Gini Coefficient Formula
The Gini coefficient measures income inequality on a scale from 0 to 1.
Learn the formula based on the Lorenz curve with examples.
The Formula
or equivalently: G = 1 - 2B
The Gini coefficient is a measure of statistical dispersion used to represent income or wealth inequality within a population. It was developed by Italian statistician Corrado Gini in 1912.
The coefficient ranges from 0 to 1. A value of 0 means perfect equality (everyone has the same income). A value of 1 means perfect inequality (one person has all the income). Most countries have Gini coefficients between 0.25 and 0.60.
The Gini coefficient is derived from the Lorenz curve, which plots the cumulative share of income (y-axis) against the cumulative share of the population (x-axis). Area A is the region between the line of equality and the Lorenz curve. Area B is the region below the Lorenz curve. Since the triangle formed by the line of equality has area 0.5, G = A/0.5 = 2A, and since A + B = 0.5, we get G = 1 - 2B.
For discrete data with n individuals sorted by income: G = (2 × Σ(i × yᵢ)) / (n × Σyᵢ) - (n+1)/n, where yᵢ is the income of person i.
Variables
| Symbol | Meaning |
|---|---|
| G | Gini coefficient (between 0 and 1) |
| A | Area between the line of equality and the Lorenz curve |
| B | Area under the Lorenz curve |
| yᵢ | Income of individual i (sorted in ascending order) |
| n | Number of individuals in the population |
Example 1
A small economy has 5 people with incomes: $10k, $20k, $30k, $40k, $100k. Calculate the Gini coefficient.
Total income Σyᵢ = 200k. n = 5.
Σ(i × yᵢ) = 1(10) + 2(20) + 3(30) + 4(40) + 5(100) = 10 + 40 + 90 + 160 + 500 = 800
G = (2 × 800) / (5 × 200) - (5+1)/5 = 1600/1000 - 6/5 = 1.6 - 1.2
G = 0.40 (moderate inequality)
Example 2
A country's Lorenz curve shows that the area under the curve (B) is 0.35. What is the Gini coefficient?
Using the simplified formula: G = 1 - 2B
G = 1 - 2(0.35) = 1 - 0.70
G = 0.30 (relatively low inequality, similar to Scandinavian countries)
When to Use It
The Gini coefficient is the most widely used measure of inequality.
- Comparing income inequality between countries
- Tracking changes in inequality over time within a country
- Measuring wealth distribution, land ownership, or educational inequality
- Policy analysis — evaluating the impact of taxation and welfare programs