Angle of Elevation Calculator

Please enter the height of the object & your horizontal distance from it to calculate the angle of elevation.

To Calculate:

Angle of Elevation

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Angle of Elevation

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“Angle of Elevation Calculator”

Use this angle of elevation calculator to determine the angle formed between a horizontal line of sight and an object above it. By entering measurements such as height and horizontal distance, you can quickly calculate the angle of elevation.

With this calculator, you can find:

Angle of Elevation (θ)
Horizontal Distance (run)
Vertical Height (rise)
Elevation Grade & its Percentage

What Is Angle of Elevation?

The angle of elevation is the angle formed between a horizontal line of sight and the line of sight to an object located above that horizontal line.

angle of elevation

It represents the upward tilt from your eyes needed to see an object. The angle of elevation is widely used in surveying, astronomy, navigation, and architecture to determine heights and distances.

How to Calculate Angle of Elevation

Use the formula:

\(\text{Angle of Elevation} = \tan^{-1} \left( \frac{\text{height}}{\text{horizontal distance}} \right)\)

Or abbreviated:

\(AOE = \tan^{-1} \left( \frac{h}{d} \right)\)

Angle of Elevation Examples

Example 1:

Find the angle of elevation for an object with:

Horizontal Distance = 290 ft
Vertical Height = 134 ft

Solution:

\(\text{Angle of Elevation} = \tan^{-1}\left(\dfrac{134}{290}\right) = \tan^{-1}(0.462) = 24.8^\circ\)

Converting to radians:

\(Radians = 24.8^\circ \times \frac{\pi}{180} \approx 24.8 \times 0.01745 = 0.432 \text{ radians}\)

Example 2:

Standing at point P, you observe a bird at point Q with an angle of elevation of \(45^\circ\). If the horizontal distance to the bird is 10 meters, what is its height?

Solution:

\(\text{Vertical Height} = h = \tan(45^\circ) \times 10 = 1 \times 10 = 10 \text{ meters}\)