Sun Shadow Length
The ground shadow a vertical object casts on level ground.
Example
You enter
- Object height (ft) 10
- Sun altitude above horizon (deg) 30
You get
- Shadow length 17.32 ft
- Shadow-to-height ratio 1.73 x height
Checked against published worked examples from: Western Connecticut Council of Governments (WestCOG).
Details, formula, and sources
Scopeshadow = object height / tan(sun altitude), so the shadow is height x cot(altitude) and the shadow-to-height ratio depends only on the sun angle. A 10 ft object under a 30 degree sun throws a 17.3 ft shadow (1.73 x its height); at a 45 degree sun the shadow equals the height, and a low winter sun throws one nearly three times as long. Use the winter-design sun elevation for the worst-case shade -- the case a solar-access, tree-planting, or building-setback study turns on. Level ground and a vertical object assumed; the sun path and terrain govern.
Formula or tableshadow_length = object_height / tan(sun_altitude); shadow_ratio = 1 / tan(sun_altitude) = cot(sun_altitude).
Source and editionSun shadow-length geometry (first-principles trigonometry), by name; the sun path and terrain govern.
Free accessFirst-principles trigonometry; the sun altitude comes from the site latitude, date, and time (or a solar-position source).
What governsEstimate. AHJ and licensed professional govern.
API field namesobject_height_ft, sun_altitude_deg, shadow_length_ft, shadow_ratio
- Level ground, vertical object the object is vertical and the shadow falls on level ground; a slope or tilt is a separate correctionscope of this tile
- Worst-case sun angle use the winter-design (lowest midday) sun elevation for the longest shadowsolar-access practice