## Is there an easy way to measure the height of a tree?

111

38

I'm looking to get an antenna installed for Internet service that will need to clear some trees on my neighbor's property because it requires a clear line of sight to work.

I really don't trust my estimating skills enough to plunk down money on a utility pole that might be too short or too tall. And climbing the tree with a tape measure (in my neighbors yard) is a bit intrusive and dangerous.

Is there a clever way that I can get a reasonably close (within 5' or so) estimate of the height of the tree other than eyeballing it?

I thought about putting together a bunch of 10' runs of PVC pipe and holding it up against the tree, but that is going to get pretty unwieldy by about 30' and the trees are at least that tall.

My other thought is to break out my old Trig textbooks and use the angle/distance to tree, but it seems like it would be pretty hard to judge the angle correctly, maybe with a laser pointer or something?

Any other ideas?

9Knowing the height today is clearly useful. But don't forget that trees are not static: they grow. You might want to consider a few years of growth into your location planning.... – RBerteig – 2012-01-10T09:34:45.783

Is the ground in your yard and in your neighbour's yard perfectly flat and level? – Remus Rusanu – 2012-01-12T20:15:00.763

I think this was in a Sherlock Holmes story – DaveInCaz – 2018-02-08T00:24:33.350

NB: Most of the answers are predicated on the tree being perpendicular to the ground. – Synetech – 2014-02-08T18:03:21.950

4I'm fairly sure I had a problem just like this in high school (though that was many years ago), the trig textbook might just be the solution. – Tester101 – 2011-06-21T02:07:42.280

205

Find a stick the same length as your arm. Hold your arm out straight and level with the stick pointing straight up (90° to your outstretched arm). Walk forward/backward until the tip of the stick coincides with the top of the tree. Your feet are now at approximately the same distance from the tree as it is high. (For a more precise approximation, back up by the additional distance of the height of your arm above the ground.) The relationship is true only if the tree is significantly taller than you are, and the ground is relatively level. Time-tested logger method. Simple.

11@Vincent Robert: Remember this is a logger trick... If you cut the tree at the height of your arm, you don't have to add that height into your original estimation ;) – Tester101 – 2011-08-02T16:46:53.580

No one mentioned that the easy way to get 45 degrees for Thales pyramid sighting method is simply by folding a sheet of paper, aligning the bottom of the sheet with one side. Now you have a diagonal which is exactly 45 degrees. You don't need a special instrument. – Stewart Fist – 2016-11-03T03:28:40.837

1I Have actually used this with some degree of accuracy. the only change is that i used a clear ruler and looked through the plastic to get the actual length of the tree (at perspective view) – Hightower – 2012-09-05T13:27:04.617

2used it many times when I worked temporarily with an arborist. Works well, give or take a couple of feet, but then, if you got a 100 foot tree, what difference does 5 feet make? If your cutting it that close, you are already in trouble! LOLOLOL – shirlock homes – 2012-09-06T22:34:19.213

8Historical fact: that's how Thales measured the height of the great pyramid in 7 BC ;-) – Philippe – 2013-03-28T17:03:14.003

3The diagram is incorrect. Your eyeball is not at your shoulder; therefore, there is no triangle. You could correct this by raising your hand to be level with your eye, not your shoulder. – Reid – 2013-09-14T16:09:19.167

13I like this one, no tools or math (especially if you know your stride length). Just a stick and a little walking. – Tester101 – 2011-06-21T12:12:21.450

+1, I'll keep this one in mind next time I'm chopping down a tree. – BMitch – 2011-06-21T12:30:38.647

I am having trouble visualizing this one. Can you offer some visual aids? – JD Isaacks – 2011-06-21T17:48:16.707

10sorry about the ???? lol. This is a method to see where the end of the tree will be when it falls. Don't have a visual, sorry. The math of it is simple, if your arm is 36" long and the stick is 36" long, holding the stick straight up with your arm extended out at eye level creates a 45 degree angle line of sight, thus an isosceles triangle. So it follows that the height of the tree is the same as your distance from the tree. Give or take a foot or so. A good quick accurate estimate. – shirlock homes – 2011-06-21T18:34:50.043

What shirlock said; you're creating an isoceles right triangle (45-45-90) with the stick and your arm, that is projected over the tree in your perspective; when the top of the tree lines up with the stick, the tree is now part of a much larger triangle with the same angles, and the two sides of the 45-45-90 triangle which form the 90* angle (which are the height of the tree, and the distance from the trunk to your feet) will be the same length. It's beautiful. – KeithS – 2011-06-21T22:42:16.707

