Angle of Depression Calculator

Calculate the angle of depression from an observer to a point on the ground using height and distance measurements

Input Parameters

Calculation Results

Calculation Formula

tan(θ) = height / distance

Where:
θ = Angle of Depression
height = Observer's height above the ground
distance = Horizontal distance from observer to the point on the ground

Angle of Depression Calculator Calculator Usage Guide

Learn how to use the Angle of Depression Calculator and its working principles

What is the Angle of Depression?

The angle of depression is the angle formed between a horizontal line from the observer's eye level and the line of sight to an object below the observer. This concept is commonly used in surveying, astronomy, and various real-world applications where determining the height of objects or distances is necessary.

How to Use the Calculator

  1. Enter the height of the observer above the ground in meters (m).
  2. Enter the horizontal distance from the observer to the point on the ground in meters (m).
  3. Click the "Calculate" button to compute the angle of depression.
  4. The results will be displayed in both degrees and radians.

Principle Behind the Calculation

The angle of depression can be calculated using trigonometry. When you form a right triangle with:

  • The height as the opposite side
  • The horizontal distance as the adjacent side

The tangent of the angle θ is equal to the opposite side divided by the adjacent side:

tan(θ) = height / distance

From this, we can find the angle θ using the arctangent function:

θ = arctan(height / distance)

Example Application

Imagine you are standing on a cliff 50 meters high and you see a boat in the ocean at a horizontal distance of 100 meters from the base of the cliff. Using this calculator with height = 50m and distance = 100m, you can determine that the angle of depression to the boat is approximately 26.5651 degrees.