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Vertical Drop & Angle of Depression Calculator

Find a downward sight-line angle from vertical drop and horizontal separation, or solve for either distance.

  • Formula & worked example
  • Private in your browser
  • No signup
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A vertical drop of 10 m across a horizontal separation of 10 m gives a 45° angle of depression. The angle is measured downward from the horizontal.

Angle of depression = atan(vertical drop ÷ horizontal distance)

Worked example

Enter these known values and leave the other values blank.

Vertical drop
10 m
Horizontal separation
10 m
Angle below horizontal
45 deg

Assumptions and limitations

  • Uses a flat right-triangle model. Horizontal separation must be positive and vertical drop can be zero.
  • Enter horizontal separation, not the slanted line-of-sight distance. Heights must share the same vertical reference.
  • Earth curvature, refraction, observer eye height and terrain profiles are not added automatically. This does not assess structural or access-code compliance.

Common questions

Can the angle of depression be zero?

Yes. When both points have the same height and their horizontal separation is positive, the vertical drop and angle are zero.

How do I find a drop from the angle?

Leave Vertical drop blank and enter the angle plus horizontal separation. For 45° across 10 m, the drop is 10 m.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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