Lorenz Curve Plotter

Visualize inequality in income, wealth, or any numeric distribution

Gini Coefficient: 0.00
Options
Lorenz Curve
Cumulative Distribution Data
Population % Value % Cumulative Value Individual Value
How to Use
Enter Data

Input comma-separated values (e.g., incomes, assets) in the left panel

Adjust Settings

Toggle options like Gini coefficient display and area shading

Interact

Hover over the chart to see exact values at any point

Export

Download the chart as PNG/SVG or export data as CSV

About Lorenz Curves

The Lorenz Curve shows the cumulative distribution of a variable (like income or wealth) compared to perfect equality. The further it bows below the diagonal line, the greater the inequality. For a deeper understanding, you might also explore how the Gini coefficient is calculated separately or examine other measures of distribution.

Gini Coefficient measures inequality on a 0 to 1 scale (0 = perfect equality, 1 = maximum inequality).

Learning Center: Lorenz Curve & Inequality Measurement

What This Calculator Teaches

This tool helps you understand how economists measure inequality using visual and numerical methods. You'll learn:

  • How to convert raw data into cumulative percentages
  • Why we sort data from smallest to largest
  • How to interpret the "bowing" of the Lorenz curve
  • The relationship between visual curve shape and Gini coefficient
  • Practical applications in economics, sociology, and business

Concept in Simple Terms

Imagine lining up 100 people from poorest to richest. The Lorenz curve answers: "What percentage of total income do the poorest X% of people have?"

Perfect equality: Poorest 20% have 20% of income, poorest 50% have 50% of income.

Real world: Poorest 20% might only have 5% of income, showing inequality.

Meaning of Each Input Field

Comma-separated values: Enter individual incomes, wealth amounts, or any numeric variable you want to analyze. Example: monthly salaries of employees.
Show Gini Coefficient: Toggles the numerical inequality score (0-1). Higher = more unequal.
Shade inequality area: Visualizes the gap between perfect equality (diagonal) and actual distribution.

Step-by-Step Calculation Breakdown

Step 1: Your data is sorted from smallest to largest value
Step 2: Total sum of all values is calculated
Step 3: For each person/unit, we calculate:
  • What percentage of people they represent (X-axis)
  • What percentage of total value they own (Y-axis)
Step 4: Points are connected to form the Lorenz curve
Step 5: Gini = (Area between diagonal and curve) ÷ (Total area under diagonal). You can also explore this using our dedicated Gini tool for more precise calculations.

How to Interpret Results

  • Gini below 0.3: Relatively equal distribution
  • Gini 0.3-0.4: Moderate inequality. Compare with the Gini index ranges for context.
  • Gini 0.4-0.5: High inequality
  • Gini above 0.5: Very high inequality
  • Curve close to diagonal: More equal society
  • Curve bows downward: Concentration of wealth/income

Why This Formula Matters

The Lorenz curve and Gini coefficient are used worldwide to:

  • Compare inequality between countries
  • Track inequality changes over time
  • Evaluate policy effectiveness (taxation, welfare)
  • Analyze market concentration in business
  • Measure diversity in environmental studies. You might also find the Shannon diversity index useful for ecological applications.
Exam Tip: Always sort data first! Forgetting to sort is the #1 mistake in Lorenz curve problems. Remember: poorest to richest.

Practice Tips

  1. Start with extreme cases: all equal values vs. one person has everything
  2. Try doubling one value and observe Gini change
  3. Compare different datasets using the same scale
  4. Practice calculating cumulative percentages manually
  5. Sketch expected curve shape before plotting. For additional practice, try our interactive Ginexamples.

Visual Understanding Tips

  • The diagonal line represents "perfect equality" - always at 45°
  • The further the curve sags below the diagonal, the greater the inequality
  • If the curve follows the bottom axis then jumps up, wealth is concentrated at the top
  • The shaded area visually represents the Gini index value
  • Curve will always start at (0,0) and end at (100,100)

Formula Overview (Plain Language)

Lorenz Curve Points: For each person, plot (percentage of population, percentage of total value they own)

Gini Coefficient: (Area between equality line and Lorenz curve) ÷ (Area under equality line). For more on related distribution measures, explore other inequality metrics.

Equality line: Straight line where Y = X always

Learning Shortcuts

  • Gini ≈ 0? Nearly perfect equality
  • Gini ≈ 1? One person has almost everything
  • Curve is straight line? Perfect equality
  • Most of curve near bottom-left corner? High inequality
  • Check symmetry: If you flip data, Gini stays same

Graph Explanation Help

X-Axis (Horizontal): Cumulative percentage of population, sorted from smallest to largest value holders.
Y-Axis (Vertical): Cumulative percentage of total value/wealth/income.
Green dashed line: Line of perfect equality (everyone has equal share).
Purple curved line: Actual Lorenz curve showing real distribution.
Purple shaded area: Visual representation of inequality gap.

Beginner FAQ

Q: Why do we sort data from smallest to largest?

A: To line people up from poorest to richest, which is essential for understanding cumulative distribution.

Q: Can Gini coefficient be negative?

A: No, Gini always ranges from 0 (perfect equality) to 1 (maximum inequality). You can verify this with our Gini calculator.

Q: What's a "good" Gini value?

A: Context matters! Economic equality (lower Gini) vs. incentive for innovation (some inequality). Most developed countries range 0.25-0.45.

Q: Can I use this for non-income data?

A: Yes! Lorenz curves analyze any distribution: company market shares, land ownership, website traffic, ecological diversity.

Q: Why does curve always start at (0,0) and end at (100,100)?

A: 0% of people have 0% of wealth, and 100% of people have 100% of wealth (by definition).

Q: How accurate is this calculator for exams?

A: Mathematically correct for educational purposes. For research, use specialized statistical software with more decimal precision.

Accuracy Disclaimer

This calculator provides educational accuracy suitable for classroom learning and concept understanding. For official research or policy analysis, consult specialized statistical software and consider additional factors like sampling error, data weighting, and methodological variations in Gini calculation.

Update Notice

Educational Content Updated: November 2025 | Version 2.1 | All calculations remain mathematically unchanged. Added student learning aids, exam preparation content, and step-by-step explanations.