Continuing with the theme of ArcGIS lessons started in December’s *Geospatial Frequently Asked Question* (G-FAQ), this month we look at the steps required to calculate the area of a polygon shapefile. In this G-FAQ, we cover some of theory behind calculating areas in ArcGIS and then also offer a short video showing you the exact steps required to complete the calculation.

Specifically, this G-FAQ will address the following set of core questions:

*What is the easiest way to calculate the area of a polygon file in ArcGIS 10.x? What projection does the data need to be in to support this calculation? What field type should I use for area calculations?*

Before you watch the short video accompanying this G-FAQ, take a few moments to read through some of the theory behind area calculations in ArcGIS. We have ordered the information below to mimic the steps taken in the video.

## Choosing the Correct Projection

In order to complete an area calculation for a polygon shapefile, it needs to be in a projected coordinate system as opposed to geographic, as a geographic system projects data on to a round surface so it is impossible to accurately measure distances, areas, etc. Data in a projected coordinate system is displayed as if sitting on a flat plane so it is now possible to accurately calculate distances, areas, etc.

If you are working with polygons in a small area, you can chose a local projected coordinate system that you commonly work in, for instance UTM. However, for area calculations that include polygons spread over a large region, you will need to choose an equal-area, global projected coordinate system. A projected coordinate system can prevent distortion in one spatial dimension but will then always distort in another. Projected systems can control for: equal area, equal distances, equal angles, direction and scale; but they cannot control for all at once.

My equal-area, global projection of choice is: *Cylindrical Equal Area (World)*. It models the world with perpendicular latitude and longitude lines. Longitudes are spaced equally while latitudes are unequally spaced to account for the shrinking volume of our global as you move to the poles. A WGS84 datum is used as it is the mostly widely accepted global datum. There are other equal area projections you could choose, for instance you can shift the latitude lines used for baseline calculations farther north to de-emphasize area miscalculations in high latitudes.

## Choosing the Correct Field Type

Once you have re-projected your data into the equal-area system of your choice, it is time to add a field to your attribute table to hold the area calculations. We will walk you through the exact steps of doing this in the short video that accompanies this G-FAQ, but for now a bit of theory behind the field types you can add. For numeric values, you are able to create these types of fields (or columns):

*Short Integer*– numbers without decimal places between -32,768 and 32,767*Long Integer*– numbers without decimal places but of any length or number of digits*Float*– numbers with decimals with less than 7 digits total (including decimal places)*Double*– numbers with decimals and no length limit

For each of these four field types, you are also able to define the precision and scale for the new column. Precision equals the total number of digits you can store and is an option for all four field types. Scale is the total number of decimal places and so is only an option for float and double field types.

When I calculate polygon areas in Arc, I typically choose a *double* field with *“20”* for precision and *“10”* for scale.

## Comparison of Area Calculations With Different Equal-Area Projections

We have one final item to cover quickly before you check out the short video here. To show you how close equal area projections are to each other, I projected the same shapefile into three different systems. The polygon file I used spanned the globe and contained 176,987 individual polygons. Here is the total area calculated by each of the three equal-area projections:

- South Pole Lambert Azimuthal Equal Area – 256,117,937.745012 square kilometers (sq km)
- Sphere Cylindrical Equal Area – 255,623,570.713166 sq km
- World Cylindrical Equal Area – 256,123,154.208427 sq km

To put these figures a different way, if you set the total area calculated by World Cylindrical Equal Area as the ‘true value’ then here is how close the other two projections come:

- South Pole Lambert Azimuthal Equal Area – 99.998% of the true value
- Sphere Cylindrical Equal Area – 99.805% of the true value

So then, what you see from these comparisons is that shifting the baseline latitude line north or south has little impact on the final area calculations as the South Pole equal area projection was very close to our true value. The bigger impact on these calculations is the datum used in the re-projection as Sphere Cylindrical Equal Area is much farther off since it uses a spherical representation of the globe; and not the most widely-regarded (and accurate) global datum, WGS84, used in the other two projections.

*Do you have an idea for a future G-FAQ? If so, let me know by email at brock@apollomapping.com.*

## Find Out More About This Topic Here

- State University of New York, Syracuse – About XY Domain & Precision in ArcGIS
- University of California, Santa Barbara – Lecture 5
- University of Colorado – Map Projection Overview
- University of Maine – Coordinate Systems and Map Projections for GIS
- University of Notre Dame – Creating Vector Data in ArcGIS
- University of Washington – Projections and Coordinate Systems

Brock Adam McCarty

Map Wizard

(720) 470-7988

brock@apollomapping.com

Dear,

How I calculate the square of raster file of the world (land cover)? Actually, there are not active geometry. I changed the coordinate system but I could not.

Sincerely,

Thanks for the comment Narnaa – I am guessing that your raster file is not projected. I will reply to you directly.