Sun Position & Shadow Length Calculator
Calculate the approximate solar elevation angle and the resulting shadow length for any vertical object at a given latitude, day of year, and solar hour.
Results
What is it?
The sun's position in the sky changes with latitude, time of year (solar declination), and time of day (hour angle). Solar elevation — how high the sun sits above the horizon — directly determines the length of shadows cast by vertical objects.
How to use
Enter the object's height, your latitude, the day of the year, and the solar hour. The calculator uses the standard astronomical formula to compute sin(solar elevation) and derives the shadow length from trigonometry. A value of 999 m means the sun is at or below the horizon.
Example scenario
A 10 m flagpole at latitude 40°N on the summer solstice (day 172) at solar noon: solar declination ≈ 23.45°, hour angle = 0°. sin(elevation) ≈ sin(40°)×sin(23.45°) + cos(40°)×cos(23.45°) ≈ 0.959. Shadow length ≈ 10 × sqrt(1 − 0.959²) / 0.959 ≈ 2.94 m.
Pro tip
Solar noon is not always 12:00 clock time — it varies with your longitude within your time zone and the equation of time. Shadow length is shortest at solar noon and infinitely long at sunrise/sunset. This calculation is invaluable for positioning solar panels (optimize tilt), designing sundials, or planning architectural shading features.