Angle of Depression Calculator
Calculate angle of depression for surveying, construction, and trigonometry applications
Calculate Angle of Depression
α = arctan(v/h)
From vertical & horizontal distances
h = v / tan(α)
From vertical distance & angle
v = h × tan(α)
From horizontal distance & angle
Height difference between observer and object
Ground distance between observer and object
ℹ️ Enter both vertical and horizontal distances to calculate the angle of depression
Calculation Results
Formula used:
• Angle of depression: α = arctan(0.00 / 0.00) = 0.00°
• Line of sight: d = √(v² + h²) = √(0.00² + 0.00²) = 0.00 meters
Example Calculation
Playground Slide Example
Scenario: Boy on top of slide looking down at girl on ground
Vertical distance: 1.5 meters (height difference)
Horizontal distance: 3.0 meters (ground distance)
Question: What is the angle of depression?
Step-by-step Calculation
1. Given: vertical = 1.5m, horizontal = 3.0m
2. Formula: α = arctan(vertical / horizontal)
3. Calculate: α = arctan(1.5 / 3.0) = arctan(0.5)
4. Result: α = 26.565°
5. Line of sight: d = √(1.5² + 3.0²) = √(2.25 + 9) = √11.25 = 3.35 meters
Answer: The angle of depression is 26.565° with a line of sight of 3.35 meters
Surveying Instruments
Theodolite
Precision angle measurement
±1 second accuracy
Clinometer
Slope angle measurement
Portable and accurate
Inclinometer
Digital angle measurement
Uses accelerometer
Common Applications
Angle Ranges
0° - 30°
Gentle slopes, roads
30° - 60°
Moderate slopes, roofs
60° - 90°
Steep slopes, cliffs
90°
Straight down (maximum)
Understanding Angle of Depression
What is Angle of Depression?
The angle of depression is the angle between the horizontal and the part of a line that is below the horizontal. It's measured from the horizontal downward to the line of sight of an object below the observer.
Key Characteristics
- •Always measured downward from horizontal
- •Range from 0° to 90°
- •Complementary to angle of elevation
- •Used in surveying and navigation
Mathematical Formulas
Angle Calculation
α = arctan(vertical / horizontal)
From two distances
Distance Calculations
h = v / tan(α)
v = h × tan(α)
From angle and one distance
Line of Sight
d = √(v² + h²)
d = v / sin(α) = h / cos(α)
Direct distance to object
Relationship with Angle of Elevation
Important: The angle of depression from one point equals the angle of elevation from the other point.
If Person A looks down at Person B with a 30° angle of depression, then Person B looks up at Person A with a 30° angle of elevation. These are alternate angles formed by parallel lines (horizontal at each person's eye level) and a transversal (line of sight).