# Antenna Coordinate Systems

Each of the antenna models in STK uses one of three coordinate systems to define the directional gain pattern:

Each system is defined by two angles, azimuth and elevation, that are measured relative to the antenna body axes.

The antenna boresight for all coordinate systems corresponds to the +z axis.

## Polar Coordinate System

**Azimuth**: The azimuth angle is defined as the clock angle about the positive z axis, starting at the positive x axis toward the positive y axis. The azimuth angle can range from -180 degrees to +180 degrees.

**Elevation**: The elevation angle is defined as the cone angle between the direction of interest and the antenna body z-axis. The elevation angle can range from 0 degrees to 180 degrees. An elevation angle of 0 degrees means the direction aligns with the positive z axis. An elevation angle of 180 degrees means that the direction aligns with the negative z axis.

## Rectangular Coordinate System

This coordinate system is traditionally used by geo-stationary satellites where azimuth is from the boresight (z axis) toward the east, and elevation is from the equator to the north.

**Azimuth**. The azimuth angle is defined as the angle between the projection of the direction vector onto the zx plane and the z axis. Positive azimuth is measured toward the positive x axis. The azimuth angle can range from -180 degrees to 180 degrees.

**Elevation**. The elevation angle is defined as the angle between the projection of the direction vector onto the zy plane and the z axis. Positive elevation is toward the negative y axis, and negative elevation is toward the positive y axis. The elevation angle can range from -180 degrees to 180 degrees.

## Spherical Az/El Coordinate System

**Azimuth**. The azimuth angle is defined as the angle measured from the z axis to the projection of the direction vector into the zy plane. The azimuth angle can range from -180 to 180 degrees. Positive azimuth is the z axis toward the positive y axis and negative azimuth is from the z axis toward the negative y axis.

**Elevation**. Elevation is defined as the angle between the zy plane and the direction vector. The elevation angle can range from -90 degrees to 90 degrees. Positive elevation is toward the positive x axis.