The most simple centroid, the area centroid, is the geometric midpoint of a polygon on a plain. In other words, the centroid calculates the middle of often irregular shapes by averaging out length and width values (x and y axis values) for the space. In applied geography projects like city planning, this value can be extremely useful. In order to determine the optimal placement for a cell phone or radio tower, for instance, centroid calculations are often used to find the geometric center of a space and locate the point where the signal will be most evenly distributed.
A three-dimensional version of the area centroid, the volume centroid represents a volumetric midpoint of an object. In addition to the ground plain taken into account for an area centroid, the volume centroid considers height and depth to calculate the middle of an object in relation to the space it occupies. Volume centroids are often used in structural analyses and engineering projects. An engineer, for instance, may need to identify the centroid of a mountain in order to evaluate the structural viability of building a tunnel through the mountain, just as an architect may want to identify the centroid of a large open space to select an ideal point to place lighting.
While geometric centroids calculate the midpoints of enclosed spaces, geographers are often interested in finding middle positions between unrelated areas or points. A number of points or lines on a map, for example, do not form a closed space, but you may still be interested in finding an equidistant point between the separate objects. For these purposes, a number of arithmetic centroid calculations, from mean and median centroids to the minimum-distance centroid, exist. The often used minimum-distance centroid calculation, as an example, calculates the point where the distance to all of the related points from the center is the least and is often used for regional planning and the placement of social services like hospital or schools where they will be more easily accessible to the different population centers in the area.
Although geographers are primarily concerned with the study of space, they are also very aware that the social phenomena that take place in those spaces can fundamentally change the nature or interpretation of the area. As a result, centroids are not only calculated in relation to central points in space, but as central points of a social phenomenon. A population centroid, for example, would take the population density of different areas into account in order to find the point where the highest number of people would be closest to a given point. This point may or may not be the same as the area centroid of the region, but would be a better guideline for where to locate social services like schools.