A density map depicts a number of objects per unit area. It is almost always represented as a grid (in raster format). The calculation typically computes a weighted average of objects found within a specified distance (the "radius") where the weights depend on distance. The pattern of weights (which usually decrease with distance) is called the kernel. A generalization of this procedure further weights the density by a numerical attribute of the object, such as a count. For example, the objects may be points designating housing units, the counts may represent people in those units, and the resulting density is population per unit area.
The results of a density calculation, because they are values per unit area, typically have different numeric ranges than the original data. Continuing the previous example, there may be one to 12 people in the housing units, but the number of people per square kilometer may run into many thousands.
Densities can be converted back to counts: multiplying the density in a grid cell by the cell's area (not its side length) estimates the total in that cell (such as the total number of people living in it). Summing those counts over a region (a "zonal sum" operation) uses the density map to count things lying within the region. A good check of a density calculation is to perform this summation for the entire map and compare it to the count of the original objects (or the sum of their attributes, as appropriate). Except for edge effects, the two values should be equal.
Often a GIS will compute densities in units per square meter but the results are needed in units per square kilometer, square mile, or some other unit of area. To make the conversion, multiply by the factor needed to convert the new area units to the old area units. For example, one square kilometer equals 1,000,000 square meters, so to convert a density grid from people per square meter to people per square kilometer, multiply all its values by 1,000,000. Misunderstanding the areal units of measure used in the GIS density calculation is a likely explanation when large discrepancies are found in the check described in the preceding paragraph.
Density maps are often thought of as a form of interpolation, but this can be deceiving, because they have little in common with true interpolation methods (such as trend surfaces, IDW, splines, or natural neighbor), except that they all produce a grid that looks like a continuous surface. It is useful to think of a kernel density calculation as spreading the original objects out. The kernel function itself describes the spread. The larger the radius, the greater the spreading.
Two choices are made when specifying a kernel density calculation: the shape of the kernel and its radius. The radius is the most important parameter: a large radius spreads everything so far out that the resulting density map shows little variation, whereas a small radius results in sharp isolated peak-like features with little consolidation or clustering of points. Often experimentation is required to select an appropriate radius. The shape of the kernel determines the apparent smoothness of the density map. A kernel with abrupt changes in weights (such as one with constant weights, dropping to zero beyond the radius) can create evident discontinuities in the density map. A gaussian kernel tapers off with distance so smoothly that its density map is guaranteed to be very smooth (in theory, having derivatives of all orders).
Another term for a kernel density calculation is convolution.