Window Overhang Shading Calculator (Eaves, Pergola, Awning Depth)
How far an overhang, pergola or awning must project to keep a window or wall in shade at a given sun position, and how deep the shade of your existing one reaches.
Results
The dashed line marks the value you entered.
What this tool does
What matters for shading is not the sun's altitude but its profile angle — its altitude as seen in a vertical slice square to the wall: tan(profile) = tan(altitude) ÷ cos(azimuth difference). The projection needed to shade a height below the overhang is that height ÷ tan(profile). Read the altitude and azimuth for the moment you most want shade, for example mid-afternoon in July, from the sun position calculator; a projection that shades a south-facing window at noon is not enough at 16:00 when the sun has swung to the side, where fins or a deeper projection help. A fixed overhang cannot tell July from May, so it is a compromise.
Formula
profile angle = atan(tan(altitude) ÷ cos(azimuth difference)) · projection = height ÷ tan(profile angle)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
al | Sun altitude above the horizon | ° |
az | Angle between the sun's direction and the line straight out from the wall | ° |
ht | Height to keep in shade, below the underside of the overhang | m |
pj | Projection of the overhang you have | m |
P | Projection needed to shade that height | m |
PA | Profile angle of the sun | ° |
SD | Depth of shade your overhang casts down the wall | m |
Worked example
- Sun altitude above the horizon62 °
- Angle between the sun's direction and the line straight out from the wall0 °
- Height to keep in shade, below the underside of the overhang1.5 m
- Projection of the overhang you have0.5 m
- Projection needed to shade that height0.80 m
- Profile angle of the sun62.0 °
- Depth of shade your overhang casts down the wall0.94 m
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Declination and the equation of time come from Spencer's 1971 series, good to a small fraction of a degree. Atmospheric refraction, which lifts the Sun by about half a degree at the horizon, is not included.