Shadow study calculator

Shadow length = Object height ÷ tan(sun altitude angle). At 45° sun altitude, shadows equal object height. Lower angles create longer shadows—at 20° altitude, shadows are about 2.7× object height.

The shadow length formula is L = H / tan(θ), where L is shadow length, H is object height, and θ is solar elevation angle. At 30° elevation, shadows are about 1.7× the object height. Use our shadow length calculator for precise calculations.

Solar elevation (altitude) directly affects shadow length. Higher elevation angles create shorter shadows. At 90° (directly overhead), there are no shadows. At 30° elevation, shadows are approximately 1.7× the object height. Lower angles create dramatically longer shadows.

To calculate shadow length from solar altitude: divide object height by the tangent of the solar altitude angle. For example, a 50ft building at 45° solar altitude casts a 50ft shadow. A 50ft building at 20° altitude casts a 139ft shadow. Use our interactive calculator for instant results.

Shadows are longest at sunrise and sunset (when the sun is lowest) and during winter months (when the sun's path is lower in the sky). Summer solstice has the shortest midday shadows.

Solar noon is when the sun reaches its highest point in the sky, directly due south (in the northern hemisphere). This is when shadows are shortest and point true north.

Higher latitudes experience lower sun angles, creating longer shadows year-round. At the equator, the midday sun can be directly overhead (no shadow). At 45° latitude, the sun never exceeds about 68° altitude.

Shadow length is affected by: 1) Object height (taller = longer shadows), 2) Solar elevation angle (lower angle = longer shadows), 3) Time of day (lowest at noon), 4) Season (lowest in summer), and 5) Latitude (higher latitudes = longer shadows).

Shadow length calculations help architects determine setback requirements, solar access for adjacent properties, and optimal building orientation. Calculate shadow projections to ensure compliance with zoning codes and prevent shading of neighboring solar panels or outdoor spaces.

Solar altitude and elevation refer to the same angle - the height of the sun above the horizon. Both terms are used interchangeably in shadow calculations. The complementary angle is the solar zenith angle (90° - elevation).