Angle of Depression Calculator (from height & distance, or find distance / height)

Understanding the angle of depression calculator — concept and principle

This calculator finds the angle of depression from a height and a horizontal distance, or finds the distance or the height from the angle. It also gives the line-of-sight distance and the gradient. Use it for trigonometry problems, surveying sketches, drone or lighthouse questions, and checking slopes.

The angle is measured down from the horizontal; it equals the elevation angle from below.

How it is calculated

tan θ = h ÷ d

θ = arctan(h ÷ d); d = h ÷ tan θ; h = d × tan θ

Line-of-sight distance = √(h² + d²)

Gradient (%) = h ÷ d × 100

h = height of the observer above the object, d = horizontal distance; use the same unit for both.
The angle of elevation from the object back to the observer equals the angle of depression.

The principle

The angle of depression is measured downward from the horizontal line through the observer's eye to the line of sight to an object below. The height, the horizontal distance and the line of sight form a right triangle, so the tangent of the angle is the opposite side over the adjacent side. Because the horizontal at the top and the horizontal at the bottom are parallel, the angle of depression and the angle of elevation are alternate angles and therefore equal.

Worked example

Default inputs: find the angle; height 30 m, horizontal distance 120 m.

tan θ = 30 ÷ 120 = 0.25.
θ = arctan 0.25 = 14.04°.
Line of sight = √(30² + 120²) = √15,300 = 123.69 m.
Gradient = 30 ÷ 120 × 100 = 25 %.
The angle of elevation from the object is also 14.04°.

Each point is the calculator re-run with only “Horizontal distance to the object (m)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Horizontal distance to the object (m)	Answer
30	45°
60	26.57°
90	18.43°
120	14.04°
150	11.31°
180	9.46°
240	7.13°

How to read the result

Small angles mean the object is far away compared with the height; 45° means distance equals height. Note that a 25 % gradient is only about 14°: percent slope and degrees are not the same scale. In the "find distance" mode, small angles make the result very sensitive: an error of half a degree at 5° changes the distance by about 10 %.

Common mistakes

Measuring the angle from the vertical instead of the horizontal.
Mixing units for height and distance.
Using the line-of-sight distance as if it were the horizontal distance.
Leaving the calculator in radians when working by hand.

Keep in mind: The model is a flat right triangle. Over long distances at sea or across land, Earth's curvature and refraction are ignored; real surveys need proper instruments and methods.

Frequently asked questions

Is the angle of depression equal to the angle of elevation?

Yes, they are alternate angles between parallel horizontals.

How do I find the distance from a lighthouse?

Use d = h ÷ tan θ with the lighthouse height above the water and the measured angle of depression.

What angle is a 100 % slope?

45°, because the rise equals the run.

Sources: OpenStax, Algebra and Trigonometry 2e (2021), §7.2 Right Triangle Trigonometry

Checked 9 Nov 2026. OpenStax, Algebra and Trigonometry 2e (2021), §7.2 Right Triangle Trigonometry — “Using Right Triangle Trigonometry to Solve Applied Problems” (angle of depression: the angle between the horizontal and the line from the object to the observer’s eye, for an object below the observer).

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