To estimate a shadow’s length, divide the object’s height by the tangent of the sun’s elevation angle. In plain English: a low sun makes a very long shadow; a high sun makes a short one.
shadow length = object height ÷ tan(sun elevation)
| Sun elevation | Approximate shadow for a 6 ft / 1.8 m person |
|---|---|
| 15° | 22.4 ft / 6.7 m |
| 30° | 10.4 ft / 3.1 m |
| 45° | 6 ft / 1.8 m |
| 60° | 3.5 ft / 1.0 m |
Why photographers care
Shadow length decides whether a portrait subject has room to stand, whether a building facade is in shade, and whether a foreground shadow becomes a useful leading line or a giant accidental selfie-stick. It also explains why a location that looked perfect at 7 p.m. can be unusable at noon.
Elevation is measured upward from the horizon: sunrise and sunset are near 0°, a sun directly overhead is 90°. The direction of the shadow is the opposite of the sun’s compass bearing. The formula estimates a flat, level surface; hills, stairs and nearby buildings add their own small acts of sabotage.
Use the estimate, then scout the real scene
Math gives you a starting point, not a permit to skip the location. A tree, overhang or glass tower can create a second shadow with no respect for trigonometry. Save a note about the obstruction, the lens used and the time when the scene works. On the return visit, you have a plan rather than a hunch.
For a location you use often, compare the estimate with a photo taken at the same time of year. After two or three visits, you will know the site better than an astronomical table can.