Stock and Flow Equilibrium Calculator
Calculate the equilibrium stock level where inflow equals outflow, time to reach equilibrium, and analyze stock dynamics using system dynamics principles.
units
units/period
fraction/period (0–1)
periods
Formulas
Equilibrium Stock: S* = I / f
Analytical Stock Path: S(t) = S* + (S₀ − S*) · e−f·t
Discrete Recursion: S(t+1) = S(t) · (1 − f) + I
Time Constant (Avg Residence Time): τ = 1 / f
Half-life to Equilibrium: t½ = ln(2) / f ≈ 0.693 / f
Gap Closed after T periods: (S(T) − S₀) / (S* − S₀) × 100%
Assumptions & References
- Inflow (I) is constant and exogenous (does not depend on stock level).
- Outflow is proportional to the current stock: Outflow(t) = f · S(t), where f is the fractional drain rate (0 < f ≤ 1).
- At equilibrium, inflow equals outflow: I = f · S*, giving S* = I / f.
- The system is first-order linear; stock converges exponentially to S* from any initial condition.
- The time constant τ = 1/f is the average time a unit spends in the stock (Little's Law analog).
- Discrete simulation uses Euler integration with period step Δt = 1.
- References: Forrester, J.W. (1961) Industrial Dynamics; Sterman, J.D. (2000) Business Dynamics, MIT Press.