How to Estimate Shadow Length From the Sun Angle
When the sun is 45 degrees above the horizon, an upright object's shadow is as long as the object is tall. At 15 degrees, the shadow is about 3.7 times its height. A modest change in a low sun angle can make a large difference on the ground.
Suppose you want a two-metre-tall subject's shadow to fit inside a four-metre patch of pavement. At 30 degrees, it is about 3.46 metres long and fits. At 15 degrees, it stretches to about 7.46 metres. The composition that works earlier in the afternoon may run out of room near sunset.
The formula in plain terms
shadow length = object height ÷ tan(sun elevation)
Use the same length unit throughout: metres produce metres, feet produce feet. Set a calculator to degrees when entering an angle such as 30°. In code that expects radians, convert first: radians = degrees × π ÷ 180.
| Sun elevation | Shadow ÷ height | Shadow for a 2 m object |
|---|---|---|
| 15° | 3.73 | 7.46 m |
| 30° | 1.73 | 3.46 m |
| 45° | 1.00 | 2.00 m |
| 60° | 0.58 | 1.15 m |
Length and direction are separate questions
Elevation is the angle above the horizon. It determines the length in this model. The sun's compass direction, or azimuth, determines where the shadow points: approximately 180 degrees opposite the sun.
If the sun is to the southwest, the shadow falls toward the northeast. Knowing its length without its direction will not tell you whether it crosses the road, reaches a wall or enters your frame.
Why low angles deserve extra care
Near the horizon, the denominator becomes small and the calculated shadow becomes very long. A small angle error then creates a large length error. At exactly zero degrees this simple expression is undefined. It does not predict a visible, infinitely long shadow.
Atmospheric effects, an obstructed horizon and diffuse light can make the observed edge less clear. Use a low-angle estimate to allow extra space, then inspect the actual scene.
A location-planning workflow
- Choose the subject and ground. Estimate its upright height and check whether the surface is level.
- Check the date and time. Solar position changes through the day and across the year.
- Estimate length and direction. Mark the rough endpoint on a map or scout photograph.
- Check obstructions. Buildings, trees and overhangs may block direct sun before the astronomical sunset.
- Confirm on location. Keep a note of the time, camera position and usable patch of light for a return visit.
Where the model stops working
The formula assumes an upright object, level ground and direct sunlight. A hillside changes the receiving surface; stairs interrupt it; a leaning object changes the triangle. A building can put the whole scene in shade even when the sun is high enough for the calculation.
For photography, a rough estimate is often enough to decide where to stand. For surveying or engineering, the missing geometry matters and should be included.
Method and further reading
The curve uses 1 ÷ tan(angle) from 10° to 80°. Download its calculated values. NOAA's solar calculator describes elevation and azimuth; its page states that the tool is no longer actively maintained, so confirm the solar-position source you use.
Photospots helps with location planning. Pair a time-of-day plan with a scout visit and a photograph of the actual obstructions.