Gini Coefficient Calculator

The Gini coefficient calculator converts Lorenz curve areas into an inequality index from 0 to 1. A value near 0 means the measured distribution is close to equal. A value near 1 means the distribution is highly concentrated. Economists, statistical agencies, and development organizations often use Gini measures to summarize income inequality, though the same concept can also be applied to wealth, land ownership, emissions, or any distribution that can be ordered from lowest to highest.

This tool is deliberately an area-based calculator. It does not ask for each household’s income. Instead, it assumes you already have a Lorenz curve, a table that can be integrated, or a chart where the two relevant areas are known. Area A is the gap between the line of perfect equality and the Lorenz curve. Area B is the area under the Lorenz curve. The calculation method divides area A by the sum of area A and area B, then shows both the decimal coefficient and percentage version. If both areas are zero, the inputs are invalid because there is no reference area to compare.

How to use the calculator

Start with a Lorenz curve. The horizontal axis should show cumulative population share, ordered from lowest income or wealth to highest. The vertical axis should show cumulative income or wealth share. The 45-degree equality line represents a world where 20% of the population receives 20% of the income, 50% receives 50%, and so on. Real distributions normally bow below that line because lower-income groups receive less than their population share.

Measure area above Lorenz curve as the space between the equality line and the Lorenz curve. Measure area below Lorenz curve as the space under the Lorenz curve. The units do not matter as long as both areas use the same scale. Square pixels, chart grid units, or numerical integration units all work if they are consistent. The calculator also displays the total reference area, the share represented by area A, and the share represented by area B.

Formula

The area formula used by the calculator is:

$\text{Gini coefficient} = \frac{\text{area A}}{\text{area A} + \text{area B}}$

The displayed percentage is the coefficient multiplied by 100:

$\text{Gini percentage} = \text{Gini coefficient} \times 100$

Because area A and area B are nonnegative and their sum must be positive, the coefficient stays between 0 and 1:

$0 \leq \text{Gini coefficient} \leq 1$

Worked example

Use the default inputs in the form. Area above the Lorenz curve is 1,200, and area below the Lorenz curve is 3,800. The total reference area is 1,200 plus 3,800, or 5,000. The Gini coefficient is 1,200 divided by 5,000, which equals 0.240. The calculator also displays that as 24%. Area A represents 24% of the total area, while the equality-line share represented by area B is 76%.

Interpreting the number requires context. A coefficient of 0.240 is relatively low compared with many national income distributions, but the calculator is not assigning a policy grade. It is simply translating the Lorenz curve geometry into the standard index. If area A were 2,500 and area B were 2,500, the result would be 0.500. If area A were 4,000 and area B were 1,000, the result would be 0.800, which signals a much more concentrated distribution.

Real applications

National statistical offices use Gini estimates to compare income inequality over time, across regions, and before or after taxes and transfers. Development researchers use them alongside poverty rates, median income, education, and labor market data. A city might compare neighborhoods, while a company could use a similar curve to study concentration in customer revenue or sales territories. The same geometry also appears in market analysis: a highly bowed curve signals that a small share of people or firms accounts for a large share of the measured amount.

For household-level work, a Gini coefficient is usually too broad. Use the budget calculator to study spending categories, the salary calculator to translate pay into comparable periods, and the savings goal calculator to model a specific financial target. If you are interested in how concentrated firms are within a market rather than how income is distributed among households, the hhi calculator is the closer sibling because it squares market shares rather than measuring a Lorenz curve area.

Tips and common mistakes

• Do not mix chart scales. If area A is measured in pixels, area B must be measured in pixels from the same chart.
• Do not compare a pre-tax income Gini with a post-tax income Gini unless that difference is the point of the analysis.
• Do not treat income and wealth Gini values as interchangeable. Wealth is often more concentrated than annual income.
• Watch whether the unit is person, household, equivalized household, or region. The same raw data can produce different estimates after adjustment.
• Use the Gini coefficient with other statistics. Two distributions can have the same Gini but differ in poverty, middle-income share, or top-end concentration.

Sources

• World Bank, Inequality Calculator — inequality concepts and country comparisons.
• U.S. Census Bureau, About the Gini Index — definition and interpretation of the Gini index.