Fundamentals

Lorenz Curve: What It Shows and How to Read It

By Daniel Sardá · Published on October 22, 2026

7 min read1,422 words

The Lorenz curve visualizes how income, wealth, or another total is distributed across a population. This guide explains how to read and construct it, and where its limits lie.

How is a total divided among the people who receive or own it? An average alone cannot answer that question. Two populations can have the same average income and yet distribute it in very different ways. The Lorenz curve makes that difference visible.

It is a graphical representation of a distribution. It ranks people or households from the lowest to the highest value and compares two cumulative shares: the share of the population and the share of income, consumption, wealth, or another variable held by that population.

The curve shows how concentrated a total is, but it is important to be precise about what it measures. Income and wealth are not the same; nor are individuals and households. Describing a distribution is also different from explaining its causes or judging it.

Key idea: The Lorenz curve does not show how much a society has in absolute terms. It shows how the total of a particular variable is distributed across the population.

What the chart represents

A Lorenz curve is drawn inside a square whose axes run from 0% to 100%:

• The horizontal axis represents the cumulative share of the population, ranked from lowest to highest by the variable under study.
• The vertical axis represents the cumulative share of that variable.

A point at 40% on the horizontal axis and 20% on the vertical axis therefore means that the bottom 40% of the population by income—if income is the chosen variable—receives 20% of total income.

The word cumulative is crucial. The point does not describe only those exactly at the 40th percentile. It adds together everything received by the bottom 40% of the population.

The curve starts at (0, 0), because 0% of the population accumulates 0% of the total, and ends at (100, 100), because the entire population accounts for the whole measured total.

The line of perfect equality

The chart includes a diagonal known as the line of perfect equality. On this line, each share of the population receives the same share of the total: 20% accumulates 20%, 50% accumulates 50%, and so on.

When nonnegative values are being analyzed, the Lorenz curve lies below that diagonal. The farther it is from the line, the greater the relative concentration of the variable. A curve close to the diagonal describes a more even distribution; a curve that bows sharply toward the lower-right corner indicates that a smaller share of the population holds a larger share of the total.

This reading calls for care when comparing two curves. If one remains below another throughout its range, the first reflects greater concentration. If the curves cross, the chart does not establish an unambiguous ordering: one distribution may be more concentrated in one range and less concentrated in another.

Key idea: The distance from the diagonal helps guide a visual reading, but one point is not enough. The full shape of the curve matters.

How to construct a Lorenz curve

The basic procedure has four steps:

1. Define the variable, unit of analysis, and period—for example, annual household income.
2. Rank the units from the lowest value to the highest.
3. Calculate the cumulative percentage of the population represented by each group.
4. Calculate the cumulative percentage of the variable's total held by those groups.

The resulting pairs are plotted and connected to form the curve. In real-world studies, methodological choices matter: results can vary depending on whether the unit is an individual or household; whether income is gross or disposable; whether the measure is consumption or wealth; and how taxes, transfers, household size, and extreme values are treated.

That is why two curves or two indices are comparable only when they use sufficiently similar concepts and methods. The OECD emphasizes the need to identify the observed variable and unit precisely.

A simple example

Imagine five people with incomes of 10, 10, 20, 20, and 40 units. Total income is 100. Since each person represents 20% of the population, the cumulative shares are as follows:

• The bottom 20% receives 10% of total income.
• The bottom 40% receives 20%.
• The bottom 60% receives 40%.
• The bottom 80% receives 60%.
• The full population receives 100%.

The points on the curve are therefore (0, 0), (20, 10), (40, 20), (60, 40), (80, 60), and (100, 100). Every intermediate point lies below the line of perfect equality, except the starting and ending points.

This example is deliberately small and hypothetical. Its purpose is not to represent a real economy, but to make the logic of ranking and accumulation visible. In a survey with thousands of observations, the principle is the same.

The Lorenz curve and the Gini coefficient are not the same thing

The curve provides a picture of the entire distribution. The Gini coefficient summarizes that picture in a single number: it relates the area between the line of equality and the Lorenz curve to the total area below the diagonal.

It is usually expressed from 0 to 1, though some sources present it on a 0-to-100 scale. A value of 0 corresponds to perfect equality in the variable being measured. Higher values indicate greater relative concentration.

In the example above, joining the points with straight line segments produces a Gini coefficient of 0.28. The number makes comparisons and tracking easier, but it compresses information. Two distributions with differently shaped curves can have the same coefficient: one may show pronounced differences near the bottom, while another concentrates them near the top.

The curve and the index are therefore complementary. The Gini offers a single figure for overall concentration; the curve shows where the differences occur. Percentiles, medians, and group shares can complete the assessment. Both the World Bank and the U.S. Census Bureau present the Gini as a summary measure linked to the curve, not as a substitute for all distributional information.

Key idea: The curve retains the distribution's shape; the Gini summarizes it. The clarity of one number comes at the cost of detail.

What the curve cannot tell you

A Lorenz curve answers a narrow question: how is a total distributed? By itself, it does not answer several other important questions.

It does not measure poverty

Inequality is a relationship among different parts of a distribution. Poverty, by contrast, is usually assessed against a threshold. A society can reduce absolute poverty while its Gini coefficient rises, or have a very even distribution at low material levels. Discussing well-being requires information about absolute levels, not only proportions.

It does not show mobility

The curve is a snapshot of a distribution at a given time. It does not reveal whether the same people remain at the bottom or top over time. Two societies with identical curves could offer very different opportunities for mobility.

It does not identify causes

The chart does not explain which processes produced the distribution. Education, age, innovation, competition, legal privilege, discrimination, family structure, taxes, and transfers can all matter, among many other factors. Determining their relative weight requires additional evidence.

It contains no criterion of justice

The line of perfect equality is a mathematical benchmark, not an automatic definition of fairness. The chart alone does not yield a public policy or a moral judgment. Evaluating a distribution requires considering how it arose, which rights and institutions were involved, what opportunities were available, and what consequences the alternatives would have.

This distinction is especially important from a classical liberal perspective. Statistical equality of outcomes is not the same as equality of rights, distribution, and justice. At the same time, defending general rules, property, contractual freedom, and limits on power does not require ignoring distributional data. Such data can reveal phenomena worth explaining, provided measurement is not mistaken for a verdict.

A descriptive tool, not a complete answer

Reading a Lorenz curve well requires asking three questions: which variable is being distributed, across which units, and over what period? Then one can observe how much each ranked share of the population accumulates and how far the curve lies from the diagonal.

That exercise provides a view that an average cannot. The Gini can condense it, but it cannot replace the curve's shape or settle questions about poverty, mobility, causes, or justice. The curve is useful precisely because of its limits: it clearly describes one dimension of reality and shows what evidence is still needed before that reality can be explained or judged.