Calculate angle of elevation or depression from horizontal distance and vertical change, or solve for height, ground distance, grade, and line-of-sight length.

Solve right-triangle elevation geometry

Required: horizontal distance greater than zero and a vertical change. Use a negative vertical change for a drop or angle of depression.

Angle of elevation—
Horizontal distance—
Vertical change—
Line-of-sight distance—
Direction—
Grade—
Vertical : horizontal—
Calculation

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Interpretation

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This calculator assumes a right triangle, a level horizontal reference, a vertical height difference, and a straight line of sight. It does not account for ground curvature, atmospheric refraction, terrain changes, or instrument height.

Related Calculators

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 to Angle Conversion Table (h = 1.00 m)
Distance (m) Angle (degrees)
0.563.435
0.7553.130
145.000
1.533.690
226.565
318.435
414.036
511.310
7.57.595
105.711
124.764
153.814
202.862
252.291
301.909
401.432
501.146
750.764
1000.573
2000.286
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.

  1. First, determine the height of the object (H) in meters.
  2. Next, determine the distance to the object (D) in meters.
  3. Next, gather the formula from above θ = atan(H / D).
  4. Finally, calculate the angle of elevation (θ) in degrees.
  5. 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