Shadow Length Calculator By Date

Shadow Length Formula:

\[ Shadow = \frac{Height}{\tan(Sun\ Altitude\ on\ Date)} \]

Shadow Length:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Shadow Length Calculation?

Shadow length calculation determines the length of a shadow cast by an object based on its height and the sun's altitude angle. This is useful in architecture, photography, solar energy planning, and various outdoor activities.

2. How Does the Calculator Work?

The calculator uses the trigonometric formula:

\[ Shadow = \frac{Height}{\tan(Sun\ Altitude)} \]

Where:

\( Height \) — Height of the object in meters
\( Sun\ Altitude \) — Angle of the sun above the horizon in degrees
\( \tan \) — Tangent trigonometric function

Explanation: The tangent of the sun's altitude angle represents the ratio of the object's height to its shadow length.

3. Importance of Shadow Length Calculation

Details: Accurate shadow length calculation is crucial for architectural design, solar panel placement, photography lighting planning, and understanding seasonal sun patterns for various applications.

4. Using the Calculator

Tips: Enter the object height in meters and the sun's altitude angle in degrees (0-90). The sun altitude can be determined by date, time, and location using astronomical tables or apps.

5. Frequently Asked Questions (FAQ)

Q1: How do I find the sun's altitude for a specific date?
A: Use astronomical calculators, mobile apps, or online tools that provide sun position data based on date, time, and geographic location.

Q2: Why does the shadow length change throughout the day?
A: The sun's altitude changes throughout the day, being lowest at sunrise/sunset (longer shadows) and highest at solar noon (shortest shadows).

Q3: How does season affect shadow length?
A: In winter, the sun is lower in the sky, creating longer shadows. In summer, the sun is higher, resulting in shorter shadows.

Q4: What is the maximum possible shadow length?
A: Theoretically infinite as the sun approaches the horizon (0° altitude), but practically limited by atmospheric refraction and other factors.

Q5: Can this calculator be used for artificial light sources?
A: Yes, the same trigonometric principles apply to any light source, though the calculations assume a point light source at infinity (parallel light rays).