How the shadow formula works
Shadow length follows a simple trigonometric relationship: length = height / tan(solar altitude). At solar noon the altitude is highest, so shadows are shortest. Near sunrise and sunset, the altitude approaches zero and shadows stretch toward infinity.
Shadow direction is opposite the sun: direction = solar azimuth + 180°. At solar noon in the northern hemisphere, the sun is due south, so shadows point north.
This calculator uses the same solar position algorithm as the Golden Hour tool (NOAA/Meeus), applied in real time as you drag the scrubber. No API calls, no delay.