What the Gini Coefficient Measures
Italian statistician Corrado Gini published the coefficient in 1912, and it remains the most quoted single-number summary of income spread. The scale runs from 0, where everyone earns an identical amount, toward 1, where a single earner captures everything. Institutions like the World Bank usually report it as an index on a 0-100 scale, so 0.41 and 41 describe the same distribution. The number is unit-free, which is what makes a village, a metro area, and a nation directly comparable.
The coefficient works off the Lorenz curve, a graph that plots the cumulative share of population against the cumulative share of income. If income were spread evenly, the poorest 10% would hold 10% of income and the curve would follow the 45-degree diagonal. Real distributions sag below that line, and the Gini grows as the sag widens. Formally G = A / (A + B), where A is the area between the diagonal and the curve and B is the area under the curve.
A Gini summarizes spread, not level, so pair it with a mean before drawing conclusions. Two regions can share a Gini of 0.40 while one has triple the average income of the other. Analysts usually read it next to the GDP per capita calculator, which covers the level side, because a rising average with a stable Gini and a flat average with a rising Gini tell very different stories.
The Lorenz Curve and the Area Math Behind the Number
This tool traces the Lorenz curve through six points: (0, 0), then the cumulative income share at each fifth of the population, ending at (1, 1). With the default quintiles of 3, 9, 16, 27, and 45, the cumulative shares read 3%, 12%, 28%, 55%, and 100%. The curve connects those points with straight segments, and the calculator sums the five trapezoids underneath: heights of 0.015, 0.075, 0.200, 0.415, and 0.775 with a shared width of 0.2 give a total area of 0.296.
The Gini is then 1 - 2 x 0.296 = 0.408. Doubling the area and subtracting from 1 works because the equality diagonal encloses exactly 0.5 of the unit square, so the gap between 0.5 and the Lorenz area is the A in the classic formula. The same triangle-and-trapezoid geometry appears throughout welfare economics — the consumer surplus calculator measures buyer benefit with the same shaded-area reasoning on a demand curve.
The trapezoid method also shows why small transfers matter. Move two points of income from the richest fifth to the poorest, giving quintiles of 5, 10, 16, 27, and 42, and the Gini falls from 0.408 to 0.364. That is the Dalton transfer principle at work: any pure rich-to-poor transfer must lower the coefficient, which is why the metric responds directly to tax and transfer policy.
Why Quintile Grouping Caps the Maximum at 0.80
Five equal-size groups limit how extreme the Lorenz curve can get. If the richest fifth holds absolutely everything, the curve lies flat at zero until the final point and jumps to 1 at the right edge. The area under it is a single trapezoid of width 0.2 and average height 0.5, equal to 0.1, so G = 1 - 0.2 = 0.8. No quintile input can produce a higher value, which is why this calculator clamps results at 0.800.
Intermediate extremes land proportionally lower. Concentrating all income in the top two fifths, entered as 0, 0, 0, 50, 50, scores 0.600. A distribution where the bottom 40% has nothing and the rest spreads as 20, 30, 50 scores 0.520. With individual-level data the ceiling rises to a true 1.0, which is the value most textbooks quote for the theoretical maximum.
Grouping also understates the number for ordinary distributions, because the real Lorenz curve is convex and the straight trapezoid tops ride above it. Running the same underlying distribution as deciles lifts the measured Gini from 0.408 to 0.478 in our test data. When you compare against a published figure, match the source's bin count first — a gap of several points can come from that difference alone.
Gini Values Around the World and What Moves Them
On the World Bank's index, the most equal countries cluster in the low 30s and below: Norway and Denmark around 28, Sweden around 31, Germany around 32. The United Kingdom sits near 36, the United States near 41, and Mexico around 45. Brazil has run near 52, and South Africa near 63, the highest of any major economy. These figures drift a few hundredths between years and data programs, so treat them as bands rather than precise scores.
Two forces dominate the movements. Growth in average income shifts the whole distribution and is tracked by the GDP calculator and the GDP growth calculator, while changes in who captures that growth move the Gini. Recessions often lift measured inequality as job losses concentrate at the bottom — the output shortfall shows up in the GDP gap calculator months before it lands in the income statistics.
