A Gini Index Calculator is an analytical tool used by economists, sociologists, and policymakers to measure the level of income or wealth inequality within a specific population. The calculator processes a set of income or wealth data for a group of individuals and produces a single number known as the Gini Index or Gini coefficient.
This index provides a clear, quantitative measure of distribution. Its value always falls between 0 and 1. A score of 0 represents perfect equality, a theoretical scenario where every individual in the group has the exact same income or wealth. Conversely, a score of 1 represents perfect inequality, where a single individual holds all the income or wealth, and everyone else has none. Therefore, a higher Gini Index signifies greater inequality in the distribution. Governments and researchers use this tool to analyze economic trends, compare inequality levels between different countries or regions, and assess the impact of economic policies over time.
formula
To calculate the Gini Index from a collection of individual data points, you can use a common formula designed for discrete data. It is important to note that for this formula to yield the correct result, you must first sort the income or wealth data in ascending order, from the lowest value to the highest.
Primary Formula for Discrete Data
This is the most common and practical formula for calculating the Gini Index from a set of individual income or wealth data points. For this formula to work correctly, the data must first be sorted in ascending order.
G = (2 * Σ(i * y_i)) / (n * Σy_i) – (n + 1) / n
Variable Definitions:
G: The Gini Index.
y_i: The income or wealth of the i-th individual in the dataset, where the data points are sorted in ascending order (from lowest to highest income).
i: The rank of the individual based on their income (e.g., 1 for the lowest income, 2 for the second lowest, and so on).
n: The total number of individuals in the population (the total number of data points).
Σ: The summation symbol, indicating that you should sum the values that follow.
Breakdown of Calculation Steps:
Σy_i (Sum of all incomes): Add up all the individual income values in the dataset.
Σ(i * y_i) (Sum of weighted incomes): Multiply each individual’s income (y_i) by their rank (i) and then add all of those products together.
Plug the calculated sums and the total number of individuals (n) into the main formula to find the Gini Index.
Gini Index Interpretation Table
To quickly interpret the meaning of a Gini Index score, you can refer to the following table. It provides a general framework for understanding what different value ranges typically signify about the level of inequality.
| Gini Index Value | Level of Inequality | General Interpretation |
| 0.0 – 0.2 | Very Low | Indicates a state of near-perfect income equality. Very rare in real-world economies. |
| 0.2 – 0.3 | Low | Represents a relatively equitable distribution of income. Often seen in Scandinavian countries with strong social welfare systems. |
| 0.3 – 0.4 | Moderate | A common range for many European countries. Indicates a noticeable but not extreme gap between the rich and poor. |
| 0.4 – 0.5 | High | Signifies a significant level of income inequality. This range is common in large, diverse economies. |
| 0.5 and above | Very High | Represents a state of severe income inequality, where a small portion of the population holds a large share of the total income. |
Example
Let us work through a simple example to see how the Gini Index formula is applied.
Imagine a small population of 5 individuals (n = 5) with the following annual incomes: $10,000, $20,000, $30,000, $50,000, and $90,000.
Step 1: The data is already sorted in ascending order (y_1 to y_5).
y_1 = 10,000
y_2 = 20,000
y_3 = 30,000
y_4 = 50,000
y_5 = 90,000
Step 2: Calculate the sum of all incomes (Σy_i).
Σy_i = 10,000 + 20,000 + 30,000 + 50,000 + 90,000 = 200,000
Step 3: Calculate the sum of the weighted incomes (Σ(i * y_i)).
Σ(i * y_i) = (1 * 10,000) + (2 * 20,000) + (3 * 30,000) + (4 * 50,000) + (5 * 90,000)
Σ(i * y_i) = 10,000 + 40,000 + 90,000 + 200,000 + 450,000 = 790,000
Step 4: Plug these values into the Gini Index formula.
G = (2 * 790,000) / (5 * 200,000) – (5 + 1) / 5
G = 1,580,000 / 1,000,000 – 6 / 5
G = 1.58 – 1.2
G = 0.38
The Gini Index for this population is 0.38. According to the interpretation table, this indicates a moderate level of income inequality.
Most Common FAQs
There is no universally “good” or “bad” Gini Index. A lower score, closer to 0, indicates less inequality, which is often seen as a positive social outcome associated with fairness and social stability. A higher score, closer to 1, indicates greater inequality. While high inequality can be linked to social unrest and economic instability, some economic arguments suggest that a certain level of inequality can drive innovation and economic growth. The ideal level is a subject of ongoing debate among economists and policymakers.
While the Gini Index is a very useful measure, it has some limitations. First, it does not reveal the underlying structure of the inequality; two countries with the same Gini Index could have very different income distributions. Second, it is sensitive to what is happening in the middle of the distribution but less sensitive to changes at the extreme ends (the very rich or very poor). Finally, it does not account for non-monetary factors like access to education, healthcare, or overall quality of life, which are also important aspects of inequality.