Shade Sail & Awning Shadow Calculator (Sun Angle, Shadow Length & Coverage)

How it works

declination δ = 23.44° × sin(360° × (284 + day of year) ÷ 365) · hour angle H = 15° × (solar hour − 12) · sin(altitude) = sin φ sin δ + cos φ cos δ cos H · cos(azimuth) = (sin δ − sin φ sin alt) ÷ (cos φ cos alt) · shadow offset = height ÷ tan(altitude), cast away from the sun · awning projection = window height ÷ tan(altitude)

Shade is geometry: the sun's height and bearing at a given place, date and hour follow from latitude, the season's declination and the hour angle, and any object casts its shadow away from the sun by its height divided by the tangent of the sun's altitude. A shade sail therefore never shades the ground beneath it except at noon in the tropics; it must be sized and hung offset toward the sun for the hours that matter, and the low afternoon sun on a west-facing patio needs far more reach than the high midday sun on a south one. The same numbers size a fixed awning to block summer sun while letting the lower winter sun through.

Worked example

At latitude 40° on July 15 at 3 pm solar time the sun stands about 48° high in the west (azimuth ≈ 258°), so a sail 3 m up casts its shadow 2.7 m to the east. To shade a 4 × 3 m patio then, the sail needs to be roughly 6.7 × 3.6 m and hung about 2.7 m west and 0.6 m south of the patio's centre; an awning shading a 1.5 m window at that hour projects 1.36 m, though only 0.45 m at June noon (73° sun).

Frequently asked questions