Centroid

A centroid is a calculated geometric center of a shape. On a map, it can provide one point to represent a larger area. The point describes the shape under a particular calculation; it does not identify where residents are concentrated, where a building stands, or where an incident happened.

What the center represents

For a simple filled area, the centroid can be understood as its balance point if the area were made from material of uniform density and thickness. More complicated shapes require the same idea to be applied mathematically. The result does not have to fall inside the mapped area. Esri's centroid documentation explicitly notes that a shape with a hole can have a centroid in that hole. Esri centroid operator documentation.

A map may use a different representative point chosen to stay inside an area or to position a label. Such a point should not be assumed to be a geometric centroid merely because it looks central.

Example

Hypothetical: A dashboard places one marker at the centroid of a service district and labels it “120 calls.” The underlying calls occurred throughout the district.

The marker summarizes the district's total. It does not mean 120 calls occurred at the marker's location. If the centroid happens to fall beside a school or business, that proximity is a result of the display method and provides no evidence about the property.

Common confusion

A geometric centroid differs from a population-weighted center, which takes the distribution of people into account. A large uninhabited portion of an area can affect the geometric center without having the same effect on the population-weighted center.

A centroid also differs from an address match. Geocoding an address seeks a location for that address; calculating an area's centroid seeks a representative center of the area. Substituting one for the other changes what the point means.

Interpreting points used for summaries

Read whether the layer represents individual events or totals assigned to areas. Multiple records placed at one representative point can create an apparent cluster that comes from processing rather than from the original event locations.

That matters for distance calculations and heat maps. Measuring from a district centroid to a station does not measure the distance traveled for each call in the district. A meaningful analysis needs location detail appropriate to the question, along with a clear description of any representative points used.

Related terms

• Geocoding
• Geographic Information System
• Location masking
• Census tract

Sources

• Esri: centroidOperator reference — Defines the geometric center and explains why the result is not guaranteed to lie within the shape. The district marker is hypothetical.