Calculate height of objects

Knowing whether a tree has the potential to crash into your house

 March 31, 2016

Here is a classic scenario: Local would-be lumberjack decides to cut-down tall tree right beside house. Tree falls towards house. Disaster ensues. Others have a laugh at the homeowner's expense. This post will not help if you find yourself in a similar situation. Instead, this post will allow you to make an informed decision when that tree has a little bit of distance between itself and the house and its height makes the outcome a little blurry.

Tools you will need

Build a homebrew clinometer

If you are you going the phone-app. route or already have a clinometer, skip this part.

How to use the homebrew clinometer

Finding the height of the tree

In order to do this effectively, the area surrounding the tree needs to be flat-ground. Any slope will produce inaccurate results.

Tangent to the rescue

Tangent is a trigonometric function leveraging two-sides of a right triangle and is defined as: \(tan\theta = "opposite"/"adjacent"\). In our case, we know \(\theta\) (our clinometer reading) and the \("adjacent"\)-value (distance from inclination measurement to tree). To get \("opposite"\) (height), we just re-order the equation: \("opposite" = tan\theta * adjacent\).


But wait, there's more...

Unless the clinometer reading took place on the ground, we need to add the height the reading occurred to our previous result. This is normally the distance from your eyes to the ground. For our example, we will go with fifty inches. Then, our estimated height becomes: \(24 ft. + 50 "in." = 28 ft. 2 "in."\). Lastly, take the estimated value and subtract from the previously obtained baseline.

45°–45°–90° rule

If you want to bypass using \(tan\), then use this shortcut. Given the sum of all interior angles of a triangle equal 180 and we already know one-angle of our imaginary triangle is ninety, then if our clinometer-angle is fourty-five, the remaining angle is also fourty-five. With these angles, the two sides of importance to us are equal. This means the only measurement needed is from the clinometer reading-point to the tree!


While both methods for calculating height are effective, they both depend on a couple factors:

The clinometer will most-likely be the greatest source of error. The further the reading moves away from fourty-five degrees, the greater the potential for error (\(tan45 = 1\)). If you are getting readings in the eighties, either you are dealing with a super tree, or you are just too close to the tree. Lastly, be careful and take several measurements. And remember, if you decide to cut down the tree, sometimes it is better to hire a professional.