Phillips Curve Calculator

This calculator models inflation and unemployment tradeoffs using three versions of the Phillips curve. The traditional option converts a wage-growth shortfall into an implied unemployment gap. The new classical option estimates inflation from expected inflation, the unemployment gap, a response coefficient, and a supply shock. The New Keynesian option estimates current inflation from expected future inflation and the output gap. Each version is intentionally distinct, so choose the one that matches your inputs instead of mixing terms across models.

The Phillips curve is different from the Okun’s Law calculator, which translates unemployment gaps into output gaps. It is also different from the Taylor Rule calculator, which uses inflation and output gaps to estimate a policy rate. For labor-market inputs, compare it with the natural rate of unemployment calculator and labor force participation rate calculator. For price-level context, the inflation calculator is a separate historical conversion tool.

The economic relationship

The Phillips curve began as an observed relationship between unemployment and wage inflation. In the short run, when labor markets are tight, firms may need to raise wages to attract workers. Higher labor costs and strong demand can feed into price inflation. When unemployment is high, wage growth and price pressure can cool because workers have less bargaining power and firms face weaker demand.

Modern versions add expectations and shocks. If households and firms expect 2.5 percent inflation, actual inflation can begin near that value before labor-market slack changes it. A supply shock, such as a jump in energy costs, can raise inflation even if unemployment is not especially low. New Keynesian versions focus on price setting: firms that cannot adjust prices continuously respond to expected future inflation and to demand pressure captured by the output gap.

Formulas used by the calculator

The new classical version is the default. It uses expected inflation, actual unemployment, the natural unemployment rate, a nonnegative response coefficient, and a supply shock:

$\pi = \pi_e - b \times (U - U_n) + v$

Here, pi is the inflation estimate, pi e is expected inflation, b is the response coefficient, U is unemployment, U n is the natural unemployment rate, and v is the supply shock. The unemployment gap is actual unemployment minus the natural rate.

The New Keynesian version uses:

$\pi_t = \beta \times E_t(\pi_{t+1}) + \kappa \times \tilde{y}_t$

The traditional wage-growth version rearranges a simple wage relationship into an implied unemployment gap:

$\text{implied unemployment gap} = \frac{\text{trend wage growth} - \text{money wage growth}}{\text{wage sensitivity}}$

All inflation, wage-growth, unemployment, and output-gap entries are entered as percentage values. A supply shock of 0.4 means a 0.4 percentage-point shock.

Examples: modeling Phillips curve scenarios

For the default new classical case, use expected inflation of 2.5 percent, unemployment of 4.0 percent, a natural unemployment rate of 5.0 percent, a response coefficient of 0.6, and a supply shock of 0. The unemployment gap is 4.0

• 5.0, or -1.0 percentage point. The inflation estimate is:

$\pi = 2.5\% - 0.6 \times (-1.0) + 0 = 3.1\%$

The calculator reports 3.10 percent and notes that unemployment is 1.00 percentage point below the natural rate, changing inflation by +0.60 percentage points before shocks. If the same economy had a +0.4 percentage-point supply shock, the result would be 3.50 percent.

For the New Keynesian option, use beta of 0.99, expected future inflation of 2.3 percent, kappa of 0.25, and an output gap of 1.2 percent:

$\pi_t = 0.99 \times 2.3\% + 0.25 \times 1.2\% = 2.577\%$

Rounded by the form, that is 2.58 percent. The expected-future-inflation contribution is 2.277 percent and the output-gap contribution is 0.30 percentage points. For the traditional option, wage growth of 3.0 percent, trend wage growth of 4.0 percent, and sensitivity of 0.5 gives:

$\text{implied unemployment gap} = \frac{4.0 - 3.0}{0.5} = 2.0\text{ percentage points}$

How economists use the Phillips curve

Economists use Phillips curve models to organize debates about inflation pressure. A central bank may ask whether inflation is high because unemployment is below its sustainable level, because expectations have moved up, or because a supply shock has temporarily lifted costs. A forecaster may compare the model’s inflation estimate with actual inflation to see whether the economy looks overheated, underheated, or hit by unusual shocks.

The curve is also a teaching tool because it separates the short run from the long run. In the short run, lower unemployment can be associated with higher inflation. In the long run, if expectations adjust, the economy may return toward its natural unemployment rate without a permanent tradeoff. That is why this calculator includes expectations explicitly rather than presenting a fixed menu of unemployment and inflation pairs.

Limitations and interpretation

The Phillips curve can be flat, unstable, or shifted by events outside the labor market. Energy prices, import prices, exchange rates, taxes, markups, supply chains, productivity, and central-bank credibility all affect inflation. A low unemployment rate does not guarantee accelerating inflation, and a high unemployment rate does not guarantee immediate disinflation. The result depends heavily on the slope, expected inflation, and natural-rate assumptions you enter.

Use the calculator as a scenario model. It is strongest when you want to see the direction and size of a specified relationship. It is weakest when treated as a standalone forecast. For serious analysis, compare the output with realized inflation, wage measures, participation, productivity, and policy settings.

Sources

• OpenStax, The Phillips Curve — overview of the unemployment-inflation relationship.
• FRED, Unemployment Rate — U.S. unemployment data for unemployment-gap scenarios.
• FRED, Noncyclical Rate of Unemployment — natural-rate estimate used in Phillips curve examples.
• Federal Reserve, Monetary Policy — policy context for inflation, employment, and expectations.

Formula references

• Claim: expectations-augmented branch only: inflation=expectedInflation−slope×(unemployment−naturalUnemployment)+supplyShock. Source: Olivier Blanchard, Macroeconomics, 8th edition (Pearson, 2021), Chapter 8, “The Phillips Curve, the Natural Rate of Unemployment, and Inflation,” equation 8.6 and the following discussion of the supply-shock term. Locator: publisher edition record. Jurisdiction: jurisdiction-neutral macroeconomic model. Accessed 2026-07-10.
• Claim: New Keynesian branch only: inflation=beta×expectedFutureInflation+kappa×outputGap, without an added cost-push shock. Source: Jordi Galí, Monetary Policy, Inflation, and the Business Cycle, 2nd edition (Princeton University Press, 2015), Chapter 3, equation 3.28, page 50, with the disturbance term fixed to zero for this calculator branch. Locator: publisher edition record. Jurisdiction: jurisdiction-neutral New Keynesian model. Accessed 2026-07-10.