Lorenz Curve Calculator
The Lorenz Curve Calculator is an interactive online tool that allows economists, researchers, policymakers, students, and analysts to visualize and quantify inequality in the distribution of income, wealth, land, or any resource. Developed by Max O. Lorenz in 1905, the Lorenz curve graphically represents the cumulative share of a resource held by the cumulative share of the population, when ordered from lowest to highest. This calculator generates the curve and computes the associated Gini coefficient using authentic, peer-reviewed methodologies.
Generate Lorenz Curve and Gini Coefficient
Enter a list of non-negative values (e.g., household incomes, farm sizes in hectares, crop yields) separated by commas, spaces, or one per line.
About the Lorenz Curve Calculator
The Lorenz Curve Calculator plots the empirical Lorenz curve by sorting input values ascendingly, computing cumulative population percentages (x-axis) and cumulative resource percentages (y-axis). The line of perfect equality (45-degree line) is overlaid for comparison. The Gini coefficient is calculated using the standard formula: G = (sum of absolute differences between all pairs) / (2 × n² × mean), equivalent to twice the area between the equality line and the Lorenz curve.
This implementation follows the exact definitions used in economics textbooks and peer-reviewed studies, ensuring scientific accuracy.
Importance of the Lorenz Curve
The Lorenz curve is a cornerstone visual tool in economics and social sciences for assessing inequality. It provides an intuitive graphical representation that reveals how far a distribution deviates from perfect equality. Unlike summary statistics alone, the curve shows exactly where inequality occurs—whether concentrated among the poorest, middle, or richest segments.
It forms the basis for the Gini coefficient, used globally by organizations like the World Bank, OECD, and UN to track inequality trends. Visualizing the curve helps communicate complex distribution patterns to policymakers and the public.
When and Why You Should Use This Tool
Use the Lorenz Curve Calculator for:
- Analyzing income or wealth inequality in households or regions
- Evaluating land distribution among farmers (critical in agrarian economies)
- Assessing yield or productivity variation across agricultural units
- Studying resource allocation (e.g., water, credit, subsidies)
- Comparing inequality before/after policy interventions (e.g., land reform)
- Educational purposes in economics, sociology, and development studies
It is essential when visual insight into distribution patterns is needed beyond a single Gini number.
User Guidelines and How to Use the Calculator
- Input raw data values (non-negative numbers).
- Click "Generate Curve & Calculate Gini".
- View the interactive chart: Green line = Lorenz curve; Dashed line = perfect equality.
- Read the Gini coefficient and interpretation below the chart.
- Hover over points for precise cumulative percentages.
Closer alignment of the green curve to the dashed line indicates greater equality.
Example Visualization
Default data: Incomes of 10,000 | 20,000 | 30,000 | 50,000 | 80,000
The curve bows below the equality line, showing the top earners hold a disproportionate share.
Gini ≈ 0.368 (moderate inequality).
Purpose of the Lorenz Curve Calculator
This free tool promotes understanding of inequality dynamics, supporting evidence-based policy in economics, agriculture, and development. In agricultural contexts, Lorenz curves reveal land concentration issues that affect productivity, food security, and rural poverty.
High land inequality (bowed curve) often correlates with inefficient resource use and social unrest.
Learn more on Wikipedia's Lorenz curve page.
Limitations: Assumes ratio-scale data; sensitive to outliers. For grouped data, more advanced interpolation may be needed.
The curve's visual power lies in its simplicity—making abstract inequality tangible.
For agriculture and development resources, visit Agri Care Hub.
Extensions include asymmetry coefficients and comparisons across countries or time periods.
The Lorenz curve remains indispensable for visualizing and quantifying distributional fairness.
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