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Finance Calc Kit
Inflation

Phillips Curve Calculator

Calculate inflation rate or unemployment rate using the expectations-augmented Phillips Curve economic model.

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Calculated inflation rate

1.75%

Model breakdown

Expected inflation
2.00%
Unemployment gap
+0.50%
Cyclical effect
-0.25%
Supply shock
0.00%

How we calculated this

Open to see each step from your inputs to the result.

  1. Compute the unemployment gap

    u−un=5.00%−4.50%u - u_n = 5.00\% - 4.50\%

    The unemployment gap equals +0.50 percentage points.

  2. Apply the cyclical inflation effect

    −α(u−un)=−0.50×(0.50)-\alpha(u - u_n) = -0.50 \times (0.50)

    The cyclical term equals -0.25 percentage points.

  3. Combine expected inflation and supply shock

    π=πe−α(u−un)+v\pi = \pi_e - \alpha(u - u_n) + v

    2.00 + (-0.25) + (0.00) = 1.75%

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What is the Phillips curve?

The Phillips curve describes an inverse relationship between unemployment and inflation in the short run. When unemployment falls below its natural rate, wage and price pressures often rise. When unemployment rises above the natural rate, inflation tends to soften. Modern macro models extend the original curve with expected inflation and supply shocks.

This calculator uses the expectations-augmented Phillips curve, the standard framework central banks use when linking labor market slack to inflation forecasts. To estimate the natural unemployment benchmark, use the natural rate of unemployment calculator. Compute the actual unemployment rate from workforce counts with the unemployment rate calculator. To relate unemployment to GDP slack, try the Okun law calculator. To see how inflation erodes cash purchasing power over time, use the inflation calculator.

Expectations-augmented Phillips curve formula

π=πe−α(u−un)+v\pi = \pi_e - \alpha (u - u_n) + v

Where π\pi is the inflation rate, πe\pi_e is expected inflation, uu is the actual unemployment rate, unu_n is the natural rate of unemployment (NAIRU), α\alpha is the sensitivity coefficient, and vv is a supply shock such as an energy price spike.

Worked example

Suppose expected inflation is 2.0%, the natural unemployment rate is 4.5%, actual unemployment is 5.0%, alpha equals 0.5, and the supply shock is 0%. The unemployment gap is 0.5 percentage points. Cyclical inflation equals -0.5 × 0.5, or -0.25%. Final inflation equals 2.0% - 0.25% + 0%, or 1.75%.

How to interpret the result

  • When actual unemployment exceeds the natural rate, the cyclical term is negative and pulls inflation below expected inflation.
  • When unemployment falls below the natural rate, the cyclical term turns positive and adds inflationary pressure.
  • A positive supply shock raises inflation regardless of labor market conditions.

Frequently asked questions

What is the natural rate of unemployment?
The natural rate, also called NAIRU, is the unemployment level expected when the economy is at full employment without accelerating inflation. It excludes cyclical unemployment tied to recessions. Estimates vary by country and time period.
What value should I use for alpha?
Alpha reflects how strongly unemployment gaps translate into inflation. Empirical estimates differ by country and model. Values between 0.3 and 0.7 are common in academic and policy discussions. Adjust alpha to match your dataset or scenario.
Does the Phillips curve always hold?
No. The relationship can break down during supply shocks, when inflation expectations become unanchored, or over long horizons when expectations adjust fully. The curve is a useful short-run forecasting tool, not a permanent law.
What is a supply shock in this model?
A supply shock is any event that shifts inflation independently of unemployment, such as an oil embargo, crop failure, or tariff-driven import price spike. Enter it as a percentage point adjustment to inflation.
Are the results stored on a server?
No. All math runs in your browser. Nothing is sent to the server.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.