Calculate Perpendicular Shade
A simple calculator for the height or depth of a shadow of a horizontal screen on a perdenpicular wall. Perpendicular shading therefore refers to the shadow of a horizontal object falling on a vertical surface. An example is the shadow from eaves on a house wall. The height of the Sun is given in degrees. Object length and shadow depth of height have the same unit, e.g. feet or meters. See also shadow casting for the shade length on a vertical ground.
Formulas:
s = l * tan(α)
α = arctan(s/l)
Example: When the sun is at an angle of 60 degrees, a horizontal overhang of 30 centimeters casts a shadow on a vertical surface below it that is 52 centimeters long. At an angle of 20 degrees, the shadow length is reduced to only 11 centimeters. The length of the shadow, therefore, decreases with the angle of the sun, unlike a vertical shadow casting. The reason for this is that a larger angle to the object casting the shadow lengthens the shadow. Now the object is horizontal to the ground in this case, whereas in the case of vertical shadow casting, it is perpendicular to the ground.
Calculating shading is relevant for architecture and building design, particularly for the energy efficiency of buildings. Targeted shading can prevent overheating in summer and reduce heating costs in winter by optimally utilizing or blocking sunlight depending on the season. The sun's position plays a crucial role in the design of sun protection systems such as awnings, canopies, or louvers, as it directly influences the length and position of the shadow. These calculations are also important for the design of open spaces, for example when placing trees in order to achieve pleasant shading.
Last updated on 01/20/2026. Author: Jürgen Kummer
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