GEOGRAPHY & CARTOGRAPHY CALCULATOR
Timeshadow Length
A precise tool.
What is the Timeshadow Length & How does it work?
The length of a shadow cast by a vertical object depends on the object’s height and the Sun’s elevation above the horizon. As the Sun rises, its rays strike the object at a steeper angle, shortening the shadow.
In geometric terms, the Sunβobjectβshadow relationship forms a rightβangled triangle where the object’s height is the opposite side and the shadow length is the adjacent side. The angle between the Sun’s rays and the ground is the solar elevation angle, often denoted u03b1.
Using trigonometry, the shadow length L can be expressed as the ratio of the height h to the tangent of u03b1. This simple formula enables quick estimation of shadow extents for planning solar panels, architecture, or outdoor activities.
L = \frac{h}{\tan\alpha}
L = shadow length, h = object height, \alpha = solar elevation angle
Parameters
Result
β
Frequently Asked Questions
How do I calculate the shadow length if I know the object's height and solar elevation?
Use the formula: Shadow Length = Height / tan(Ξ±), where Ξ± is the solar elevation angle in degrees.
What happens to the shadow length as the Sun rises higher in the sky?
As the Sun rises, its rays strike the object at a steeper angle, reducing the shadow length.
Can this calculator be used for any vertical object?
Yes, this formula applies to any vertical object, such as a tree, building, or flagpole.
What is the solar elevation angle at noon on the equator during the summer solstice?
The solar elevation angle at noon on the equator during the summer solstice is approximately 90 degrees minus the latitude of the location.
How does the shadow length change with different seasons?
The shadow length changes with the seasons due to variations in the Sun's position relative to the Earth. It is longest during the winter solstice and shortest during the summer solstice.
Results are for informational purposes only and do not constitute professional advice.