What this calculator does
This tool estimates inflation using the expectations-augmented Phillips Curve, the standard short-run macroeconomic relationship linking inflation to labor-market slack. It is the version popularized by Milton Friedman and Edmund Phelps and taught in most intermediate macroeconomics courses, distinguishing it from the original 1958 Phillips Curve, which plotted wage inflation against unemployment without an expectations term.
The formula
The calculator uses:
π = πᵉ − β(u − uₙ) + v
where π is the predicted inflation rate, πᵉ is the expected inflation rate (often approximated by last period's actual inflation under adaptive expectations), u is the actual unemployment rate, uₙ is the natural rate of unemployment (also called NAIRU, the non-accelerating inflation rate of unemployment), β is a positive sensitivity coefficient describing how strongly inflation responds to the unemployment gap, and v is an optional supply-shock term (for example, an oil price spike) that shifts inflation independently of the labor market.
Reading the unemployment gap
The term (u − uₙ) is the unemployment gap. When actual unemployment sits below the natural rate, the gap is negative, and because it is subtracted after multiplying by β, a negative gap adds to inflation — a tight labor market with plentiful jobs tends to push wages and prices up faster than expected. When actual unemployment sits above the natural rate, the gap is positive and subtracts from inflation, reflecting the disinflationary pressure of labor-market slack. This negative relationship between unemployment and inflation is exactly what gives the Phillips Curve its downward slope in the short run.
Worked example
With expected inflation of 2.5%, actual unemployment of 4.5%, a natural rate of 5.0%, a sensitivity coefficient of 0.5, and no supply shock: the gap is 4.5 − 5.0 = −0.5 percentage points. The cyclical effect is −0.5 × (−0.5) = +0.25 percentage points. Predicted inflation is 2.5 + 0.25 + 0 = 2.75%. The below-natural unemployment rate is contributing a small amount of extra inflation on top of what was already expected.
Limits of the model
The short-run Phillips Curve is a simplified, single-equation description of a much more complex economy. It does not account for shifts in the natural rate itself over time, changes in how expectations are formed, globalization effects on domestic wage-setting, or policy credibility — all of which economists have studied since the 1970s stagflation episodes complicated the simple version. Treat the output as a stylized estimate for teaching, exploration, and back-of-envelope analysis, not as a precise inflation forecast.