The human development index, or HDI, measures the quality of life in different countries on a scale from zero to one. The United Nations Development Program created the HDI to determine how countries help their citizens develop as human beings. While previous measurements, such as gross national product, or GNP, measured a country's economic power, the HDI accounted for factors such as health and education along with economic development and personal income when evaluating a country's progress.

## Life Expectancy Index

A key element in calculating the HDI is life expectancy at birth. The life expectancy factor helps to determine how long the average citizen lives, how healthy she can remain during her life and how much she can contribute in her working life. The HDI measures life expectancy from 20 to 85 years. Countries with longer life expectancies receive higher HDI scores than those in which people die at a younger age. For instance, in the fictitious country of Generica, the life expectancy at birth is 70 years. The life expectancy index would be (70-20)/(85-20), or 0.77.

## Education Index

The education index is another important component in the HDI calculation. The education index is found by dividing the number of years of schooling for adults age 25 and older by the expected years of schooling for children of school age. For instance, adult citizens of Generica typically go to school for 12 years, but school-age children are expected to go for at least 15 years. The education index for Generica is 12/15, or 0.8.

## Gross National Income Per Capita

The gross national income per capita, or GNI, measures the annual income of the average citizen based on purchasing power parity, or PPP. The GNI index uses a minimum income of $100 and a maximum of $75,000. The index uses a logarithmic scale to show the decrease in purchasing power as income increases. The GNI per capita for citizens of Generica is $50,000. The income index for the HDI would be [Log(50,000) - Log(100)]/ [Log(75,000) - Log(100)], or 0.94.

## Calculating the HDI

The HDI is found by taking the geometric mean of the life expectancy, education and income indexes. The geometric mean for three numbers is calculated by taking the product of the numbers and finding the cube root. In the equation below, taking a number to the 1/3 power is the same as finding the cube root. For Generica, the formula would look like this:

(0.77 x 0.8 x 0.94) ^ 0.3333333

= (0.58) ^ 0.3333333

= 0.83

## Inequality-Adjusted Human Development Index (IHDI)

The typical HDI calculation does not account for the inequalities in different countries. The inequality-adjusted human development index, or IHDI, takes these inequalities into account and shows the loss to human development due to inequality. The IHDI measures inequality using the same elements measured in the HDI. For instance, countries with a handful of rich citizens and millions in poverty will show a high level of inequality in the income index.