Angle of Depression Calculator

This angle of depression calculator works out the angle between the horizontal and your line of sight down to a point below you, using right-triangle trigonometry rather than a protractor or guesswork. You enter two measurements: the horizontal distance from your position to the point, and the vertical height difference between you and that point. The calculator returns the angle of depression in degrees as the headline result, along with the same angle in radians and the line of sight distance, the straight-line hypotenuse between you and the point. The maths is straightforward: the height is the side opposite the angle and the horizontal distance is the adjacent side, so the tangent of the angle equals height divided by distance, and the angle itself is the arctangent of that ratio. This is the calculation surveyors use when sighting down from a cliff or tower, navigators use when fixing a bearing to a landmark, builders use when checking roof pitches or drainage falls, and anyone tracking a sight line to a lower point. Change the distance or the height and the results update straight away, so you can see how the angle grows as height increases or distance shrinks. The calculator assumes a level base line and a true right-angled triangle between your position, the point directly below the target, and the target itself, so keep your measurements consistent and remember results are only as accurate as the distances and heights you enter.

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Horizontal distance

Vertical height

Angle (radians)

Line of sight

The formula

The angle of depression theta satisfies tan(theta) = height / horizontal distance, so theta = arctan(height / distance). The line of sight is the hypotenuse, sqrt(distance^2 + height^2).

Worked example

With a horizontal distance of 10 and a height of 10, tan(theta) = 10 / 10 = 1, so theta = 45 degrees. Enter 10 and 10 above to confirm.

Frequently asked questions

What is the formula for the angle of depression?

theta = arctan(vertical height / horizontal distance). The tangent of the angle is the height divided by the horizontal distance.

What is the difference between elevation and depression?

Elevation is the angle looking up from the horizontal, depression is the angle looking down. The arithmetic is identical; only the direction differs.

What is the line of sight value?

The straight distance to the point, the hypotenuse, equal to sqrt(distance squared plus height squared).

Who this calculator is for

This calculator is for students, surveyors, builders and navigators measuring sight line angles.

What this calculator assumes

You enter the horizontal distance and the vertical height.
The ground is treated as level and the triangle as right angled.
Results are rounded for display.

Formula and sources

Related calculators

Trig Calculator: all six trig functions at once.
Degrees to Radians Calculator: convert angle units.
Right Angle Triangle Calculator: solve a right triangle.

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