Angle of Depression Calculator

Angle of Depression Calculator — enter height and horizontal distance to instantly find the angle in degrees and radians.

Vertical distance (height/depth)

Please enter a number greater than zero.

Horizontal distance

Please enter a number greater than zero.

Angle of Depression

0.000°

0.000 rad

Line of Sight (Hypotenuse)

0.000 m

Tangent (tan θ)

0.000

Percent Slope

0.000%

Calculation Steps

1. Calculate the ratio of vertical to horizontal distance:

Vertical / Horizontal = 0 / 0 = 0

2. Find the angle using arctangent (inverse tangent):

atan(0) = 0° (0 radians)

3. Calculate the hypotenuse using Pythagorean theorem:

√(Vertical² + Horizontal²) = √(0² + 0²) = 0

4. Calculate the percent slope:

(Vertical / Horizontal) × 100% = (0 / 0) × 100% = 0%

Precision: Result unit:

How it works

The angle of depression is calculated using the trigonometric relationship between the vertical height (opposite side) and horizontal distance (adjacent side). The formula is:

tan(θ) = opposite / adjacent = vertical distance / horizontal distance

To find the angle θ, we use the inverse tangent function:

θ = atan(vertical / horizontal)

Worked example

For a vertical distance of 1.5 meters and horizontal distance of 3.0 meters:

tan(θ) = 1.5 / 3.0 = 0.5
θ = atan(0.5) = 26.565° (0.463648 radians)
Hypotenuse = √(1.5² + 3.0²) = √(2.25 + 9) = √11.25 = 3.354 meters
Slope = (1.5 / 3.0) × 100% = 50%

Angle of Depression vs Angle of Elevation

The angle of depression is the angle between the horizontal line of sight and the line of sight downward to an object. The angle of elevation is the angle between the horizontal and the line of sight upward to an object. Both angles are equal when measured from complementary positions.

Frequently asked questions

What is the angle of depression?

The angle of depression is the angle between the horizontal line of sight and the line of sight downward to an object. It is commonly used in surveying, navigation, and construction to determine the steepness of a slope or the height of an object.

How is the angle of depression calculated?

The angle of depression is calculated using the inverse tangent (arctangent) of the ratio between the vertical distance (height or depth) and the horizontal distance: θ = atan(vertical / horizontal).

What's the difference between angle of depression and angle of elevation?

The angle of depression is measured downward from the horizontal, while the angle of elevation is measured upward from the horizontal. When two people are looking at each other from different heights, the angle of depression from the higher point equals the angle of elevation from the lower point.

Can the angle of depression be greater than 90 degrees?

No, the angle of depression is always between 0 and 90 degrees. An angle of 0° means looking straight ahead horizontally, while 90° means looking straight down vertically.

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