Shadow Length Calculator

Calculate the length of a shadow based on object height, distance from light source, and angle of light

Input Parameters

Calculation Results

Shadow Length (meters)

--

Calculation Formula

Shadow Length = Object Height × tan(90° - Light Angle)

Where:
Object Height: Height of the object casting the shadow
Light Angle: Angle between the light source and the horizontal plane
tan: Tangent trigonometric function

Shadow Length Calculator Usage Guide

Learn how to use the Shadow Length Calculator and understand the underlying principles

How to Use This Calculator

  1. Enter the height of the object that is casting the shadow (e.g., a person, a tree, a building)
  2. Enter the horizontal distance from the base of the object to the light source
  3. Enter the angle of the light source relative to the horizontal plane (90° would be directly overhead)
  4. Click the "Calculate" button to see the shadow length

Understanding the Formula

The calculator uses the following formula to calculate shadow length:
Shadow Length = Object Height × tan(90° - Light Angle)

This formula works because the shadow forms a right triangle with the object and the light ray. The tangent of an angle in a right triangle is equal to the opposite side (shadow length) divided by the adjacent side (distance from object to light source). By rearranging this relationship, we get the formula above.

Practical Applications

This calculator can be used for various real-world applications including:

  • Determining the height of objects without direct measurement
  • Planning outdoor lighting installations
  • Understanding how sunlight patterns change throughout the day
  • Astronomy: Calculating the size of celestial bodies based on shadow observations

Important Note: This calculator assumes a simple geometric model and doesn't account for atmospheric refraction, ground curvature, or other real-world factors that might affect shadow length.