Calculate distance, object height, or angle from any two values, or find slope angle and percent grade from horizontal run and vertical rise.
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Distance To Angle Formula
The following formula is used to calculate the angle of elevation to an object.
θ = atan(H / D)
Variables:
- θ is the angle of elevation (degrees)
- H is the height of the object (meters)
- D is the distance to the object (meters)
To calculate the angle of elevation, use the arctangent function (atan) on the ratio of the object’s height to the distance to the object. The result is then converted from radians to degrees.
| Distance (m) | Angle (degrees) |
|---|---|
| 0.5 | 63.435 |
| 0.75 | 53.130 |
| 1 | 45.000 |
| 1.5 | 33.690 |
| 2 | 26.565 |
| 3 | 18.435 |
| 4 | 14.036 |
| 5 | 11.310 |
| 7.5 | 7.595 |
| 10 | 5.711 |
| 12 | 4.764 |
| 15 | 3.814 |
| 20 | 2.862 |
| 25 | 2.291 |
| 30 | 1.909 |
| 40 | 1.432 |
| 50 | 1.146 |
| 75 | 0.764 |
| 100 | 0.573 |
| 200 | 0.286 |
| Assumes object height h = 1.00 m. Formula: θ = arctan(h / d). θ shown in degrees. | |
What is the Angle of Elevation?
The angle of elevation is the angle between the horizontal line from the observer to the object and the line of sight from the observer to the object. It is used in various fields such as surveying, navigation, and even photography to determine the position of an object in relation to the observer’s point of view.
How to Calculate the Angle of Elevation?
The following steps outline how to calculate the angle of elevation.
- First, determine the height of the object (H) in meters.
- Next, determine the distance to the object (D) in meters.
- Next, gather the formula from above θ = atan(H / D).
- Finally, calculate the angle of elevation (θ) in degrees.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
height of the object (H) = 5 meters
distance to the object (D) = 10 meters
