The angle of depression is measured downwards from a horizontal line at the observer’s eye to an object below – for example from a roof to a point on the ground, or from a lighthouse to a ship. It equals the angle of elevation measured from the object back up to the observer.
How to use the Angle of Depression Calculator
- Height difference
- Horizontal distance
- Every result field is editable: type into Angle of depression and Horizontal distance plus every other field update to match.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the height difference and the horizontal distance. Type an angle into the result to find the distance.
Tips for an accurate estimate
- Measure angles with a digital angle finder or sliding bevel, not by eye.
- Make a test cut in scrap before cutting expensive stock.
- Small angle errors add up over many joints – check the first assembly before cutting the rest.
- Keep a written list of the dimensions and angles you set on the saw or machine.
Common mistakes to avoid
- Reading the saw scale as the angle from the edge rather than from square.
- Rounding intermediate results too early.
- Mixing degrees and percent grade.
Inputs explained
| Field | What to enter |
|---|---|
| Height difference | Units: m, ft, cm, in, yd |
| Horizontal distance | Units: m, ft, cm, in, yd |
What each result means
- Angle of depression = deg(atan([Height difference]÷[Horizontal distance]))
- Line-of-sight distance = sqrt([Height difference]^2 + [Horizontal distance]^2)
- Slope = [Height difference]÷[Horizontal distance]×100
Example values
How the main result changes when Horizontal distance changes and everything else stays at the example values above:
| Horizontal distance (m) | Angle of depression (°) |
|---|---|
| 25 | 50.19 |
| 37.5 | 38.66 |
| 50 | 30.96 |
| 62.5 | 25.64 |
| 75 | 21.8 |
| 100 | 16.7 |
Formula
Angle = atan(height difference ÷ horizontal distance)Line of sight = √(h² + d²)Worked example
Inputs — Height difference: 30 m; Horizontal distance: 50 m.
Results — Angle of depression = 30.96 °; Line-of-sight distance = 58.31 m; Slope = 60 %.
Frequently asked questions
Is the angle of depression equal to the angle of elevation?
Yes – they are alternate angles between parallel horizontal lines.
How do I find the distance from the angle?
Distance = height ÷ tan(angle).
What formula does the Angle of Depression Calculator use?
Angle = atan(height difference ÷ horizontal distance).