Stock and Flow Equilibrium Calculator
ANA›Life Services Authority›National Calculator Authority›Stock and Flow Equilibrium Calculator
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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.
Initial Stock (S₀)
units
Constant Inflow Rate (I)
units/period
Fractional Outflow Rate (f)
fraction/period (0–1)
Simulation Periods (T)
periods
Calculate
### Results
function stoCalc() { var S0 = parseFloat(document.getElementById('sto-initial-stock').value); var I = parseFloat(document.getElementById('sto-inflow-rate').value); var f = parseFloat(document.getElementById('sto-outflow-fraction').value); var T = parseInt(document.getElementById('sto-time-periods').value); var res = document.getElementById('sto-result'); var tbl = document.getElementById('sto-table');
// --- Validation --- if (isNaN(S0) || S0 1) { alert('Fractional Outflow Rate must be between 0 (exclusive) and 1 (inclusive).'); return; } if (isNaN(T) || T 500) { alert('Simulation Periods must be between 1 and 500.'); return; }
// --- Core Formulas --- // Equilibrium: dS/dt = I - fS = 0 => S = I / f // Analytical solution: S(t) = S + (S0 - S) * e^(-ft) // Time constant (avg residence time): τ = 1 / f // Half-life to equilibrium: t½ = ln(2) / f // Gap closed after T periods: gap% = (1 - e^(-fT)) * 100
var Seq = I / f; var tau = 1 / f; var thalf = Math.log(2) / f;
// Simulate discrete periods: S(t+1) = S(t) + I - fS(t) = S(t)(1-f) + I var stockSeries = [S0]; var inflowSeries = []; var outflowSeries = []; for (var t = 0; t MetricValueNote'; rows.forEach(function(r) { html += '' + r[0] + '' + r[1] + '' + r[2] + ''; }); tbl.innerHTML = html;
res.style.display = 'block';
// --- Draw Chart --- stoDrawChart(stockSeries, Seq, T); }
function stoDrawChart(stockSeries, Seq, T) { var canvas = document.getElementById('sto-chart'); var ctx = canvas.getContext('2d'); var W = canvas.width, H = canvas.height; var padL = 60, padR = 20, padT = 20, padB = 40; var chartW = W - padL - padR; var chartH = H - padT - padB;
ctx.clearRect(0, 0, W, H);
var allVals = stockSeries.concat([Seq]); var minV = Math.min.apply(null, allVals); var maxV = Math.max.apply(null, allVals); var range = maxV - minV || 1; minV -= range * 0.05; maxV += range * 0.05; range = maxV - minV;
function xPx(t) { return padL + (t / T) * chartW; } function yPx(v) { return padT + chartH - ((v - minV) / range) * chartH; }
// Grid & axes ctx.strokeStyle = '#e0e0e0'; ctx.lineWidth = 1; for (var g = 0; g
#### 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
- References: Forrester, J.W. (1961) Industrial Dynamics; Sterman, J.D. (2000) Business Dynamics, MIT Press.
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