contrast it with verbal descriptions

• Forrester, Jay W. (1961). Industrial Dynamics. MIT Press. ISBN: 978-0-915299-88-7.

  • Original source for SFD notation; introduces stocks, flows, and auxiliary variables

• Sterman, John D. (2000). Business Dynamics: Systems Thinking and Modeling for a Complex World. Irwin/McGraw-Hill. ISBN: 978-0-07-231135-8.

  • Chapters 6–7: comprehensive academic treatment of SFD notation and simulation methodology

• Richardson, George P. and Alexander L. Pugh III (1981). Introduction to System Dynamics Modelling with Dynamo. MIT Press. ISBN: 978-0-262-18091-2.

  • Early academic textbook establishing SFD as a modelling discipline

• Kirkwood, Craig W. (1998). “System Dynamics Methods: A Quick Introduction.” Arizona State University working paper.

  • Available: https://nutritionmodels.com/papers/Kirkwood1998.pdf

Note

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