Angle Of Depression Calculator

Math

The Angle of Depression Calculator finds how far below the horizontal you look down to an object, from the vertical drop and the horizontal distance. The formula used is: angle of depression = arctan(vertical drop ÷ horizontal distance).

Formula

Angle of Depression = arctan(Vertical Drop ÷ Horizontal Distance)
  • The Angle of Depression Calculator updates instantly when you change either distance.
  • Formula: angle of depression = arctan(vertical drop ÷ horizontal distance)
  • Input definitions: • Vertical Drop: how far the target is below your eye level • Horizontal Distance: the level distance out to the target
  • The angle of depression equals the angle of elevation measured from the target back up to you (they are alternate angles).
  • Use the same unit for both distances; the resulting angle is unit-independent.
  • Practical tip: a drop of 12 m over 35 m of horizontal distance gives a shallow downward angle of about 19°.

Example Calculation

Inputs
  • Vertical Drop (m): 12
  • Horizontal Distance (m): 35

Looking down a 12 m drop over 35 m of horizontal distance: angle = arctan(12 ÷ 35) ≈ 18.92° (about 0.330 radians).

Frequently asked questions

What is the angle of depression?
It is the downward angle between the horizontal and your line of sight to an object below you. It equals arctan(vertical drop ÷ horizontal distance).
How is it related to the angle of elevation?
They are equal. The angle of depression from you to a lower object matches the angle of elevation from that object back up to you.
What units should I enter?
Enter the vertical drop and horizontal distance in the same length unit. The angle is returned in degrees and radians.
When would I use this?
In trigonometry problems, surveying, navigation, and aviation — anywhere you sight down to a lower point.
How accurate are the results?
The angle is computed exactly from the two distances and rounded only for display.
How can I verify the calculation manually?
Use the displayed formula and work through the numbers step by step. If your manual result differs slightly, check rounding and unit conversions first.
Can I use this for planning and budgeting?
Yes. Run best-case, expected, and worst-case inputs to compare outcomes and make safer planning decisions.