Apparent Angle Calculator

Calculate the apparent angle of elevation of an object based on the observer's height and distance. Useful for astronomy, surveying, and outdoor activities.

Input Parameters

Calculation Results

Apparent Angle of Elevation

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Degrees

Calculation Formula

α = arctan((h₂ + h₁) / d)

Where:
α = Apparent Angle of Elevation
h₁ = Observer's Height
h₂ = Object Height
d = Distance to Object

Apparent Angle Calculator Calculator Usage Guide

Learn how to use the Apparent Angle Calculator and understand its applications.

How to Use This Calculator

  1. Enter the observer's height in meters (your height from the ground when viewing the object).
  2. Enter the height of the object you're observing in meters.
  3. Enter the horizontal distance to the object in meters.
  4. Click the "Calculate" button to compute the apparent angle of elevation.
  5. The result will show the angle in degrees above the horizontal line.

Principle and Applications

The apparent angle of elevation is the angle between the horizontal line of sight and the line of sight to an object at a certain height. This calculator accounts for the observer's own height, providing a more accurate measure of how high the object appears above the horizon.

This concept is useful in various fields:

  • Astronomy: Determining the angle above the horizon for stars or planets.
  • Surveying: Calculating the height of tall structures from a distance.
  • Outdoor Activities: Estimating the height of trees, buildings, or mountains.
  • Navigation: Determining the elevation of landmarks.

Example

If you are standing 1.5 meters tall and are looking at a tree that is 10 meters high from a distance of 50 meters, the apparent angle of elevation would be approximately 11.31 degrees.