Essential map algebra vocabulary

Available with Spatial Analyst license.

Understanding the following list of terms is essential for gaining a complete understanding of map algebra. The definitions below will help you when reading the map algebra topics.


Map algebra

Map algebra is a simple and powerful algebra with which you can run all Spatial Analyst tools, operators, and functions to perform geographic analysis.

The power of map algebra lies in the ability to combine several tools into a single statement to represent complex interactions. For example, outRas = Slice(EucDistance(ExtractByAttributes("inlanduse" == 5)), 10).

Map algebra tool syntax

Any Spatial Analyst tool that outputs a raster takes on an algebraic form. For example, outRas = Slope("indem").

The few tools in the extension that do not output rasters require the output to be specified within the tool in the parentheses. For example, Contour("indem", "outcontours", 100).


Operators allow mathematical operations to be performed on rasters and scalars. Map algebra operators also exist in Python. Numbers can be directly input and a number is returned. For example, outVar = 5 + 6.

When processing rasters, the rasters are cast as raster objects and a raster object is returned. For example, outRas = Raster("input1") + Raster("input2").

Spatial Analyst classes

Classes in map algebra are used for defining certain input parameters for specific tools. Classes are used when the input parameter has more than one argument. Using classes for parameters allows you full access to the individual arguments to query, alter, and add to the parameter.

Raster object

A Raster object references a raster. A raster object is either created by casting a raster dataset or returned from running a Spatial Analyst map algebra expression. The raster object has properties and methods that can be used for further analysis.

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