Angle of Depression Calculator

The Angle of Depression Calculator finds the angle between a horizontal line of sight and a downward line to an object below. Enter vertical and horizontal distances, or solve for any missing value using inverse trigonometry.

Angle of depression formula

From a right triangle formed by vertical drop and horizontal distance:

$$\alpha = \arctan\left(\frac{\text{vertical}}{\text{horizontal}}\right)$$

Line-of-sight distance $d$ can be found with the Pythagorean theorem or:

$$d = \frac{\text{vertical}}{\sin(\alpha)} = \frac{\text{horizontal}}{\cos(\alpha)}$$

The angle of depression equals the angle of elevation when viewed from the lower point. Maximum angle of depression is $90°$ (looking straight down).

Frequently Asked Questions

What is the angle of depression?

It is the angle measured downward from the horizontal to a line of sight toward an object at a lower elevation. Surveyors and construction crews use it for grade and sight-line calculations.

Is angle of depression the same as angle of elevation?

They have the same magnitude when two observers look at each other from different heights. Depression is measured down from horizontal; elevation is measured up from horizontal.

What is the maximum angle of depression?

90 degrees. At that angle you are looking straight down. Practical field measurements stay well below 90 degrees.

How do I find horizontal distance from angle and height?

Use horizontal = vertical / tan(angle). If you know line-of-sight distance instead, use horizontal = distance × cos(angle).

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Angle of Depression Calculator