- The Lorenz curve plots the cumulative share of income against the cumulative share of people, ranked from poorest to richest. The further it bows below the 45-degree line, the more unequal the society.
- The Gini coefficient is the area between the line of equality and the Lorenz curve (A) divided by the whole area under the line of equality (A + B): \( G = \frac{A}{A+B} \).
- With quintile data you calculate it with the trapezium formula \( G = 1 – \sum (X_k – X_{k-1})(Y_k + Y_{k-1}) \).
- Gini runs from 0 (perfect equality) to 1 (one person has everything). The World Bank reports it as an index from 0 to 100: South Africa scores 54.1 and the Slovak Republic 23.8.
- Exam point: one number cannot show where inequality sits. Two very different Lorenz curves can share the same Gini.
What are the Lorenz curve and the Gini coefficient?
Average income tells you how rich a country is, but not how that income is shared. To compare countries you also need a measure of distribution. The Lorenz curve and the Gini coefficient are the two standard tools.
The American economist Max Lorenz proposed the curve in 1905 as a way to show how concentrated wealth was[3]. In 1912 the Italian statistician Corrado Gini set out the measure of variability that became the Gini coefficient[4]. Today the World Bank defines its Gini index as the area between the Lorenz curve and the line of equality, expressed as a percentage of the maximum area under that line[1].
You will see the measure written in two ways. Textbooks usually use a coefficient between 0 and 1, such as 0.38. The World Bank and many news reports use an index between 0 and 100, such as 38. They are the same thing, just multiplied by 100.
How to build a Lorenz curve from quintile shares
Statistical offices run household surveys. They rank households by income, split them into equal groups, and report each group’s share of total income. Five groups of 20% are called quintiles. Ten groups of 10% are called deciles.
To draw the curve you need cumulative shares, not individual shares. Follow these steps.
- List the population groups from poorest to richest.
- Work out the cumulative population share, \( X_k \): 0.2, 0.4, 0.6, 0.8, 1.0 for quintiles.
- Add up the income shares as you go to get the cumulative income share, \( Y_k \).
- Plot each pair \( (X_k, Y_k) \) and join the points, starting at the origin \( (0,0) \) and ending at \( (1,1) \).
The Gini coefficient formula
The whole triangle under the line of equality has area \( \tfrac{1}{2} \) when both axes run from 0 to 1. So \( A + B = 0.5 \), and the definition becomes:
In practice you rarely know A directly. You calculate B, the area under the Lorenz curve, and use \( G = 1 – 2B \).
With grouped data the Lorenz curve is a set of straight lines between plotted points. The area under each segment is a trapezium (a strip with two parallel vertical sides). The area of one strip is its width times the average of its two heights:
Add the strips to get B, then double it and take it from 1. The halves and the doubling cancel, which gives the formula you will use in exams:
Here \( X_k \) is the cumulative population share up to group \( k \), \( Y_k \) is the cumulative income share up to group \( k \), and \( X_0 = Y_0 = 0 \). This is often called the Brown formula. With quintiles, every \( X_k – X_{k-1} \) equals 0.2, so the formula simplifies to:
Worked example: calculating the Gini coefficient from quintiles
Suppose a country’s household survey gives these income shares by quintile: poorest 20% receive 5%, second 20% receive 10%, middle 20% receive 15%, fourth 20% receive 25%, richest 20% receive 45%. Calculate the Gini coefficient.
| Quintile | Income share | \( X_k \) | \( Y_k \) | \( Y_k + Y_{k-1} \) |
|---|---|---|---|---|
| Start | – | 0 | 0 | – |
| Poorest 20% | 5% | 0.2 | 0.05 | 0.05 |
| Second 20% | 10% | 0.4 | 0.15 | 0.20 |
| Middle 20% | 15% | 0.6 | 0.30 | 0.45 |
| Fourth 20% | 25% | 0.8 | 0.55 | 0.85 |
| Richest 20% | 45% | 1.0 | 1.00 | 1.55 |
The Gini coefficient is 0.38, or 38 on the World Bank’s 0–100 scale. The richest fifth earns nine times as much as the poorest fifth (45% against 5%). That is moderate to high inequality, similar to the level the World Bank reports for China (36.0) and a little below the United States (41.8).
Grouped data has one built-in weakness. Joining the points with straight lines assumes everyone within a quintile has the same income. In reality there is inequality inside each group too. So a Gini calculated from five quintiles is always a little lower than the true figure. More groups give a more accurate answer. Using the World Bank’s own decile shares for South Africa in 2022, the quintile method gives about 0.50, the decile method about 0.53, while the official figure from the full survey is 0.54[2].
