Calculate the angle of depression from height and horizontal distance, or find a missing side given the angle.
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How to use
Choose a mode: find the angle of depression from height and distance, or find a missing measurement given the angle. The angle of depression is measured downward from the horizontal line of sight.
Also in Triangles
Trigonometry
The angle of depression calculator finds the angle formed between the horizontal line of sight and the line from an observer down to a lower object. Enter height and horizontal distance to get the angle, or enter the angle to find a missing side.
The angle of depression is the angle between a horizontal line from the observer and the line of sight downward to an object below. It equals the angle of elevation measured from the object looking up, because they are alternate interior angles formed by a transversal crossing two parallel horizontal lines.
The angle is always measured from the horizontal, not from the vertical. A larger angle of depression means the object is more steeply below the observer.
Using right-triangle trigonometry, the angle of depression θ = arctan(opposite / adjacent) = arctan(height / horizontal distance). If you know the angle and one side, you can solve for the other side.
Angle of depression is used in surveying, aviation, and navigation. Pilots use it to calculate descent paths, and surveyors use it to measure elevations of distant points from a known height.
Frequently asked questions
They are equal in magnitude when measured between the same two points. The angle of depression is measured downward from the horizontal at the higher point; the angle of elevation is measured upward from the horizontal at the lower point.
45 degrees. When the opposite and adjacent sides are equal, arctan(1) = 45°.
Related
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
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Calculate sine, cosine, and tangent ratios for a right triangle from side lengths or find missing sides from an angle.
