Gini Coefficient Calculator
Calculate the Gini coefficient, a measure of income inequality or wealth distribution, using our online calculator. By inputting the individual incomes or wealth values, you can determine the Gini coefficient which ranges between 0 and 1. A Gini coefficient of 0 represents perfect equality, while a value of 1 indicates extreme inequality.
The Gini coefficient, named for the Italian statistician Corrado Gini, represents a dimensionless measurement of statistical dispersion that is often employed to analyze income distribution.
This coefficient, G, of a data set or income distribution curve has a range between 0 and 1, 0 being where wealth is most equally distributed (with every individual owning the same sized share) and 1 being where wealth is most unequally distributed (one individual owns everything).
Mathematically, G is the ratio of the area between the wealth distribution curve (Lorenz curve) and the line of equal distribution (straight line) to the entire area under the line of equal distribution; i.e., G = A / (A + B). It is easiest to show this as a graph:
A Lorenz curve represents the way in which wealth is cumulatively distributed, with the quantity of wealth held by individuals put in order from smallest to largest. Any given (x, y) point on this curve represents x percent of the population owning y percent of wealth.
For reference, in 1992, the U.S. Gini coefficient for household income was 0.433. Twenty six years later, by 2018, the Gini coefficient rose to 0.49.
Computing the Gini Coefficient (Empirical Distribution)
With an empirical Lorenz curve that has been generated using discrete data points, the Gini coefficient may be calculated using the formula:
with Xi being ordered from smallest to largest.
Computing the Gini Coefficient (Theoretical Distribution)
If the Lorenz curve is represented with the function f(x) over the interval [0, 1], the Gini coefficient may be calculated using integration, employing this formula:
what is Gini Coefficient Calculator
A Gini coefficient calculator is a tool that calculates the Gini coefficient, which is a measure of income inequality or wealth distribution within a population. The Gini coefficient is a widely used statistical measure in the field of economics and social sciences.
Here's how a Gini coefficient calculator typically works:
Data Input: You would need to provide the calculator with the distribution of income or wealth among individuals or households. This can be done by inputting the individual incomes or household wealth values, or by specifying the frequency or percentage of individuals or households falling into different income or wealth brackets.
Sorting: The calculator will sort the income or wealth values in ascending order, from lowest to highest.
Cumulative Percentage Calculation: The calculator then calculates the cumulative percentage of total income or wealth that each income or wealth bracket represents. This cumulative percentage helps determine the Lorenz curve.
Lorenz Curve Plotting: Based on the cumulative percentages, the calculator plots the Lorenz curve on a graph. The Lorenz curve represents the cumulative share of total income or wealth received by the corresponding cumulative percentage of individuals or households.
Gini Coefficient Calculation: The Gini coefficient is calculated by comparing the area between the Lorenz curve and the line of perfect equality (also known as the 45-degree line) to the total triangular area under the line of perfect equality. The Gini coefficient ranges from 0 to 1, where 0 represents perfect equality (all individuals have an equal share of income or wealth) and 1 represents maximum inequality (one individual has all the income or wealth).
Displaying the Result: The calculator provides the calculated Gini coefficient as the output, indicating the level of income or wealth inequality in the given population.
It's important to note that the Gini coefficient is just one measure of income or wealth inequality, and it has its limitations. Other measures and factors should be considered when examining economic disparities and social issues related to income or wealth distribution.
Gini coefficient calculators can be found online or implemented in statistical software packages like R, Python, or Excel, often as part of their built-in functions for inequality analysis.
Gini Coefficient Calculator example
Certainly! Let's consider an example of calculating the Gini coefficient for a fictional income distribution among 10 individuals.
Step 1: Arrange the data.
First, we need to arrange the incomes in ascending order. Let's say the income distribution among the 10 individuals is as follows (in arbitrary units):
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Step 2: Calculate the Lorenz curve.
The Lorenz curve represents the cumulative share of income plotted against the cumulative share of the population. We calculate the cumulative shares as follows:
Cumulative Share of Income: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55
Cumulative Share of Population (equally distributed): 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0
Step 3: Calculate the Gini coefficient.
To calculate the Gini coefficient, we compare the area between the Lorenz curve and the line of perfect equality (the 45-degree line) to the total area below the line of perfect equality.
The formula to calculate the Gini coefficient is:
Gini coefficient = (A) / (A + B)
- A is the area between the Lorenz curve and the line of perfect equality
- B is the area below the line of perfect equality
In our example, we can calculate A and B as follows:
A = 0.5 - (0.1 * (1 + 3)) - (0.1 * (3 + 6)) - (0.1 * (6 + 10)) - (0.1 * (10 + 15)) - (0.1 * (15 + 21)) - (0.1 * (21 + 28)) - (0.1 * (28 + 36)) - (0.1 * (36 + 45)) - (0.1 * (45 + 55)) = 27.5
B = 0.5 * 1 = 0.5
Gini coefficient = A / (A + B) = 27.5 / (27.5 + 0.5) ≈ 0.982
Therefore, the Gini coefficient for this fictional income distribution among 10 individuals is approximately 0.982.
Please note that this is a simplified example for illustrative purposes. In practice, Gini coefficients are calculated using more precise methods with continuous income data and larger sample sizes.