Free Gini Coefficient Calculator

Introduction to the Gini Coefficient Calculator

This income inequality calculator -- also known as a Gini index calculator, wealth distribution calculator, or Lorenz curve calculator -- offers a straightforward method to measure how evenly income or wealth is distributed among the citizens of a country or region. By leveraging the Lorenz curve as its conceptual foundation, the tool calculates the Gini index quickly and accurately.

What Is the Gini Index?

The Gini coefficient (often called the Gini index) is a statistical metric that quantifies inequality. Its value always falls between 0 and 1:

• 0 stands for perfect equality: every person receives exactly the same income.
• 1 represents perfect inequality: one individual holds all the income while everyone else earns nothing.

In practice, most nations lie somewhere between these extremes. A value closer to 0 indicates a more equal distribution, whereas a number nearer to 1 signals high inequality.

Historical Context

Italian statistician Corrado Gini introduced this index in 1912. Since its inception, the measure has been adopted by major international bodies such as the World Bank and the United Nations to compare income disparities across countries. Many national governments also monitor their own Gini coefficients over time to assess the impact of economic and social policies.

The Lorenz Curve Connection

The Lorenz curve is a graphical representation that forms the basis of the Gini coefficient. It is constructed by:

1. Ranking the population from the poorest to the richest.
2. Plotting the cumulative percentage of the population on the horizontal axis.
3. Plotting the cumulative percentage of total income on the vertical axis.

If income were distributed perfectly equally, the Lorenz curve would coincide with the 45‑degree diagonal line (the line of equality). In reality, the curve bends away from this line; the greater the deviation, the higher the inequality.

Formula and Calculation Steps

The Gini coefficient is derived from two areas defined by the Lorenz curve:

• Area $A$: the region between the Lorenz curve and the line of equality.
• Area $B$: the region under the Lorenz curve.

The coefficient is the ratio of area $A$ to the total area under the line of equality ($A + B$):

$$G = \frac{A}{A + B}$$

Because area $B$ is always positive and area $A$ is non‑negative, the coefficient always stays within the [0, 1] interval.

Worked Example

Suppose for a particular country the relevant areas have been determined:

• Area $A = 1,200$ units²
• Area $B = 3,800$ units²

Substituting into the formula gives:

$$G = \frac{1,200}{1,200 + 3,800} = \frac{1,200}{5,000} = 0.24$$

A Gini coefficient of 0.24 suggests a moderate level of inequality -- relatively far from both perfect equality and complete concentration.

Why Use This Tool?

Manually integrating the Lorenz curve or processing discrete income shares to obtain the Gini index is time‑consuming. This Gini index calculator automates the entire calculation, letting you focus on interpreting the results. Whether you are a student, researcher, or policy analyst, you can quickly generate a Gini coefficient for any region and incorporate it into your inequality analysis. Because it simultaneously handles Lorenz curve data and the Gini formula, the tool is equally useful as a Lorenz curve calculator and a wealth distribution calculator.