Gini Coefficient Calculator

Welcome to the Gini Coefficient Calculator, a comprehensive tool for measuring inequality in any distribution of values. Whether you are analyzing income disparity, wealth concentration, market share distribution, or any other dataset, this calculator provides the Gini coefficient, an interactive Lorenz curve, quintile analysis, and step-by-step calculations to help you fully understand the inequality in your data.

What is the Gini Coefficient?

The Gini coefficient (also called the Gini index or Gini ratio) is a measure of statistical dispersion developed by the Italian statistician Corrado Gini in 1912. It quantifies inequality in a distribution on a scale from 0 (perfect equality — everyone has the same) to 1 (maximum inequality — one entity has everything).

It is the most widely used single number summary of inequality and is a standard tool in economics, sociology, public policy, and data science.

Gini Coefficient Formula

Where A is the area between the line of perfect equality and the Lorenz curve, and B is the area under the Lorenz curve. Since A + B = 0.5 (the area of the triangle above the Lorenz curve):

What is a Lorenz Curve?

The Lorenz curve is a graphical representation of a distribution's inequality. Developed by economist Max O. Lorenz in 1905, it plots:

• X-axis: Cumulative share of the population (from lowest to highest value)
• Y-axis: Cumulative share of the total value held by that population share

The line of perfect equality is a 45-degree diagonal where every population share holds the corresponding value share (e.g., the bottom 50% holds 50% of the total). The further the Lorenz curve bows below this line, the greater the inequality — and the larger the Gini coefficient.

How to Use This Calculator

1. Enter your data: Input numerical values (e.g., incomes, salaries, wealth levels, market shares) in the text area. Values can be separated by commas, spaces, or line breaks.
2. Set decimal precision: Choose the number of decimal places (2–15) for your results.
3. Calculate and analyze: Click "Calculate Gini Coefficient" to see the Gini value, Lorenz curve visualization, quintile breakdown, inequality gauge, and step-by-step calculations.

Understanding Your Results

Gini Coefficient Scale

World Gini Coefficients (Income)

Applications of the Gini Coefficient

Economics & Public Policy

Governments and international organizations (World Bank, OECD, UN) use the Gini coefficient to track income and wealth inequality over time, compare inequality across countries, and evaluate the effectiveness of tax and redistribution policies.

Business & Market Analysis

In business, the Gini coefficient can measure market concentration (how revenue is distributed among companies), customer concentration (dependence on a few large clients), and salary inequality within an organization.

Health & Education

Researchers apply the Gini coefficient to measure disparities in healthcare access, health outcomes, educational attainment, and resource allocation across populations.

Ecology & Biodiversity

Ecologists use Gini-like measures to assess species abundance distributions and resource partitioning in ecosystems.

Calculation Method

This calculator uses the trapezoidal rule on the Lorenz curve to compute the Gini coefficient:

1. Sort all values in ascending order.
2. Compute cumulative shares of both population and value to construct the Lorenz curve.
3. Calculate B (area under the Lorenz curve) using the trapezoidal rule: \(B = \sum_{i=0}^{n-1} \frac{y_i + y_{i+1}}{2} \cdot \Delta x\)
4. Compute the Gini coefficient: \(G = \frac{0.5 - B}{0.5} = 1 - 2B\)

Limitations of the Gini Coefficient

• Same Gini, different shapes: Different Lorenz curves can produce the same Gini value, so it cannot tell you where in the distribution inequality occurs.
• Non-negative values only: The Gini coefficient requires all values to be zero or positive.
• Absolute levels ignored: A wealthy country and a poor country can have the same Gini coefficient — it measures relative, not absolute, distribution.
• Sample size sensitivity: For very small datasets, the Gini coefficient may not be reliable.
• No transfer sensitivity: A transfer from a richer to a poorer person always reduces the Gini, regardless of how close their incomes are.

Frequently Asked Questions

What is the Gini coefficient?

The Gini coefficient is a statistical measure of inequality in a distribution, ranging from 0 (perfect equality, where everyone has the same) to 1 (maximum inequality, where one person has everything). It is commonly used to measure income or wealth inequality within a country or group.

How is the Gini coefficient calculated?

The Gini coefficient is calculated using the Lorenz curve. First, sort values in ascending order and compute cumulative population and value shares. The area between the line of perfect equality (45-degree line) and the Lorenz curve is area A, while the area under the Lorenz curve is area B. The Gini coefficient equals A / (A + B), or equivalently (0.5 - B) / 0.5, where B is computed using the trapezoidal rule.

What is a Lorenz curve?

A Lorenz curve is a graphical representation of inequality. The x-axis shows the cumulative share of the population (from poorest to richest) and the y-axis shows the cumulative share of income or wealth. A perfectly equal distribution would be a straight 45-degree line. The further the Lorenz curve bows below this line, the greater the inequality.

What is a good Gini coefficient value?

A Gini coefficient below 0.3 generally indicates low inequality. Values between 0.3 and 0.4 represent moderate inequality typical of many developed nations. Values above 0.4 indicate high inequality, and above 0.5 represents very high inequality. For reference, Scandinavian countries typically have values around 0.25-0.30, while some developing nations exceed 0.60.

Can the Gini coefficient be used for things other than income?

Yes. While most commonly used for income and wealth inequality, the Gini coefficient can measure inequality in any non-negative distribution — health outcomes, education access, land ownership, market concentration, resource allocation, biodiversity, and even pixel intensity distributions in image analysis.

What are the limitations of the Gini coefficient?

The Gini coefficient has several limitations: it cannot distinguish between different types of inequality (e.g., different Lorenz curves can produce the same Gini value), it requires non-negative values, it does not account for absolute levels (a rich and poor country can have the same Gini), and it is sensitive to sample size for small datasets. It also does not capture where in the distribution inequality occurs.

Additional Resources

• Gini Coefficient - Wikipedia
• Lorenz Curve - Wikipedia