Angle of Depression Calculator
This angle of depression calculator finds the angle of depression, the angle between the horizontal and your line of sight to a point below you. Enter the horizontal distance to the point and the vertical height difference, and the calculator returns the angle in degrees and radians, plus the straight line of sight distance. The angle of depression is a right triangle problem: the angle has the height as its opposite side and the horizontal distance as its adjacent side, so the tangent of the angle is height over distance, and the angle is the arctangent of that ratio. This is used in surveying, navigation, construction, astronomy and any sight line measurement. The formula, a worked example and the assumptions are set out below.
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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