Angle of Depression Calculator
Enter any two of horizontal distance, your height above the object and the angle. We solve the third and show the working.
Angle of depression
—°
How it works
From a high point, your horizontal line of sight, the vertical drop to the object's level and your line of sight to the object form a right triangle. The angle of depression is measured down from your horizontal; tan θ equals the height difference divided by the horizontal distance.
Example
From a lookout 200 ft above a lake, a boat is at an angle of depression of 10°. Distance = 200 ÷ tan 10° ≈ 1,134 ft, and the line of sight is about 1,152 ft.
Related tools
Frequently asked questions
What is the angle of depression?
The angle between the horizontal and your line of sight when you look down at something, for example from a cliff, a tower or a plane.
Is the angle of depression equal to the angle of elevation?
Yes, for two points looking at each other. The horizontal lines at the two points are parallel, so the angles are alternate interior angles and equal.
What is the formula?
tan θ = height difference ÷ horizontal distance, the same as for the angle of elevation, measured downward from your horizontal.
How do I find how far away a boat is from a cliff?
Measure the angle of depression to the boat and know your height above the water; then distance = height ÷ tan θ. Choose "Distance" under Solve for.
Sources
Results are calculated from your inputs with the formulas shown on this page; no outside data is used.
How each number is produced: methodology and data sources.