4Great, even doesn't require sunny weather. – sharptooth – 2011-06-22T07:46:12.467

5Them ole Maine loggers are wicked smart. lol. – shirlock homes – 2011-06-22T10:13:58.140

@keith: Thanks for a nice clear explanation of my confusing math. – shirlock homes – 2011-06-22T10:15:45.253

Get dem smart ole loggers to import a few beavers to the stream next door for a while :) – Mark Schultheiss – 2011-06-24T17:49:18.893

I guess it was implied, but it wasn't specifically stated that your feet have to be on the same level (or close) of where the tree goes into the ground. – billoreid – 2011-06-25T02:40:19.013

@ billoreid: Ayaa that's true. – shirlock homes – 2011-06-26T09:26:21.530

1Shouldn't your arms and eye be at the ground for this to work? If you are standing, you need to add your arm height from ground to the distance measured. – Lazer – 2011-06-26T13:54:50.513

1I'm sorry but Tree+Eye+Feet does not form an isocel triangle. Much more a trapezoid. Lazer is right, you have to consider the triangle Tree+Eye/Arm and add the height of your Eye/Arm. – Vincent Robert – 2011-06-26T16:47:22.740

3I was only giving a method to estimate the height of the tree. I don't think the question asked for a way to be exact to the inch. Lazer is absolutely right as far as the math goes. you need to add the distance from the ground to your eye to be more accurate. – shirlock homes – 2011-06-27T22:46:11.760

14Many thanks to the person that did the edit and added the diagram. Right on, Perfect! – shirlock homes – 2011-07-08T10:48:52.847

91

2. Measure yourself.

You'll have to do this on a sunny day (you might also need an assistant), and the ground will have to be relatively flat (a slope will throw off the measurement).

How long is your shadow at noon? You won't get a shadow past the drip line of the tree. Furthermore and moreover, shadows change throughout the day. You'd have to measure both shadow lengths at the same time or introduce rotational error. – Jules Bartow – 2016-07-18T23:46:23.157

@JulesBartow The noon shadow would depend on where in the world you are, and what time of year it is. And yes, you'd have to measure the shadows at the same time. – Tester101 – 2016-07-19T03:06:04.130

This also wouldn't work to well if other trees or buildings were interupting the shadow, but otherwise this is a great idea. – hortstu – 2013-09-21T18:34:15.707

@BinaryWorrier - The slope does not have to be continuous at all. What happens between the base of the tree and the tip of it's shadow is irrelevant. What is necessary is that the slope of the (imaginary) line between the base of the tree and the tip of the tree shadow is the same as slope of the imaginary line between your feet and the tip of your shadow. – mike – 2013-10-01T03:39:53.690

11+1: Unless the slope is continuous for the length of the longest shadow, and you measure both shadows on the slope. If the slope is constant then the ratios of the shadows will still work :) – Binary Worrier – 2011-06-21T12:15:24.660

Can't you also use the tree plus shadow, plus angle of tip of shadow to tip of tree to create a triangle and figure it out that way? – JD Isaacks – 2011-06-21T12:59:27.453

6@John Isaacks: Trying to avoid angles, as they are difficult to measure without proper equipment. – Tester101 – 2011-06-21T13:11:18.373

This must be hard to do at night or in the rain... sorry,hehe, couldn't resist. my devil horns are out. – shirlock homes – 2011-06-21T20:12:43.517

5@shirlock I mentioned you have to do it on a sunny day, besides whose measuring trees in the rain? – Tester101 – 2011-06-21T20:26:26.377

60

Take a pencil, move some meters away from the tree. Outstrech your arm and hold the pencil so that you can measure the height of the tree on the pencil with your thumb. Then turn the pencil at the bottom of the tree by 90 degrees. Note where the distance measured by thumb hits the earth and measure the way from this point to the tree. This is the height of the tree.

This is a method that we would teach the Boy scouts in our neighborhood. It won't necessarily get you down to the inch accuracy, but it's pretty good for getting a close estimate. – Scott Ramboz – 2017-02-06T20:23:01.060

When I learned this it was called the "tree felling" method. – Pete Becker – 2013-03-07T14:38:01.143

5+1. This is by far the most simple and reliable method. – pboin – 2011-06-21T11:44:17.253

14I can't make heads or tails of this suggestions :/ – Alain – 2011-06-21T12:35:38.107

-1 This needs some serious clarification to make sense. – JYelton – 2011-06-21T14:56:11.107

4Start with the pencil upright -- top aligned with the tree top, bottom marked by your thumbnail. Turn it horizontal, line the trunk up with your thumbnail and the end of the pencil marks the exact hight of the tree. It's just a giant compass. – pboin – 2011-06-21T15:55:16.667

2bennymo is just transferring the measurement of the tree from the vertical where you can't reach to two known points on the ground that you can measure using a pencil (or a stick would do). – BMitch – 2011-06-21T21:43:12.943

2Love this option. Simple and fairly accurate and not requiring the math ;o) – DA01 – 2011-06-24T00:44:33.550

49

You can do this with some basic trigonometry (bring your calculator), if you have a way of measuring the angle (eg, using a digital protractor, laser level that has a protractor/angle tool, angle ruler, etc).

• D is the distance between you and the tree
• a is the angle to the top of the tree
• b is the angle to the bottom of the tree (if you do it from the ground, you don't need to bother with measuring b)

So then you just use the tan button on your calculator to find:

• A = Tan a * D
• B = Tan b * D
• (you can also just estimate/measure B directly - if you're standing on level ground with the tree, it's the height of your eyes or wherever you measured the angle from)
• Height = A + B

This method also works even if you are standing on ground that's at a different height than the base of the tree - eg, you can be on a hill, standing with your eye-level half-way up the tree and it will still work.

1@JohnFx - agreed, if you are on flat ground with the tree. If you are on a hill, with the base of the tree below you, this method still works. – gregmac – 2011-12-23T04:44:26.500

9cough treegonometry – Ambo100 – 2012-01-11T20:32:24.430

1+1 for the most precise answer without cutting off all the branches and dropping a tape measure from the top. – Alain – 2011-06-21T12:38:07.090

6Great answer, but seems a little silly to calculate B when you could just as easily measure that (or estimate it and be within 1-2 feet margin of error) – JohnFx – 2011-06-21T20:09:12.633

1Yes, I basically had the same answer, but said to add your height to the calculated height if you were standing when taking the angle measurement. – KeithS – 2011-06-21T22:36:50.000

19

Man there are some great answers here. I found one more on another site that I'll add for the sake of anyone else visiting this question.

The Digital Camera Method

1. Get a piece of PVC pipe of known length (10' seems easiest).
2. Mark at measured intervals (to your desired precision) on the pipe.
3. Tie the pipe to the base of the tree or have someone hold it.
4. Take a picture of the tree, standing as far away as you can, but zooming in as needed to make the tree the full height of the frame.
5. Using a photo editing tool, copy the pipe in the photo and paste it on top of itself (stacking them virtually) to see how many it takes to equal the tree.

wide angle lens? :) – garik – 2013-03-10T08:15:31.763

8You'll lose accuracy on this with tall trees. For example, compare the height of floors of a tall building in a picture taken from the ground. The building doesn't really get smaller at the top. – BMitch – 2011-06-21T21:38:56.127

1

That's unless you happen to have a tilt-shift lens which provides perspective corrected images. http://en.wikipedia.org/wiki/File:Bashford_views_-_perspective_control.jpg

– Mark Renouf – 2011-06-26T13:13:03.777

4You should change '4' to be: Take a picture of the tree, standing as far away as you can, but zooming in as needed to make the tree the full height of the frame. - This reduces errors induced by the perspective. – quamrana – 2011-06-26T15:35:59.920

2@quamrana good suggestion, I updated the answer as you described. – JohnFx – 2011-07-01T14:41:25.443

17

You might also try one of the existing smart phone applications like this one: Smart Measure

I use Smart Measure, and it seems to work pretty well at calculating my friends' heights. I haven't tried it on a large scale object that I knew the height of though. – Doresoom – 2011-12-19T15:21:27.487

This actually seems to work pretty well. I first tried it on some relatively tall objects of known height and it had decent accuracy. Thanks! – JohnFx – 2011-07-01T14:42:35.117

12

A second option to the shadows, use a level mirror and some geometry:

1. Fill a black pan with water, this makes a great mirror during the day (it's best you don't use your wife's best pan for this)
2. Place pan a known distance from the tree, call the distance from the middle of the pan to the tree B1 in the equations
3. Stand back from the pan until you see the top of the tree in the middle of the reflection. Measure from your eye level to the ground, straight down, can call it A2. From that point on the ground to the center of the pan is B2.
4. You now have two right angle triangles that are proportional and only one unknown, the tree height (A1). A1/B1 = A2/B2 or A1 = A2 * B1 / B2. Or back in English, the tree height is your height times the distance from the pan to the tree divided by the distance from you to the pan.

For example, if you're eyes are 6' above the ground, the pan is 40' from the tree, and you stand 5' back from the pan, you get 6 * 40 / 5 or a 48' tree. For more accurate measurements, get yourself on top of a step ladder or some other high point.

Note that if you can't determine how level the ground is between you and the pan, you may be better off measuring from eye level to the pan and then do some geometry to get your height above the pan (A2 = square root(eye to pan squared / pan to foot squared)).

FWIW, the formula would be more accurate if it used the height of your eyes above the water surface, as opposed to above the ground. – mike – 2013-09-30T22:06:37.643

8

Just use balloon with string or rope. Fill up balloon with smoke from cigarette (hot air), for example, or light gas: helium.
Measure the length of string.

how do you know how much string to let out? – mike – 2013-09-30T22:07:21.913

1@mike use any of high voted answers to this post :). It's a funny solution. It depends on string weight, balloon, wind...It's boring of using formulas for me. :) Have a nice day, Mike. – garik – 2013-10-01T07:19:33.230

5

just take a picture of the tree with some objects you know the height of in it (such as your wife of your neighbour). Then simply measure the height in pixels of known object and compare with tree.

[Height of tree] = [pixels of tree] * [known height] / [known height pixels]

If you compare multiple objects, average results. The more "known" objects, the closer to the base of the tree, the better the result.

4

## Use a yard-stick.

Walk up to the tree. Tie two ribbons around the tree, one at the base and the other as high as as possible. Measure the distance between the ribbons. Walk away from the tree. Face the tree. Hold the yard-stick plumb at arms length such that:

1. the 0" mark is aligned at the base of the tree, and
2. the 1" mark is aligned with the marker

Note how tall the tree is on the yard-stick.

The height of the tree is ribbon distance multiplied by yard stick measurement. If the ribbons are 70" apart, and the yardstick measurement is six and an eighth inches, then the height of the tree is 70 x 6.125 = 429 inches = 36 feet.

To obtain the 0-1 alignment:

1. walk towards or away from the tree, or
2. move the yard-stick closer or farther away from yourself, or
3. tilt the yard-stick forward or backwards.

A ruler, tape measure, sheet of graph paper, sheet of lined notebook paper, or any object/straightedge with containing regular intervals, such as an egg-crate, piece of chicken wire, page of text such as page of newspaper, sheet of unfolded copy paper that had been folded in half repeatedly, venetian blinds ... will suffice for the 'yard-stick'.

Instead of the ribbons, one could lean a pole, or 2x, or ladder or use select low tree branch.

4

Some basic trigonometry can tell you:

Measure the distance between you (or any point of reference from which the tree is close and relatively visible) and the base of the tree.

From the same point of reference, measure the angle in degrees between the ground and the top of the tree. A sextant is the correct tool for the job; if you have access to surveying tools you should be able to get a real one, or you can fake it by sighting down a level with an adjustable-angle bubble, or build a sextant using a straw, a protractor, and a weighted string.

By definition, tan(theta) = height/distance. So, height = tan(theta) * distance. When using your calculator, make sure it's set to calculate sin/cos/tan in degree mode, not radian mode.

Add your height to the number you get, if you were standing at the point of reference instead of lying prone, and that's as close as you'll get without climbing the tree to its top and dropping a plumb line.

4

get a clear pipe and use level of water. Measure height at which you see water level from ground = tip of tree. For 2-3 points as far apart on your terrace as possible roughly on the same line as you want your antenna to be. Use basic trigo.

benefits over other methods: No need to know the distance between tree and home No need to know height of home. You know the height of pole you need, no need to know the height of tree :D

3

## Use an open container of water, such as a bucket, the easy way.

When standing, measure the height of your eyes, say 63". Fill a container with water, then measure the water depth, say 8". Subtract the two (55").

Walk away from the tree and find the spot where the reflection of the top of tree is in the center of the bucket when the bucket is on the ground and you are standing 55" away from the center of the bucket. This sets up 45 degree angles.

The bucket is now as far away from the tree as the tree is tall, assuming your feet are at the same elevation as the tree base. (If not, then the bucket is now as far away from the tree as the top of the tree is above your feet)

sounds good assuming you are standing at the same height as the tree. Or said another way, when you use this technique, the spot you are standing on is your zero-height reference. – skiggety – 2014-09-05T16:40:18.797

3

As a generalization of shirlock's method, when you can't move far enough away for the same-length-of-your-arm trick to work, but you can still move far enough away to see the top of the tree:

If you know the height of a vertical member that looks the same height as the tree (`H1`), your distance to the vertical member (`D1`), and your distance to the tree (`Dt`), then the height of the tree (`Ht`) is a simple ratio:

`Ht / Dt = H1 / D1`

`Ht = Dt * ( H1 / D1 )`

And of course, in shirlock's test, (H1/D1) = 1, so for that case, it simplifies to

`Ht = Dt`

I personally find this to be much easier than trying to measure an angle, even if you have a transit.

1

Foresters use a clinometer to determine the height of a tree. Since another answer mentioned the use of a phone, I looked to see if a clinometer app was available for my iPhone. There are several and one has a very strong 5 rating. Good luck.

3Please give the app's name so others don't have to go searching for it. – Niall C. – 2013-09-14T03:17:22.273

1

## Use an open container of water, such as a bucket, the ABC way.

Set the bucket down a good ways away from the tree. Stand back from the bucket, positioning yourself such that the top of the tree is reflected in the middle of the bucket.

A. measure the distance from the tree to the bucket
B. subtract water depth from eye height
C. measure how far away you are from the middle of the bucket

The height of the tree is approximately: A x B / C

For better accuracy, repeat the measurements and calculations with the bucket moved to a new spot as far away from the tree as the calculated tree height.

1

It's Easy.

Let's consider the height of the tree is x. Measure the shadow length of x.

Take a Stick and measure it's height. Measure it's shadow too. Let's say stick is "y" tall and it's shadow is "b" long.

Do the proportion. y:b::x:a. We need to find x. Do Y*A. Divide thaat answer with b. That answer is x and therefore it is the height of the tree.

As long as the angle of incidence of the sun is the same between the stick and the tree, this is quite clever :) – ThreePhaseEel – 2015-04-26T17:17:16.647

1

Climb the tree with an length of ethernet cable or fiber optics. Cut the cable/fiber at the bottom and terminate. Use a \$15,000 Fluke Versiv cable/fiber certifier with a Time Domain Reflectomer (TDR) or Optical TDR to measure the height within a couple of wavelengths.

0

I had one that was more for fun than anything else. You can use a rock (Assuming that the height of the tree is within throwing distance, you can choose a small rock) and use the 1 dimensional kinematic equations from classical mechanics.

That might sound kind of scary, but really just throw the rock as hard as you can and start counting seconds, and when you see it reach the top of the tree, and record this time.

You can then use the equations:

Where delta x is the height of the tree, v0 is initial velocity, vf is final velocity (Which is 0 since it stops at the height of the tree, or approximately the height of the tree), and t is the time you measured to get to the top, which you have from counting. You have two equations and two unknowns (delta x and v0), you can solve this by substitution, elimination, or by matrix algebra (RREF) to get the height of the tree). NOTE: the height of the tree will be in meters, you know, the better format :D

NOTE: That's the complicated way, the simple way, after derivations is reduced to:

We see that the result is easy to compute in your head, it's: So, if the rock takes 2 seconds to stop in the air, it went a height of approximately: 5 * 2^2 = 20m

0

Use a Drone! (or a Kite or a Balloon)

This seems rather obvious, but if you fly a gps unit to the top of the tree, you can subtract the altitude of the base of the tree and determine the tree's height.

The drone is by far the easiest method: measure the altitude of the base of the tree while setting up the drone, press the up button until your drone is hovering over the tree, and read off the altitude.

This method is probably the fastest if you have multiple trees you need to measure.

2The real advantage is that you now have a drone after you are done measuring the tree. – JohnFx – 2015-10-20T19:34:49.067

Consumer grade GPS isn't accurate to more than 5m for altitude. You may be able to do this with a quadcopter equipped with a barometer and thermocouple, but I'm still not sure you'd end up with high enough accuracy. – Doresoom – 2014-10-07T16:15:13.620

True, but you can buy this gadget: http://gizmodo.com/cheap-drone-gps-unit-is-100-times-more-accurate-than-y-1055906323 and get it to a few centimeters.

– gbronner – 2014-10-07T19:15:29.000

3While your method is technically feasible, you'll have to already have a \$300-500 quadcopter AND spend \$900 on a super accurate GPS module. I think I'll just use a stick the same length as my arm. – Doresoom – 2014-10-07T19:37:42.743

The advantage is that it works for many different kinds of trees. I have an entire forest full of overlapping broad-branched trees, and getting a clear view of the top of any tree is difficult, especially in summer, when they all have leaves.

You could also have the drone pick up a monofilament line and measure the length of that, but that's quite a bit trickier. – gbronner – 2014-10-07T19:46:41.063

0

To augment other answers, if you need to know the angle towards something in front of you like a tree or a house or a hill or whatever, you can use the stars or other celestial bodies or even satellites. They all have a specific angle (altitude) at which they appear at a certain time from a certain spot on Earth. It can give you a high precision measurement without any tool. Maybe just the internet to figure out the values in planetarium software of websites.