Policy moves the number just as hard as the cycle does. Most European welfare states record market-income Ginis in the low-to-mid 0.40s, similar to the United States, but taxes and transfers pull their disposable-income figures down to roughly 0.27 to 0.31. That compression of 12 to 15 index points is the signature of redistribution, and comparing market versus disposable figures is the standard way to measure it.
The 80/20 Ratio and Palma Ratio as Companion Metrics
The Gini compresses everything into one number, which hides where the inequality lives. The 80/20 ratio — the richest fifth's income divided by the poorest fifth's — exposes the tails directly. The default distribution scores 15.0x, the US-like pattern of 3, 9, 15, 23, 50 scores 16.7x, the Nordic-style 7, 13, 18, 23, 39 scores 5.6x, and the extreme case of 1, 3, 8, 18, 70 reaches 70x.
The Palma ratio divides the top 40%'s income by the bottom 60%'s. It was built on the observation that the middle of the distribution is fairly stable across countries while the tails swing. The default reads 2.57, the Nordic case 1.63, and the extreme case 7.33. When the bottom fifth holds zero income the 80/20 ratio blows up, but the Palma keeps working — in the 0, 0, 20, 30, 50 case it reads a clean 4.00.
Read the three metrics together. A rising Gini with a flat Palma points at dispersion in the middle of the distribution, while a flat Gini with a soaring 80/20 ratio points at tail changes the Gini barely registers. For household budgeting context on the bottom quintile specifically, the buying power calculator shows what a fixed income actually purchases as prices move.
How the Gini Fits With Other Economic Measures
Inequality is one branch of distributional economics, and the same data often feeds several tools. A tax that narrows the income spread usually creates a wedge between what buyers pay and what sellers receive, and the deadweight loss calculator sizes the efficiency cost of that wedge. Policy analysis routinely trades a lower Gini against that lost surplus.
Relative-price changes redistribute too, and not always through income. When two goods' prices move differently, buyers shift between them, and the cross price elasticity calculator quantifies that substitution. A full distributional study checks these channels alongside the Gini rather than stopping at the headline number.
Keep the metrics in their lanes. The Gini measures spread, poverty rates count people under a fixed line, and income-share figures track specific groups. Countries with identical Ginis can have different poverty rates if the shape below the median differs, so a dashboard of two or three indicators beats any single statistic.
Running the Numbers on Real Distributions
The US-like quintile set of 3, 9, 15, 23, 50 returns a Gini of 0.432 with cumulative shares of 3%, 12%, 27%, 50%, and 100% — a curve that sags hard through the lower half. The Nordic-style 7, 13, 18, 23, 39 scores 0.296, and the high-inequality case of 1, 3, 8, 18, 70 scores 0.612. Entering a published quintile table takes under a minute and reproduces the shape behind any country's headline figure.
Policy testing is where the tool earns its keep. Entering the post-transfer quintiles of 5, 10, 16, 27, 42 beside the market distribution of 3, 9, 16, 27, 45 shows the Gini dropping from 0.408 to 0.364 and the 80/20 ratio falling from 15.0x to 8.4x. Run the same comparison on salary bands inside a company and you get an internal-inequality snapshot for compensation reviews.
When comparing distributions across years, remember that the Gini is scale-invariant: proportional growth for every quintile leaves it untouched, so pure inflation never changes the score. What does change it is uneven nominal growth across the distribution. To track what those nominal incomes actually buy, pair this tool with the inflation calculator and the CPI inflation calculator.
Limitations, Definitions, and Why Sources Disagree
Published Ginis for the same country often disagree by several points, and definitions explain most of the gap. The US Census Bureau's household money income series runs near 0.48 to 0.49, while the World Bank's comparable figure sits near 0.41. Household versus person as the unit, market versus disposable income, and equivalence adjustments for household size all move the number materially. Always compare figures built on the same definitions.
The coefficient has known blind spots. It is most sensitive near the middle of the distribution and least sensitive at the tails, two distributions with the same Gini can cross on the Lorenz curve, and surveys underreport top incomes — tax-record studies in the Piketty-Saez tradition find more concentration at the top than household surveys show. That is why the Palma and 80/20 outputs sit next to the headline number.
Use the metric for what it does well: a fast, unit-free comparison of spread across places and times on consistent data. Quote the source, the income definition, and the reference year with every figure. When a headline claims inequality rose, check whether the change survives rounding — a move from 0.408 to 0.410 sits within the noise of most survey revisions.