ATRONOMY – OLAR PHYIC (28) CALCULATOR
Shadow Length
A precise tool.
What is the Shadow Length & How does it work?
The altitude of the Sun above the horizon determines how long shadows appear on the ground. When the Sun is low, its rays strike objects at a shallow angle, producing long shadows; as the Sun climbs higher, shadows become shorter. Geometrically, the Sun, the top of an object, and the tip of its shadow form a right‑angled triangle. The object’s height is the side opposite the Sun‑altitude angle, while the shadow length is the adjacent side. Trigonometry relates these sides through the tangent function. Knowing shadow length is useful in fields such as solar panel positioning, architectural design, and even archaeological dating, where the angle of the Sun at a historic time can be inferred from ancient shadows.
L = \frac{H}{\tan \alpha}
L = shadow length, H = object height, \alpha = sun altitude angle
Parameters
Result
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Frequently Asked Questions
How do I calculate shadow length using this tool?
Enter the object's height and the Sun's altitude angle to get the shadow length.
What is the relationship between Sun altitude and shadow length?
As the Sun's altitude increases, shadows become shorter. Conversely, lower altitudes result in longer shadows.
Can this calculator be used for any object?
Yes, it can be used for any object as long as you know its height above the ground.
How accurate is this shadow length calculation?
The accuracy depends on precise measurements of the Sun's altitude and the object's height. Small errors in these values will affect the result.
Is there a formula behind this calculator?
Yes, the formula used is based on trigonometry: shadow length = object height / tan(Sun altitude angle).
Can I use this calculator for solar eclipse predictions?
No, this calculator is specifically for determining shadow lengths and not for predicting eclipses.
What units should I use when entering values?
Use consistent units for both height and angles. Typically, heights are in meters or feet, and angles are in degrees.
Results are for informational purposes only and do not constitute professional advice.