Enter Values
Gini Formulas
Individual: G = (2∑i·yi) / (n·∑yi) − (n+1)/n
Lorenz Curve
Gini Coefficient Results
| Quintile | Share (%) | Cumulative (%) | Equality Line (%) |
|---|
Formula Breakdown
Country Comparison
| Country | Gini |
|---|---|
| Sweden | ~0.29 |
| Germany | ~0.32 |
| United States | ~0.42 |
| Brazil | ~0.52 |
| South Africa | ~0.63 |
Approximate values from World Bank (SI.POV.GINI). Years and methodology vary by country.
Model Assumptions
- Income measured before or after taxes/transfers (user should note which)
- Quintile data assumes each quintile contains exactly 20% of the population
- Quintile method produces a grouped-data approximation (theoretical max ~0.80 with 5 groups)
- Does not capture wealth inequality (income ≠ wealth)
- Gini coefficient is scale-independent (proportional, not absolute measure)
- Country comparison values are from World Bank surveys and may not match the income definition used in your calculation
- For educational purposes. Not financial advice. Market conventions simplified.
Understanding the Gini Coefficient and Lorenz Curve
What Is the Gini Coefficient?
The Gini coefficient is the most widely used single-number measure of income inequality. It ranges from 0 (perfect equality, where everyone earns the same) to 1 (perfect inequality, where one person earns everything). The Gini is derived from the Lorenz curve — it equals twice the area between the Lorenz curve and the 45-degree line of perfect equality.
Where A = area between equality line and Lorenz curve
B = area under the Lorenz curve
How to Read a Lorenz Curve
The Lorenz curve plots cumulative population share (x-axis, from poorest to richest) against cumulative income share (y-axis). The diagonal 45-degree line represents perfect equality. The further the Lorenz curve bows below this line, the more unequal the distribution. The shaded area between the two lines (Area A) directly determines the Gini coefficient.
Key Assumptions
- The Gini measures relative inequality — it is scale-independent
- Two different distributions can have the same Gini but different Lorenz curves
- Quintile data provides a grouped approximation with a theoretical maximum around 0.80
- Individual data yields an exact sample Gini via Brown's formula
- The Gini does not distinguish income vs. wealth inequality
Frequently Asked Questions
Disclaimer
This calculator is for educational purposes only. It uses simplified models to illustrate income inequality concepts from introductory economics courses (Mankiw, Principles of Microeconomics, Chapter 20). Real-world income measurement involves complex survey methodology, tax adjustments, and transfer accounting not captured here. This tool should not be used for policy or financial decisions.
