Angle of Elevation Calculator
This angle of elevation calculator turns a height difference and a horizontal distance into the viewing angle. Example: a target 30 m higher and 40 m away is seen at an angle of elevation of 36.8699°.
Source: Wikipedia – Angle of elevation (Horizontal coordinate system). Updated: .
How it is calculated
The angle of elevation is the angle between the horizontal and the line of sight upwards to a target, such as a tower top. Looking down, it is called the angle of depression.
Working
The observer, the point on the ground below the target and the target form a right triangle. The height difference h is the side opposite the angle, the horizontal distance d the adjacent side. So tan α = h / d. The angle follows from α = arctan(h / d); from a known angle you get h = d · tan α and d = h / tan α. The line of sight is the hypotenuse s = √(h² + d²).
Worked examples
A target is 30 m higher and 40 m away: tan α = 30 / 40 = 0.75, so α = 36.8699°, the line of sight is 50 m long and the slope is 75%. How tall is a tree seen at 35° from 50 m away? h = 50 · tan 35° = 35.0104 m, plus eye height. From a 45 m tower a ship is seen at an angle of depression of 20°: d = 45 / tan 20° = 123.636 m.
- Angle of elevation and angle of depression are equal because they are alternate angles between parallels.
- The angle must lie between 0° and 90°.
- Slope in percent is tan α · 100.
Frequently asked questions
How do you calculate the angle of elevation?
With α = arctan(h / d). For a 30 m height difference and 40 m distance, α = arctan(0.75) = 36.8699°.
What is the difference between angle of elevation and depression?
Elevation measures looking up, depression looking down. Over the same distance both have the same size.
How do I find the height from the angle?
h = d · tan α. At 35° and 50 m away that is 35.0104 m; add the eye height afterwards.
Sources and legal basis
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