Causal Loop Diagram Polarity Analyzer
Analyze causal loop diagrams by entering link polarities (+/-) to determine whether feedback loops are Reinforcing (R) or Balancing (B), and understand system behavior.
Enter each causal link polarity as + (same direction) or - (opposite direction). A loop must have at least 2 links.
Optional: Enter multiple loops, one per line. Overrides single loop input above.
Results will appear here.
Formula
Loop Polarity = Product of all link polarities in the loop
- Each causal link is assigned a polarity: + (positive) if the cause and effect change in the same direction, or − (negative) if they change in opposite directions.
- Loop Polarity = P₁ × P₂ × P₃ × … × Pₙ, where each Pᵢ ∈ {+1, −1}
- If the product = +1 (even number of negative links, including zero): Reinforcing Loop (R)
- If the product = −1 (odd number of negative links): Balancing Loop (B)
Example: Links: +, −, + → Product = (+1)(−1)(+1) = −1 → Balancing Loop
Example: Links: +, −, − → Product = (+1)(−1)(−1) = +1 → Reinforcing Loop
Assumptions & References
- Each link polarity is binary: positive (+) meaning variables change in the same direction (both increase or both decrease), or negative (−) meaning variables change in opposite directions.
- Loop polarity is determined solely by the product of individual link polarities — an even number of negative links yields a Reinforcing loop; an odd number yields a Balancing loop.
- Reinforcing (positive feedback) loops amplify deviations and drive exponential growth or collapse (e.g., compound interest, population growth).
- Balancing (negative feedback) loops counteract deviations and drive goal-seeking or oscillatory behavior (e.g., thermostat, predator-prey dynamics).
- This tool analyzes structural polarity only; it does not account for time delays, nonlinearities, or relative loop strengths.
- A loop must contain at least 2 causal links to be meaningful.
- References: Sterman, J.D. (2000). Business Dynamics: Systems Thinking and Modeling for a Complex World. McGraw-Hill. | Meadows, D.H. (2008). Thinking in Systems. Chelsea Green Publishing.