Calculating Area in Degrees Arcmap

What is Area in Degrees?

When working with geographic coordinates, area is often measured in square degrees. A degree of latitude is approximately 69 miles (111 kilometers) at the equator, but this distance decreases as you move towards the poles. Similarly, a degree of longitude varies from about 69 miles at the equator to 0 miles at the poles.

The concept of area in degrees is particularly important in cartography, where precise measurements of land areas are required. Understanding how to calculate and interpret area in degrees helps professionals in fields like urban planning, environmental science, and geology.

How to Calculate Area in Degrees

Calculating area in degrees involves several steps. First, you need to determine the coordinates of the area you're measuring. These coordinates are typically given in latitude and longitude. Once you have these coordinates, you can use a formula to calculate the area in square degrees.

The calculation involves converting the coordinates into a format that can be used to determine the area. This often requires using trigonometric functions to account for the curvature of the Earth. The result is an area measurement that represents the size of the geographic region in square degrees.

The Formula

The formula for calculating area in degrees is based on the spherical nature of the Earth. The exact formula depends on the specific coordinates and the shape of the area being measured. However, a common approach involves using the following steps:

This formula accounts for the fact that the length of a degree of longitude decreases as you move away from the equator. The cosine function is used to adjust for this variation.

Worked Example

Let's consider a rectangular area defined by the coordinates (30°N, 90°W) and (40°N, 80°W). To calculate the area in square degrees:

1. Calculate the difference in latitude: 40°N - 30°N = 10°
2. Calculate the difference in longitude: 90°W - 80°W = 10°
3. Calculate the average latitude: (30°N + 40°N)/2 = 35°N
4. Convert the average latitude to radians: 35° × (π/180) ≈ 0.6109 radians
5. Calculate the cosine of the average latitude: cos(0.6109) ≈ 0.8165
6. Multiply the differences and the cosine: 10° × 10° × 0.8165 ≈ 81.65 square degrees

The area of this rectangular region is approximately 81.65 square degrees.

Using ArcMap for Area Calculations

ArcMap is a powerful GIS software that can be used to calculate areas in degrees. Here's a step-by-step guide on how to perform these calculations using ArcMap:

1. Open ArcMap and load your data.
2. Use the "Create Features" tool to draw the area you want to measure.
3. Select the area using the "Select Features" tool.
4. Right-click on the selected area and choose "Calculate Geometry."
5. Choose "Area" as the geometry property and "Square Degrees" as the unit.
6. The calculated area will be displayed in the results.

ArcMap provides a user-friendly interface for performing these calculations, making it an essential tool for professionals in the field.