Gini Coefficient Calculator

What this calculator does

The Gini coefficient compresses an entire distribution of income into a single number between 0 and 1. It is the figure quoted whenever anyone says one country is more unequal than another, and this calculator produces it from the two areas of the diagram it is defined on:

Gini coefficient = Area A ÷ (Area A + Area B)

Most inequality calculators ask for income data and do the geometry invisibly. This one asks for the areas themselves, which makes it the definitional tool rather than the data one. That is more useful than it first appears, because it means you can measure a Lorenz curve off a printed chart, or off your own plot, and get the coefficient without needing the underlying survey. What it does require is knowing what A and B are.

The two areas, and where they come from

Both come from a Lorenz curve, which is a specific and rather elegant way of drawing a distribution. Line everyone up from poorest to richest. Along the horizontal axis, plot the cumulative share of the population. Up the vertical axis, plot the cumulative share of total income they hold between them. Then trace the curve.

If income were shared perfectly equally, the poorest 20 percent would hold 20 percent of income, the poorest half would hold half, and the curve would be a straight diagonal line at 45 degrees. That line is the line of perfect equality, and no real distribution reaches it. Real curves sag below it, because the poorest 20 percent always hold less than 20 percent of the income. The further the curve sags, the more unequal the society.

That sag creates the two areas the calculator wants.

• Area A is the gap: the region between the diagonal line of perfect equality and the Lorenz curve itself. It is a direct measure of how far the actual distribution departs from an equal one.
• Area B is the region underneath the Lorenz curve, down to the horizontal axis.

Together they fill the whole triangle beneath the equality line. So the coefficient is asking a proportion question: of the total triangle, how much of it is the inequality gap? All of it and the society is maximally unequal. None of it and the society is perfectly equal.

Why you can measure those areas in any units at all

Here is the practical feature of this formula that makes the calculator genuinely usable, and it is worth spelling out because it is not obvious.

Formally, the Lorenz diagram is drawn in a unit square, so the triangle beneath the equality line has an area of exactly 0.5, and A plus B always equals 0.5. That gives the well-known shortcut that the Gini coefficient is simply twice area A. But you do not need to work in those units, because the formula is a ratio and any consistent scaling cancels out.

Measure a printed Lorenz chart with a ruler and find A is 15 square centimetres and B is 35, and the coefficient is 15 divided by 50, which is 0.30. Work in the formal unit square with A at 0.15 and B at 0.35, and it is 0.15 divided by 0.5, which is also 0.30. Use arbitrary grid squares and get 3 and 7, and you still land on 0.30. The units disappear in the division.

So enter the areas in whatever you measured them in, as long as both come from the same diagram measured the same way. That is what allows the coefficient to be extracted from a chart in a report without access to the numbers behind it.

Reading the result

The scale runs from 0 to 1, and both ends are theoretical rather than observed.

Zero means perfect equality: every person has exactly the same income, the Lorenz curve lies on the diagonal, and area A vanishes. One means perfect inequality: a single person holds everything and everyone else has nothing, so the curve hugs the axes and area B vanishes. Neither has ever been observed in a real economy, and both are useful mainly as anchors.

Actual countries occupy a much narrower band, roughly 0.20 to 0.65. The more equal European economies sit near the bottom of that range, many middle-income countries in the middle, and the most unequal economies at the top. The World Bank treats a Gini index above 0.40 as marking high inequality, which is a reasonable rule of thumb for reading an unfamiliar figure.

Two cautions on comparisons. Whether the underlying data measures income or consumption matters, and whether it is before or after taxes and benefits matters even more, since redistribution can move a country's figure substantially. Before setting two countries side by side, check that both numbers were built the same way. And wealth is distributed far more unequally than income everywhere, so a wealth Gini and an income Gini for the same country are not comparable at all.

Two countries, one Gini, different problems

The most important limitation is one the World Bank states plainly: Gini coefficients are not unique. Two entirely different Lorenz curves can produce exactly the same coefficient.

This follows from the geometry. The coefficient measures the size of the gap between the curve and the equality line, not its shape. A curve that sags mostly near the left of the chart describes a society where the poorest are very badly off relative to everyone else. A curve that stays close to the diagonal until the far right and then drops away sharply describes a society where most people are fairly similar but a small group at the top holds a great deal. Those are different problems, calling for different policies, and they can share a coefficient.

One consequence is worth knowing because it recurs in public debate. Because the Lorenz curve compresses the upper tail, the Gini responds sluggishly to changes right at the very top. A large shift of income towards the wealthiest fraction of a percent can barely move the coefficient, so a stable Gini does not prove that concentration at the top has not changed.

Another is that the Gini is a measure of relative distribution, not of absolute living standards. A developing country's coefficient can rise, indicating more inequality, at the same time as the number of people in absolute poverty falls. Both statements can be true together, and reporting only one of them tells half a story. This is also why the Gini pairs naturally with GDP per capita: one describes how much there is, the other how evenly it is spread, and neither substitutes for the other.

Questions people ask

Where do I get areas A and B?

From a Lorenz curve. A is the region between the 45-degree equality line and the curve; B is the region under the curve. You can measure them from a printed chart or compute them from plotted data.

Do the areas need to be in particular units?

No. The formula is a ratio, so any consistent units give the same answer, provided both areas come from the same diagram measured the same way.

What is a typical Gini coefficient?

Real economies mostly fall between about 0.20 and 0.65. The World Bank treats figures above 0.40 as indicating high inequality, though comparisons depend on whether the data covers income or consumption and whether it is before or after redistribution.

What is the main weakness of the Gini?

Different distributions can share the same coefficient, since it measures the size of the inequality gap rather than its shape. It is also relatively insensitive to changes at the very top of the distribution.

References

The Gini index measures the extent to which the distribution of income or consumption within an economy deviates from a perfectly equal distribution, using a Lorenz curve that plots cumulative shares of income received against cumulative shares of recipients ordered from poorest upward. It expresses the area between the Lorenz curve and the line of absolute equality as a proportion of the maximum area beneath that line, so that 0 represents perfect equality and the maximum represents perfect inequality. The World Bank notes that Gini coefficients are not unique, since two different Lorenz curves can produce the same coefficient, that the measure captures relative rather than absolute wealth, and that it is not additive across sub-groups.

1. World Bank, Gini index, World Development Indicators metadata (Poverty and Inequality Platform). https://databank.worldbank.org/metadataglossary/world-development-indicators/series/SI.POV.GINI
2. World Bank, Gini index indicator notes and limitations, Sovereign ESG Data Portal. https://esgdata.worldbank.org/data/indicators?lang=en&ind=SI.POV.GINI