What is the radian equivalent of 180 degrees?

The radian equivalent of 180 degrees is π radians. This equivalence comes from the relationship between degrees and radians in the context of circles.

A complete circle is defined as 360 degrees, which corresponds to 2π radians. To find the radian measure for a semicircle—or 180 degrees—you can set up a proportion. Since 180 degrees is half of 360 degrees, the radian measure is half of 2π radians:

[ \text{Radian measure} = \frac{1}{2} \times 2\pi = \pi \text{ radians}. ]

This relationship is foundational in trigonometry and is often used in various applications within Geographic Information Systems (GIS), especially when working with angular measurements in spatial analysis and when transforming data between different formats or systems. Understanding the conversion between degrees and radians is essential for accurate calculations involving angles, distances, and spatial orientation.