# Gini Coefficient Calculator

This Gini coefficient calculator can be employed for swift and simple computations of the Gini coefficient for any specified income distribution.

**How to use the calculator:** Enter a set of incomes separated by commas, line breaks, or spaces, and click on the "Calculate" button.

## Reference

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 **X _{i}** 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: