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How to calculate tree height using a smartphone

May 15, 2011

Gabriel Hemery

Foresters use a clinometer to calculate the height of a tree.  These can be quite expensive to buy so you’re not likely to invest in one unless you need to measure trees frequently. However, don’t despair as it is quite possible to achieve good results with a smartphone; with the advantage that you nearly always have one with you.  This is a method I’ve developed that I hope others will find useful.

Preparations

Install a spirit level app

iPhone and Google Android phones (sorry, I have no working knowledge of Blackberrys) allow apps to be downloaded.  There are a number of apps available that use the smartphone’s accelerometer to provide a virtual spirit level.  Some of these include a tilt meter or level meter and it’s this kind that you will need to be able to measure an angle of elevation.

For the example below I use an iPhone and the Carpenter app from iHandy.  The full version costs under $2 and I’ve found that it works very well.  Even better the Level app, which you need for this method, is currently free as a stand-alone app.

Calibrate – the level … and yourself

  1. Zero your virtual spirit level
    If you’ve installed a good spirit level app it should allow you to calibrate your smartphone to reasonable accuracy.  On a shelf that you’ve checked to be perfectly level with a real spirit level, place your smartphone on its side , then ‘zero’ it (calibrate it to read ‘0’).
  2. Calibrate your pacing
    You will need to be able measure the distance that you are standing away from a tree.  You can of course carry a long tape measure with you when you think you’ll need one but I find it very helpful to know my pacing with reasonable accuracy.  For example I know that 21 of my strides equal 20m.
  3. Measure the height above ground of your eye
    Simply measure the distance from the ground under your feet to one of your eyes.

The data and the maths

The data required

You will need to know three things:

  1. The angle of elevation to the top of the tree from the horizontal
    As shown below the horizontal will be equivalent to a line between your eye and someone of the same height standing next to the tree.
  2. The distance from where you stand to the base of the tree
  3. The height of your eye above the ground
how to calculate tree height

The three measurements needed to calculate the height of a tree

The maths

Don’t be put off if you’re not confident about the maths as, although it may seem daunting, it’s actually quite simple.  You will use trigonometry but your smartphone’s calculator will do all the hard calculations for you.

The equation you will use is:

Tan angle of elevation   x  distance to tree

then

+ height of eye above ground

Step by step guide (with working example)

1.   Stand away from the tree

Stand away from the tree so that you can see its top.  The method works best if your angle of elevation is about 45o .  In other words that your distance from the tree is equivalent roughly to the height of the tree (you’ll get better at estimating this, the more trees you measure).

2.  Pace (or measure) the distance away from the tree

If you are working with someone else they can help you measure the distance from where you’re standing to the tree.  If you’re on your own, drop something where you’re standing to mark the position so that you can return once you’ve paced or measured the distance to the tree.

I was 21m away from my tree.  Write this distance down or memorise it.

3.  Measure the angle of elevation

measuring the angle of elevation with a smartphone

measuring the angle of elevation with a smartphone = 43.7 degrees

Standing at your spot (step 2) open the virtual spirit level app on your smartphone and select the angle measure.  Bring the smartphone to your eye and sight along its edge, as if you’re looking down a gunsight, aiming at the very top of the tree.  You will need to hold the phone so that your fingers are not in the way (see photo).

With the app I use there is a ‘hold’ button that freezes it when you are satisfied that you are ready to record the angle.

My angle of elevation was 43.7o.  Write this angle down or memorise it.

4.  Calculate tree height

Open the calculator on your smartphone.  You will need to access the scientific calculator.  For iPhones and HTCs you can do this by tilting your phone onto its side (landscape), where you will find the function for Tangent or Tan.

enter angle of elevation

enter the angle of elevation (43.7)

tan of angle

press tan (= 0.9556)

x distance to tree

multiply this by the distance to the tree (x 21m)

add height to eye

add height to eye (+ 1.73m)

result

press equals (result = 21.79m tall)

So my tree was 21.798m tall. Given that there is lots of room for error I would recommend that you round the result to the nearest whole number = 22m tall. It doesn’t matter whether you use metres or feet as long as you use consistently the same units throughout (i.e. don’t switch between m and cm, or between feet and inches).

Increasing accuracy

The method I describe above works well on level ground.  However, if you want to increase accuracy especially if the ground is not level, you can improve it quite simply.  Instead of using the height of your eye above ground, you substitute it with (Tan angle to the base of the tree x distance to tree).  So the full equation would be:

(Tan ∠ to tree top x distance to tree) + (Tan ∠ to tree base x distance to tree)

Other applications

You can use this method to calculate the height of other features on trees, such as the height of the lowest branch, a major fork, a bird nest or bat roost, or of course for any tall object such as a bridge or building.

Gabriel Hemery

8 Comments

Post a comment
  1. Kevin O #
    May 27, 2011

    Thank you for taking the time to lay this out and for an excellent job on breaking down the methodology, but you might care to double check the maths in your example. Subtracting your given height from your given total leaves 21.024m, which divided by the 21m distance from the tree leaves Tan ∠ to tree > 1 which would make the resulting angle greater than 45º. The true total should be 21.798, which can then be rounded up to 22.

    Regards,

    k

    • May 27, 2011

      Kevin
      Thank you so much. Firstly for spotting the error and secondly for pointing my mistake to me so helpfully. You are right in that somehow I added the incorrect value for my eye height. I’ve no idea how I managed to make such a simple error! I am indebted
      I have corrected the post. Next time I write some math I may come back to you first …
      Gabriel

  2. August 22, 2011

    Download the free Android App “Tree Height Measurement”. The App is German and English.
    https://market.android.com/details?id=ftools.baumhoehenmesser&feature=search_result

    • August 22, 2011

      Thanks for alerting me to this. Has anyone else tried this app and found it easy to use and accurate?
      Gabriel

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