Angle of Elevation Calculator

Calculate the angle of elevation and angle of depression by entering the vertical height (rise) and horizontal distance (run) below.

Angle of Elevation:

Degrees:
 
Radians:
 
Learn how we calculated this below


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How to Calculate the Angle of Elevation

Angle of elevation is the positive, or upwards, angle of a line of sight from an observer to an object. For instance, if you were standing outside looking up at a tree, the angle of elevation is the angle your head would need to look up at the top of the tree.

graphic showing the angle of elevation for an observer and object

You can calculate the angle of elevation using trigonometry. Considering that the line of sight and the horizontal baseline form a right triangle, you can use a common formula to calculate the angle of elevation.

Angle of Elevation Formula

The triangle formula to calculate the angle of elevation is:

tan(θ) = opposite ÷ adjacent

The tangent of the angle θ is equal to the opposite side divided by the adjacent side. If you substitute the vertical height and horizontal distance of the object into this formula, you can calculate the angle of elevation.

tan(angle of elevation) = rise ÷ run

The tangent of the angle of elevation is equal to the vertical height (rise) divided by the horizontal distance (run).

Using the inverse tangent, you can isolate the angle of elevation on one side of the formula:

angle of elevation = atan(rise ÷ run)

Thus, the angle of elevation is equal to the inverse tangent of the vertical height (rise) divided by the horizontal distance (run).

Angle of Elevation vs. Angle of Depression

If the vertical height of the object is negative, then the angle is referred to as the angle of depression. A practical example of an angle of depression is the angle of an airline pilot looking down at a runway while landing an airplane.

graphic showing the angle of depression for an observer and object

You’ll probably also be interested in our elevation grade calculator.