How to interpret the Gini coefficient (0 to 1)
There is no official cut-off between “low” and “high” inequality, but these rough bands help when you read country data.
| Gini (0–1) | Rough reading | What the Lorenz curve looks like |
|---|---|---|
| 0 | Perfect equality | Lies exactly on the diagonal |
| Below 0.30 | Low inequality | Close to the diagonal |
| 0.30 to 0.40 | Moderate | Clear but gentle sag |
| 0.40 to 0.50 | High | Deep sag, steep at the top end |
| Above 0.50 | Very high | Hugs the bottom axis, then climbs sharply |
| 1 | Perfect inequality | Runs along the bottom and up the right edge |
Three points matter when you interpret a Gini figure.
It is relative, not absolute. If every income doubles, the Lorenz curve does not move, so the Gini is unchanged even though the poor are better off.
It is most sensitive to the middle. Any transfer from richer to poorer lowers the Gini, but transfers around the crowded middle of the distribution move it most.
The same Gini can hide different stories. Lorenz curves can cross: a very poor bottom 20% in one country and a super-rich top 1% in another could both give 0.40.
Income Gini versus wealth Gini
A Gini can be calculated for anything that is shared out: income, consumption, wealth, even land. Income and wealth are the two you will meet most.
Wealth is far more unequal than income. Wealth builds up over a lifetime, earns its own returns and can be inherited, while many households have almost none. Some households even have negative net worth because their debts exceed their assets. A study of 28 OECD countries found that the wealthiest 10% of households held, on average, 52% of total household wealth, while the bottom 60% owned little over 12%. Wealth concentration was about twice the level of income inequality[7].
There is a third measure you must watch for in World Bank data: consumption. In many lower- and middle-income countries, household surveys measure what families spend rather than what they earn, because spending is easier to record when many people are self-employed or farm. Consumption is smoother than income, since people save in good years and borrow or run down savings in bad ones. So a consumption Gini tends to be lower than an income Gini for the same country. The World Bank notes that its Gini index measures income “or, in some cases, consumption expenditure”[1].
Real-world data: Gini index by country
The table below uses the latest World Bank Gini index (indicator SI.POV.GINI) for each country, retrieved in October 2026[1], together with the survey details and decile shares from the World Bank’s Poverty and Inequality Platform[2].
| Country | Gini index (0–100) | Year | Measures | Share of richest 10% |
|---|---|---|---|---|
| South Africa | 54.1 | 2022 | Consumption | 42.1% |
| Brazil | 50.3 | 2024 | Income | 39.3% |
| United States | 41.8 | 2024 | Income | 30.7% |
| China | 36.0 | 2022 | Consumption | 28.4% |
| Pakistan | 33.5 | 2024 | Consumption | 27.7% |
| United Kingdom | 32.4 | 2021 | Income | 25.0% |
| Sweden | 29.3 | 2023 | Income | 22.3% |
| Slovak Republic | 23.8 | 2023 | Income | 18.8% |
| India | 23.0 | 2023 | Consumption | 20.5% |
| Saudi Arabia | No estimate | – | – | – |
Sources: World Bank WDI, SI.POV.GINI[1]; survey type and top-decile shares from the Poverty and Inequality Platform[2]. Year is the World Bank reporting year; some surveys span two calendar years (for example, India’s Household Consumption Expenditure Survey and Pakistan’s HIES).
Several lessons jump out.
- Southern Africa and Latin America are the most unequal regions in this list. In South Africa the richest tenth accounts for 42.1% of consumption, while the poorest tenth gets 1.4%[2]. South Africa’s index has fallen from 59.6 in 2014 to 54.1 in 2022 on comparable consumption surveys, but it remains the highest here[2].
- Rich countries differ a lot. The United States (41.8) is far more unequal than Sweden (29.3) or the Slovak Republic (23.8), even though all three are high-income economies. Being rich does not fix the distribution.
- India and Pakistan look low partly because they measure consumption. India’s index of 23.0 sits next to the Slovak Republic’s, but one is a spending measure and the other an income measure.
- Saudi Arabia has no World Bank Gini estimate in either the World Development Indicators or the Poverty and Inequality Platform[1]. Missing data is itself a limitation worth mentioning: the Gini can only be calculated where a suitable household survey is available to the World Bank.
The chart plots real Lorenz curves for the most unequal and one of the least unequal countries in the table, built from the World Bank’s decile shares.
Read the chart at the halfway point. In the Slovak Republic the poorer half of the population receives 33.5% of income. In South Africa the poorer half receives only 15.3% of consumption. South Africa’s curve then rockets upwards in the last decile, which is the visual signature of a very high Gini.
Limitations of the Gini coefficient
The Gini is popular because it is one easy-to-compare number. That simplicity is also the source of most criticisms.
