Gini Coefficient Income Inequality Calculator

Understanding Inequality: The Need for a Metric

Economic inequality is a defining feature of modern societies, but how do you measure it? Saying "the rich are getting richer" is intuitive but imprecise. Economists need quantitative tools to compare inequality across countries, track changes over time, and assess policy impacts. The Gini coefficient, named after Italian statistician Corrado Gini, is the most widely used single metric for measuring inequality. It ranges from 0 (perfect equality: everyone has the same income) to 1 or 100 (perfect inequality: one person has all income, everyone else has none). A Gini of 0.30 suggests relatively equal distribution; 0.60 suggests high inequality. By calculating this metric from actual income distributions, you can benchmark your data against historical patterns or other populations.

The Gini Coefficient Formula

The Gini coefficient is mathematically defined as $G=\frac{2\Sigma i·y_i}{n(n+1)·\text{μ}}-\frac{n}{+}$, where $yi$ are sorted incomes (smallest to largest), $n$ is the number of individuals, and $\text{μ}$ is the mean income. Equivalently, using the Lorenz curve (which plots cumulative share of income against cumulative share of population), the Gini coefficient equals twice the area between the line of equality and the Lorenz curve. Intuitively: if you plot all incomes on a graph, the Lorenz curve shows how much of total income is earned by the poorest 10%, poorest 20%, etc. A straight diagonal line means perfect equality; a curve that hugs the x-axis then shoots up means inequality.

The Lorenz Curve and Graphical Intuition

Imagine a population sorted by income. The Lorenz curve plots cumulative population percentage (x-axis) against cumulative income percentage (y-axis). If the bottom 50% of earners control 30% of total income, the curve passes through (0.5, 0.3). A perfectly equal society has a 45-degree diagonal line. A highly unequal society has a curve that stays near zero until the end (the wealthy control most income), then shoots up. The Gini coefficient captures this deviation from the diagonal as a single number. More formally, $G=2·\text{Area between curves}$. This calculator computes the Gini from income data without requiring you to manually construct the Lorenz curve.

Worked Example

Consider six households with annual incomes: $50,000, $60,000, $75,000, $120,000, $250,000, $1,500,000. Total income is $2,055,000; mean is $342,500. Sorted from smallest to largest, they already are in order. The cumulative income shares and population shares are:



Population %: 16.7%, 33.3%, 50.0%, 66.7%, 83.3%, 100.0%

Cumulative Income %: 2.4%, 5.3%, 8.9%, 13.7%, 25.8%, 100.0%



Using the formula, we calculate the Gini coefficient: $G\approx 0.634$. This is quite high, reflecting significant inequality (the millionaire dominates income). By contrast, if all six earned $342,500, Gini would be 0. If the distribution were $300k, $320k, $340k, $360k, $380k, $400k, Gini would be much lower (around 0.05), showing relative equality.

Interpreting the Gini Coefficient

A Gini of 0.0–0.25 indicates low inequality (relatively equal income distribution). Examples include Nordic countries, historically Japan, and some post-communist eastern European nations. A Gini of 0.25–0.40 is moderate: most Western European nations and some developed Asian economies fall here. A Gini of 0.40–0.60 is high inequality: the United States, China, and many Latin American nations. A Gini above 0.60 indicates extreme inequality, typically found in very poor or post-conflict nations. It's important to note that Gini measures income inequality, not wealth inequality, which is often much higher. Also, context matters: a Gini of 0.50 in a wealthy country (where even the "poor" are well-off) differs in impact from a Gini of 0.50 in a poor country (where inequality directly translates to poverty).

Why Inequality Matters: Policy and Social Implications

High inequality has been linked to reduced economic mobility, lower health outcomes, reduced social trust, and higher crime rates. Low inequality societies often have stronger social safety nets, universal healthcare, and progressive taxation. However, causation is complex: does low inequality cause stability, or does stability allow low inequality? High inequality can incentivize innovation and hard work (positive view) or perpetuate class barriers and reduce opportunity (negative view). Economists debate optimal levels of inequality; most agree that extreme inequality (whether 0 or 1) is undesirable. This calculator helps you quantify inequality in your data, enabling evidence-based policy discussion.

Limitations of the Gini Coefficient

While powerful, the Gini has weaknesses. Two very different distributions can have the same Gini coefficient. For example, one where incomes are somewhat evenly spread and another where some earn zero and others earn in clusters might both yield Gini = 0.40. The Gini is also sensitive to extreme values: a single billionaire in a population drastically changes the metric. Additionally, Gini measures income (flow), not wealth (stock). A retiree with no income but significant savings has zero income (appears poor in Gini calculations) but is wealthy. Finally, Gini doesn't account for purchasing power or cost of living, making cross-country comparisons tricky (a US income of $50,000 is vastly more valuable than a sub-Saharan income of $50,000).

Alternatives and Complementary Metrics

Other inequality metrics include the Palma ratio (ratio of income share of top 10% to bottom 40%), the Theil index (which decomposes inequality by groups), and the Atkinson index (which weights welfare losses from inequality). The 20/20 ratio (income of richest 20% divided by poorest 20%) is intuitive but ignores the middle. Some researchers prefer looking at percentile distributions: how much do the top 1% earn versus the top 10%? The Gini is popular because it's simple, comparable across countries and time, and statistically robust, but combining it with other metrics gives a fuller picture.

Time Series and Policy Analysis

Track a population's Gini over time to assess policy impacts. If Gini rises after a major tax cut, it may indicate wealth concentration. If it falls after raising minimum wages, it may indicate equalization. Comparing Gini before and after major policy changes (healthcare expansion, education reform, tax reform) helps evaluate whether policy achieved intended equity effects. Note that Gini changes can reflect either income redistribution (policy working) or changes in baseline incomes (economic growth or contraction).

Calculating from Household or Individual Data

This calculator works with any sorted income list: household incomes, individual wages, regional GDPs, or even class/cohort data. The critical step is ensuring you're comparing like with like. Comparing pre-tax incomes to post-tax incomes yields different Gini values. Comparing incomes of full-time workers to all adults (including unemployed) also differs. Be consistent in data source and definition when making comparisons.

Assumptions and Limitations

The calculator assumes all inputs are valid, non-negative numbers representing income. Zero or negative incomes (e.g., individuals in debt) are handled but may skew results. The calculator doesn't weight by household size; if you have family sizes that vary, you might want to scale incomes accordingly (or calculate separately by household vs. individual). Large datasets (thousands of income points) compute correctly but may take a moment. The Gini coefficient is mathematically precise; the calculator's limitation is ensuring your input data is representative and correctly defined. Finally, this calculator computes the Gini for a discrete population; for continuous income distributions (theoretical models), the calculation is similar but uses integration instead of summation.

Practical Use Case: Comparing Regions or Companies

HR departments use Gini to assess pay equity within organizations. If Gini for salaries is above 0.40, it may indicate wide pay disparities that could affect morale or attract regulatory scrutiny. A company with Gini 0.25 has more equitable pay, though this might reflect less differentiation between entry-level and executive roles. Nonprofit organizations often publish Gini coefficients or similar equity metrics to demonstrate fair compensation practices. Cities or regions can use Gini to track inequality trends and guide social policy.

Conclusion

The Gini Coefficient Income Inequality Calculator transforms income data into a meaningful measure of distribution equality. By calculating this metric, you gain insight into how evenly wealth is spread across a population—crucial information for economists, policymakers, and researchers. Whether you're analyzing company salaries, regional incomes, or historical trends, the Gini coefficient provides a rigorous, internationally recognized framework for quantifying inequality and guiding evidence-based discussion of equity and opportunity.