Index of Dissimilarity Calculator

What Is the Index of Dissimilarity Calculator?

The Index of Dissimilarity Calculator measures spatial segregation between two population groups across any set of geographic areas: neighbourhoods, census tracts, school enrolment zones, electoral wards, or workplace departments. Enter the population count for each group in each area, and the calculator returns the dissimilarity index D, a per-area contribution breakdown, and a comparison against real US city data from the 2020 Census.

The index was formalised by sociologists Otis Dudley Duncan and Beverly Duncan in their 1955 paper in the American Sociological Review and has since become the most widely cited measure of residential segregation in urban sociology. The US Department of Housing and Urban Development uses the dissimilarity index in its fair housing planning tools and requires grantees to report it as part of the Assessment of Fair Housing process. Urban planners, academic researchers, civil rights organisations, and journalists routinely work out D to track segregation trends over time and compare cities or districts against one another.

Unlike competing online tools that only accept a single area's data, our calculator is built for the real formula: it sums the absolute group-share differences across all your geographic units, letting you carry out a proper D calculation for an entire city or district in one pass. The per-area contribution table shows which specific neighbourhoods or tracts drive the result most, a feature absent from every other web-based dissimilarity calculator. If you want to measure income inequality alongside spatial segregation, run your data through our Gini Coefficient Calculator to compare the two dimensions.

How to Read a Dissimilarity Score: The Three Tiers

The dissimilarity index D ranges from 0 to 1 (or 0 to 100 on a percentage scale). A D of 0 means the two groups are distributed identically across all areas; every neighbourhood has exactly the same group composition as the city as a whole. A D of 1 means complete separation; every area is entirely one group or the other. In practice, D is almost never at either extreme.

The three standard tiers come from academic and government sources including CensusScope at the University of Michigan and the Brown University US2020 project:

As a result of decades of fair housing advocacy and some demographic mixing, the average Black-White D across the 88 largest US cities fell from roughly 0.67 in 1980 to 0.455 in 2020 -- but progress has been uneven. In cities like Chicago and Milwaukee, D remains above 0.75 even after two decades of modest decline.

The Modifiable Areal Unit Problem: Why Geography Matters

The most important technical limitation of the dissimilarity index is that the D value depends heavily on the size of the geographic units you use. This is a specific case of the modifiable areal unit problem (MAUP), well documented in spatial statistics. When researchers calculate D at the census-block level (smaller areas), they consistently get higher values than when they calculate it at the census-tract level (larger areas). A city that appears moderately segregated at the tract level may turn out to be highly segregated at the block level.

In practice, this means you should never compare D values computed at different geographic resolutions. A school district D computed at the individual school level is not directly comparable to a city D computed at the tract level. The Measuring Residential Segregation with the ACS study in Population Research and Policy Review found that measurement error from Census sampling alone can shift D by 2 to 5 percentage points in smaller cities, adding to the geographic sensitivity problem. When using this calculator, always make sure all your area rows represent the same type and size of geographic unit.

Index of Dissimilarity vs Exposure Index: Two Different Questions

D answers the question: "How unevenly are the two groups distributed?" The exposure index answers a different question: "What is the average group composition of the neighbourhood where a typical member of Group A lives?" Both are important, but they measure fundamentally different things, and researchers routinely use both together.

A small minority group can be completely concentrated in one district, producing a high D, but the exposure index (the average fraction of Group A's neighbours who belong to Group B) can still be low simply because Group B is a small share of the total population. On top of that, D is symmetric: the Black-White D is identical to the White-Black D. The exposure index is not symmetric; the fraction of Black residents' neighbours who are White is typically higher than the fraction of White residents' neighbours who are Black, because the two groups have different population sizes. For a full picture of segregation, our demographic distribution tools and the Exposure and Isolation Index Calculator (coming soon to this category) work alongside the dissimilarity index to cover both the evenness and contact dimensions.

Accuracy and Limitations of This Calculator

The formula D = 0.5 times the sum of absolute group-share differences is exact for the data you enter. There is no estimation, rounding, or sampling error within the calculation itself. What introduces uncertainty is the quality and resolution of the input data. Census population counts carry a margin of error, particularly for small geographies; the American Community Survey (ACS) introduces additional sampling variance that can be 3 to 8 percentage points in cities under 100,000 residents.

The two-group constraint is the core structural limitation: D cannot be calculated for three or more groups simultaneously. To analyse three racial or income groups, you must run three separate pairwise calculations. The Othering and Belonging Institute at UC Berkeley recommends using the multigroup entropy index (H index) when comparing segregation across cities with very different demographic compositions, as D values from cities with 5% minority populations are not directly comparable to D values from cities with 40% minority populations. This calculator is best suited for straightforward two-group comparisons at a consistent geographic level.

The Most Common Index of Dissimilarity Misreading

The mistake I see most often is treating the D value as the probability that a randomly selected member of Group A will encounter a member of Group B in their neighbourhood. That is the exposure index, not the dissimilarity index. A D of 0.50 does not mean that 50% of Group A's neighbours are from Group B. It means that 50% of Group A members would need to relocate to produce an even distribution. In cities where one group is a small minority, these two numbers can be extremely different. With that in mind, always pair D with the exposure index when you want to describe what everyday neighbourhood life looks like for the average group member. Using D alone to describe social mixing is the most common misapplication in journalism and policy documents, and it consistently overstates the degree of cross-group contact in segregated cities. This turns up most often in analyses that cite D as evidence of either integration or segregation without checking what the exposure index shows for the same population.