Angle of Depression Calculator
Angle of Depression Calculator
To calculate Angle of Depression, input Height of observer above the ground and Horizontal Distance to object in calculator. Select your preferred units (feet, meters, or inches).
The calculator determines the Angle of Depression, Actual Distance to the object, and provides the corresponding Angle of Elevation from the object’s perspective.
How to Calculate Angle of Depression?
To calculate the Angle of Depression, measure the Vertical Height difference between the observer’s position and the object below. Measure the Horizontal Distance to the object.
Use the arctangent (inverse tangent) function with the ratio of height to horizontal distance. The formula uses Height divided by Distance to find the angle in degrees. This angle represents the downward tilt from the horizontal plane to the line of sight.
Formula for Angle of Depression Calculations
Basic Angle of Depression Formula:
θ = arctan(H/D)
where:
θ = Angle of Depression
H = Height difference
D = Horizontal distance
Actual Distance Formula:
Actual Distance = √(H² + D²)
where:
H = Height difference
D = Horizontal distance
Complementary Angle:
Angle of Elevation = Angle of Depression
when measured from object to observer
Example 1: Building Observation
- Observer Height = 100 feet
- Horizontal Distance = 150 feet
- Angle of Depression = 33.69 degrees
- Actual Distance = 180.28 feet
- Application = Building Surveillance
Example 2: Cliff Viewing
- Observer Height = 250 meters
- Horizontal Distance = 200 meters
- Angle of Depression = 51.34 degrees
- Actual Distance = 320.16 meters
- Application = Geological Survey
Example 3: Tower Measurement
- Observer Height = 75 feet
- Horizontal Distance = 50 feet
- Angle of Depression = 56.31 degrees
- Actual Distance = 90.14 feet
- Application = Construction Planning
Example 4: Drone Operation
- Observer Height = 120 meters
- Horizontal Distance = 300 meters
- Angle of Depression = 21.80 degrees
- Actual Distance = 323.11 meters
- Application = Aerial Photography
Example 5: Mountain Observation
- Observer Height = 500 meters
- Horizontal Distance = 400 meters
- Angle of Depression = 51.34 degrees
- Actual Distance = 640.31 meters
- Application = Topographical Survey
What is Angle of Depression?
The Angle of Depression is angle formed between the horizontal plane and the line of sight when looking downward at an object below the observer’s position. It is measured in Degrees from the horizontal reference line to the line of sight. The Angle of Depression is equal to the Angle of Elevation when viewed from the opposite perspective.