Phillips curve calculator

See how an unemployment rate lines up with inflation in a simple expectations augmented sketch, or solve the arithmetic the other way. You choose expected inflation, a natural rate, and a positive slope. Every step stays visible. This is classroom arithmetic, not a forecast, and not a claim that a central bank steers from one scatter plot. The arithmetic runs entirely in your browser.

What people are assumed to expect for inflation, in percent. A classroom example is 2, near common Bank of England and Federal Reserve goals. This number is an assumption you type, not a live survey.

A benchmark unemployment rate, sometimes discussed as the rate consistent with stable inflation. Default 4.5 is a classroom example, not an official BLS, ONS, or central bank estimate. Read the natural rate of unemployment.

Positive. How many percentage points inflation falls when unemployment rises 1 point above the natural rate. Default 0.5 is a classroom example. The formula already subtracts this slope times the unemployment gap, so type a positive number.

Direction

From an unemployment rate, implied inflation equals expected inflation minus the slope times the unemployment gap. From an inflation rate, the calculator solves for the unemployment rate that lines up with that inflation.

Example default 5.5, which sits 1 point above the default natural rate of 4.5. Type the rate yourself. This is not a live BLS or ONS print.

Unemployment gap (u minus u*)

Inflation gap versus expectations (π minus πe)

Arithmetic

In words

How to read this. The headline number is classroom arithmetic from numbers you typed. The unemployment gap is the unemployment rate minus the natural rate. Positive means unemployment sits above that benchmark. Negative means it sits below. The inflation gap is inflation minus expected inflation. Positive means inflation sits above expectations. Negative means it sits below. In this sketch the inflation gap equals minus the slope times the unemployment gap. None of these figures is a forecast of the next BLS, ONS, Bank of England, or Federal Reserve release.
Example defaults

Defaults use expected inflation of 2 percent, a natural rate of 4.5 percent, a slope of 0.5, and an unemployment rate of 5.5 percent. The unemployment gap is 1 percentage point. Implied inflation is 1.5 percent, which is 0.5 percentage points below expected inflation. Switch to the inflation direction and enter 2.5. Implied unemployment is 3.5 percent, which is 1 percentage point below the natural rate. Those figures are classroom arithmetic. They are not a claim about current inflation or unemployment.

Educational only

Not a forecast, not policy advice, and not investment advice. The slope and the natural rate are assumptions. The curve shifts when expectations change or when supply shocks hit prices. Modern central banks do not steer from one scatter plot. Nothing here recommends buying, selling, or holding any security, or choosing a tax, spending, or interest rate. The calculator does not fetch live data.

The classroom formula

This page uses an expectations augmented short run sketch taught after the original Phillips diagram:

inflation ≈ expected inflation minus slope × (unemployment rate minus natural rate)
inflation gap ≈ minus slope × unemployment gap

The unemployment gap means the unemployment rate minus the natural rate, in percentage points. The inflation gap means inflation minus expected inflation, also in percentage points. A slope of 0.5 is a familiar classroom starting point. It is not a law. Research slopes differ by country, by inflation measure, and by sample. Say which slope and which natural rate you used.

For the ideas and the loose spots, read the Phillips curve explained. For the benchmark unemployment rate, read the natural rate of unemployment. For a related classroom link from growth to unemployment, read Okun's law and try the Okun's law calculator.

Where to find the inputs

Type your own numbers. This page does not download official series. For a US sketch, look up the unemployment rate at BLS or on FRED (UNRATE) and an inflation measure at BLS (CPI) or BEA (PCE). For a UK sketch, look up Labour Force Survey unemployment and CPI or CPIH at ONS. Expected inflation can be a target, such as 2 percent, or a survey you have already read. The natural rate is an assumption. Broader context sits on the inflation pillar and the unemployment pillar.

UK and US framing

Do not paste a US slope onto UK data and call the result a fact. Labour market institutions, price indexes, and the meaning of slack differ. US discussions often pair unemployment with PCE inflation and the Federal Reserve dual mandate. UK discussions often pair unemployment with CPI and the Bank of England inflation target. A classroom slope is not a policy rule. For a separate benchmark that maps inflation and an output gap into a suggested policy rate, see the Taylor rule calculator.

Sources

All calculators · Okun's law calculator · Taylor rule calculator · Phillips curve explained · Natural rate of unemployment · Output gap · Inflation topic · Unemployment topic · FAQ