Enter the solar azimuth angle and the surface (facade) azimuth angle into the calculator to determine the horizontal shadow angle.

Horizontal Shadow Angle Calculator

HSA from Sun Azimuth & Surface Azimuth (Main)
Vertical Shadow Angle (Profile)
HSA from Orientation

Enter any 2 values to calculate the missing variable

Horizontal Shadow Angle Formula

The following formula is used to calculate the horizontal shadow angle (HSA) from the solar azimuth angle and the surface (facade/window) azimuth angle, using the same azimuth reference and sign convention for both angles.

HSA = ((Az_{sun}-Az_{surface}+180)\bmod 360)-180

Variables:

  • HSA is the horizontal shadow angle in degrees (commonly reported in the range −180° to 180°)
  • Azsun is the solar azimuth angle in degrees (commonly 0–360°)
  • Azsurface is the surface (facade/window) azimuth angle in degrees (commonly 0–360°)

To calculate the horizontal shadow angle, subtract the surface azimuth from the solar azimuth and then normalize (wrap) the result into the range −180° to 180°. No trigonometry is required for HSA; just keep both azimuths in the same convention (same reference direction and clockwise/counterclockwise sign).

What is a Horizontal Shadow Angle?

The horizontal shadow angle (HSA) is the angle, measured in the horizontal (plan) view, between the direction a surface faces (its azimuth) and the direction to the sun (solar azimuth). In building and solar shading applications, HSA is commonly treated as the azimuth offset between the sun and the facade/window, and it is used when designing vertical fins and other shading devices.

How to Calculate Horizontal Shadow Angle?

The following steps outline how to calculate the Horizontal Shadow Angle.

  1. First, determine the solar azimuth angle (Azsun).
  2. Next, determine the surface (facade/window) azimuth angle (Azsurface).
  3. Next, calculate the horizontal shadow angle using HSA = Azsun − Azsurface, then wrap the result into the range −180° to 180°.
  4. Finally, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Solar Azimuth Angle (Azsun) = 225 degrees

Surface Azimuth Angle (Azsurface) = 180 degrees