Vertical Angle Calculator | Find the Angle of Elevation or Depression

Vertical Angles are formed by two intersecting lines or rays. In trigonometry, vertical angles play a crucial role in various calculations, especially in determining distances or heights using known angles or sides. The formula for calculating the vertical angle involves the use of tangent inverse or arctan function in trigonometry.

Vertical Angle Calculator – Instantly Find the Angle of Elevation or Depression

Calculation Type Find Angle (degrees) Find Height (vertical rise) Find Horizontal Distance

Horizontal Distance (m)

Distance along the ground between observer and object.

Vertical Height Difference (m)

Difference in height between observer and object.

Angle (°)

Angle of elevation (up) or depression (down) from observer to object.

Example Presets:

Angle to Top of Building: 50m away, 20m tall Find Height: 30° elevation, 40m away Find Distance: 10m hill, 15° depression Steep Slope: 8m rise, 12m run Gentle Ramp: 2° angle, 25m distance

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To calculate the vertical angle, two inputs are crucial: the height and the distance. The height represents the vertical distance, and the distance denotes the horizontal separation between the observer and the object.

Formula for Vertical Angle Calculation

The formula used for calculating the vertical angle is:

Vertical Angle = arctan ( Height / Distance ​)

where:

• arctan⁡arctan denotes the inverse tangent function.
• HeightHeight is the vertical distance from the observer to the object.
• DistanceDistance is the horizontal separation between the observer and the object.

The result obtained from the formula is in radians. To convert it to degrees, multiply the result by 180​/π, where π is approximately 3.14159.

Using the Vertical Angle Calculator

This calculator simplifies the process of computing vertical angles. Simply input the height and distance values, then press the “Calculate” button. The calculator will instantly provide the vertical angle in degrees.