There are two main ways to measure social inequality: inequality of conditions, and inequality of opportunities. Inequality of conditions refers to the unequal distribution of income, wealth and material goods. Housing, for example, is an inequality of conditions with the homeless and those living in housing projects sitting at the bottom of the hierarchy while those living in multi-million dollar mansions sitting at the top.
Inequality of opportunities refers to the unequal distribution of "life chances" across individuals. This is reflected in measures such as level of education, health status, and treatment by the criminal justice system. For example, why do upper-class white males typically have more opportunities for wealth and success compared to lower-class black males, who have a higher chance of landing in the criminal justice system?
Read more about social inequality, including how and why sociologists study it.