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Height by Clinometer

Also known as tree height from angle and distance · clinometer formula · height by tangent · measuring height with a clinometer · cliff height from elevation angle

H=dtan⁡θ+eH = d\tan\theta + e

Worked example: 45 degrees at 40 m, eye 1.6 m → tree is 41.6 m — press Try an example to run it live, then adjust anything.

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See also
Ground Distance on a Slope — The same right triangle stood on its side: horizontal leg, vertical leg, and the line between them.Distance from Pace Count — How the horizontal distance d usually gets measured in the field — by counting paces to the trunk.
Here the solver did the work — could you?

Slope distance and height →

UniversityApplied Field Engineering

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Height by Clinometer explained

Stand back from the tree, sight the top, read the angle: the height is your distance times tan θ — plus your own eye height, because the triangle you measured starts at your eyeball, not your boots. Forgetting the eye height is the classic slip, and it is worth about a metre and a half on every measurement, always in the short direction.

The 45° trick is the formula collapsing into something you can do without instruments: walk until the treetop sits at 45°, and tan 45° = 1 means the height equals your distance — pace it and you are done. One discipline makes it all honest: pace the distance on LEVEL ground from directly below the top, because a distance measured up or down a slope is neither the horizontal leg nor the hypotenuse of the triangle you think you are solving.

Height by Clinometer formula

H=dtan⁡θ+eH = d\tan\theta + e
Where
  • HH= Height of the object (m)
  • dd= Horizontal distance (m)
  • θ\theta= Elevation angle to the top (°)
  • ee= Eye height (m)

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