- It does not show where inequality is. As explained above, crossing Lorenz curves can produce the same Gini. Measures such as the Palma ratio (the income share of the top 10% divided by that of the bottom 40%) or the top 1% share focus on the tails, which is often what policy debates are about.
- It depends on survey quality. Household surveys tend to miss the very rich, who are hard to reach and may under-report income. This usually pushes measured Gini down.
- Income versus consumption. As the table shows, countries use different welfare measures, which limits cross-country comparison.
- Before or after taxes and benefits. A “market income” Gini (before taxes and transfers) and a “disposable income” Gini (after) can be very different. Always check which one you are reading.
- It says nothing about living standards. A poor and a rich country can share the same Gini, and free public services such as health care and schooling are ignored.
- Data gaps. Surveys are not annual in many countries, and some countries, such as Saudi Arabia, have no World Bank estimate at all.
The Kuznets curve and policy: can governments change the Gini?
The Kuznets curve
In 1955 Simon Kuznets suggested that inequality first rises and then falls as an economy develops[5]. The idea is that early industrialisation moves workers from low-income farming into higher-paid urban jobs, widening the gap. Later, as most workers have moved, education spreads and political pressure for redistribution grows, inequality narrows. With GDP per head on the horizontal axis and the Gini on the vertical axis, this gives an inverted U: the Kuznets curve.
Kuznets himself stressed that his evidence was thin and his argument largely speculative[5]. Later work has challenged the pattern. Thomas Piketty, using long-run tax data, argues that the fall in inequality in rich countries during the mid-twentieth century was driven largely by wars, depression and policy, and that inequality rose again in many rich countries from around 1980[8]. For exam purposes, treat the Kuznets curve as a hypothesis to evaluate, not a law.
Taxes and transfers
Governments change the final distribution of income mainly through progressive taxes (where higher earners pay a larger share of their income in tax) and transfers (cash benefits such as pensions, unemployment benefits and child allowances). These shift the Lorenz curve for disposable income closer to the line of equality than the curve for market income.
OECD research found that taxes and transfers reduce market-income inequality by slightly more than 25% on average across OECD countries, ranging from about 40% in Ireland to about 5% in Chile[6]. The same research notes that Japan and Norway start with similar market-income Gini levels of about 38, but end up at roughly 32 and 27 respectively after taxes and transfers[6]. Policy, not just the market, shapes the final Gini.
Redistribution has trade-offs to weigh in an essay. High marginal tax rates may weaken incentives to work and invest, means-tested benefits can create poverty traps, and capital may move abroad. On the other side, very high inequality may itself harm growth through weaker human capital and lower social mobility. Other tools act before tax: education, health spending and minimum wages. The right balance is partly a value judgement.
Practice questions
EasyQ1. On a Lorenz curve, the point (40, 12) is plotted. Explain what this point means. Show worked answer
The poorest 40% of the population receive 12% of total income. Under perfect equality they would receive 40%, so this point lies well below the line of equality, showing inequality.
EasyQ2. The area between the line of equality and a Lorenz curve is 0.2. Both axes run from 0 to 1. Calculate the Gini coefficient. Show worked answer
The total area under the line of equality is 0.5, so \( G = \frac{A}{A+B} = \frac{0.2}{0.5} = 0.4 \). Equivalently \( B = 0.3 \) and \( G = 1 – 2(0.3) = 0.4 \).
MediumQ3. Using World Bank decile data for Sweden in 2023, the quintile income shares are 7.9%, 13.8%, 17.8%, 23.3% and 37.2%. Calculate the Gini coefficient using the trapezium formula. Show worked answer
Cumulative shares: \( Y = 0.079,\ 0.217,\ 0.395,\ 0.628,\ 1.000 \).
Pair sums: \( 0.079,\ 0.296,\ 0.612,\ 1.023,\ 1.628 \). Total \( = 3.638 \).
\( G = 1 – 0.2 \times 3.638 = 1 – 0.7276 = 0.272 \) (to 3 d.p.).
The official World Bank figure is 29.3, a little higher, because grouping into quintiles ignores inequality within each group.
MediumQ4. Country X and Country Y both have a Gini coefficient of 0.35, but their Lorenz curves cross. Explain how this is possible and why it matters for policy. Show worked answer
The Gini only measures the total area between the curve and the line of equality. Country X could have a very poor bottom 20% but a fairly equal middle and top, while Country Y has a better-off bottom but a very rich top 10%. The areas can be equal even though the shapes differ, which is why the curves cross.
For policy, the problems differ: Country X may need targeted support for the poorest, Country Y higher top tax rates or wealth taxes. The single figure hides this.
ExamQ5. Using World Bank data, South Africa’s quintile consumption shares in 2022 were 3.7%, 6.9%, 10.8%, 19.1% and 59.5%. (a) Calculate the Gini coefficient from these figures. (b) Evaluate the usefulness of the Gini coefficient for comparing inequality between South Africa and the United States. [12 marks] Show worked answer
(a) [4 marks] Cumulative shares: \( 0.037,\ 0.106,\ 0.214,\ 0.405,\ 1.000 \) (1). Pair sums: \( 0.037 + 0.143 + 0.320 + 0.619 + 1.405 = 2.524 \) (1). \( 0.2 \times 2.524 = 0.5048 \) (1). \( G = 1 – 0.5048 \approx 0.495 \) (1).
(b) [8 marks] Mark scheme points:
- Usefulness (up to 3): a single, widely published number on a common 0–1 scale; allows quick ranking (South Africa 54.1 against the United States 41.8 suggests South Africa is far more unequal); can track change over time, such as South Africa’s fall from 59.6 in 2014.
- Limitations (up to 4): South Africa’s figure is based on consumption, the United States figure on income, so they are not directly comparable, and consumption Gini figures tend to be lower; the Gini does not show where the inequality lies (the top 10% share of 42.1% against 30.7% is more revealing); surveys miss the very rich; it ignores absolute living standards and free public services; grouped data, as in part (a), understate the true Gini (0.495 against the official 0.541).
- Judgement (1–2): for example, “The Gini is a useful first indicator, and the gap between the two countries is large enough that the ranking is probably robust, but a sound comparison should use the same welfare measure and look at the full Lorenz curves or top and bottom shares.”
Top-band answers use the data, make the income/consumption point explicitly, and reach a supported conclusion.
Frequently asked questions
What is a good Gini coefficient?
There is no single “good” value. Most high-income European countries have income Gini indices between about 24 and 33, which is generally seen as low to moderate. Values above 40 are usually considered high, and above 50 very high. Whether a level is acceptable is a normative judgement about fairness.
How do you calculate the Gini coefficient in Excel?
Put the cumulative population shares in column A and the cumulative income shares in column B, starting with a row of zeros. In column C, for each row after the first, enter =(A3-A2)*(B3+B2) and fill down. The Gini is =1-SUM(C3:C7) for five quintiles. This is exactly the trapezium formula.
What is the difference between the Lorenz curve and the Gini coefficient?
The Lorenz curve is a graph that shows the whole distribution of income. The Gini coefficient is a single number calculated from that graph: the area between the curve and the line of equality, as a share of the total area under the line. The curve gives detail; the Gini gives a quick summary.
Can the Gini coefficient be greater than 1?
Not for income or consumption, which cannot be negative. For wealth it can, in rare cases, slightly exceed 1, because some households have negative net worth, which pushes the Lorenz curve below the horizontal axis.
References
- World Bank (2026). “Gini index (SI.POV.GINI)”. World Development Indicators, data retrieved 14 October 2026. https://api.worldbank.org/v2/country/ZAF;BRA;USA;CHN;IND;GBR;PAK;SAU;SWE;SVK/indicator/SI.POV.GINI?format=json&date=2000:2025 (indicator page: https://data.worldbank.org/indicator/SI.POV.GINI)
- World Bank (2026). “Poverty and Inequality Platform: survey estimates (welfare type, Gini, decile shares)”. World Bank, data retrieved 14 October 2026. https://pip.worldbank.org
- Lorenz, M. O. (1905). “Methods of Measuring the Concentration of Wealth”. Publications of the American Statistical Association, 9(70), 209–219. https://doi.org/10.2307/2276207
- Ceriani, L. and Verme, P. (2012). “The origins of the Gini index: extracts from Variabilità e Mutabilità (1912) by Corrado Gini”. Journal of Economic Inequality, 10(3), 421–443. https://ideas.repec.org/a/kap/jecinq/v10y2012i3p421-443.html
- Kuznets, S. (1955). “Economic Growth and Income Inequality”. American Economic Review, 45(1), 1–28. https://www.jstor.org/stable/1811581
- Hermansen, M. and Causa, O. (2018). “Income redistribution through taxes and transfers across OECD countries”. VoxEU, CEPR. https://cepr.org/voxeu/columns/income-redistribution-through-taxes-and-transfers-across-oecd-countries
- Balestra, C. and Tonkin, R. (2018). “Inequalities in household wealth across OECD countries: Evidence from the OECD Wealth Distribution Database”. OECD Statistics Working Papers, 2018/01. OECD Publishing. https://www.oecd.org/en/publications/inequalities-in-household-wealth-across-oecd-countries_7e1bf673-en.html
- Piketty, T. (2014). “Capital in the Twenty-First Century”. Harvard University Press. https://www.hup.harvard.edu/books/9780674430006
