# 4 Ways to Measure the Height of a Tree

In a secret location somewhere in Northern California, USA, a tree called Hyperion was measured and set the world record for height, reaching 115, 61 m! Believe it or not, the measurement was taken with an extra-long measuring tape. However, there are much easier methods you can try. Even if you can't get the exact measurement in centimeters, these methods will give you a good approximation and will work on any tall object. Posts, buildings or magic beans: as long as you can see the top of them, you can measure them.

## Steps

### Method 1 of 4: Using a Piece of Paper

#### Step 1. Use this method to find the height of a tree without doing any math

All you need is a piece of paper and a measuring tape. No calculation is needed, but if you're interested in how it works, you may need to know a little trigonometry.

### The method using an inclinometer or theodolite explains all the calculations and why they work, but it is not necessary to read it if you are going to use the following method

#### Step 2. Fold a piece of paper in half to form a triangle

If the paper is rectangular, you'll need to make it into a square: fold one corner so it forms a triangle with the opposite one, then cut the extra paper below them to get the shape you need.

### The triangle will have a right angle and two 45° angles

#### Step 3. Place the triangle in front of your eyes

Hold the right-angled corner and point the rest of the triangle towards you. One of the short sides should be horizontal and the other vertical. You should be able to see "through" the longer side by looking up.

### This long side that you will look through is called the hypotenuse

#### Step 4. Move away from the tree until you can see the top of the tree at the top end of the triangle

Close one eye and use the other to look straight down the triangle's hypotenuse until you see the top of the tree. You need to find the point where your line of vision follows the hypotenuse of the triangle to the top of the tree.

#### Step 5. Mark this point and measure the distance from it to the base of the tree

This distance is almost the full height of the tree. Add your own height to it, as you were looking at the tree from the height of your eyes. Now you have the answer!

### Method 2 of 4: Comparing Shadows

#### Step 1. Use this method if you only have a measuring tape or a ruler

You don't need other equipment for it and you should get an accurate estimate of the tree's height. All you need to do is solve multiplications and divisions.

### If you want to avoid all calculations, you can use an online calculator like this one and put the measurements you find into that method

#### Step 2. Measure your height

Use a measuring tape to measure yourself while standing and putting on the shoes you will be wearing for this method. Since you'll need a paper anyway, write down its height so you don't forget the exact number.

• You will need a single number, such as your height in centimeters, not a combination of meters and centimeters. If you're not sure how to convert one number to another, you can use a vertical meter ruler, it works too. Use the height and length of the ruler's shadow whenever your measurements are requested.
• If you are in a wheelchair or cannot stand up for any other reason, measure your height in the position you will be in when you go out to measure the tree.

#### Step 3. Stay on a flat, sunny spot near the tree

Try to find a place where your shadow falls to the ground so you can get an accurate measurement. For best results, use this method on a clear, sunny day, as if the sky is cloudy, it will be difficult to measure shadows accurately.

Use a measuring tape or meter to measure the distance from your heels to the tip of the shadow. If you don't have anyone to help you, you can mark the end of the shadow by throwing a stone at it while you're standing, or even better, place the stone anywhere on the ground and position yourself so that the tip of the shadow is on it; then measure from where you are to the stone.

### Write down and label each measurement you take to avoid confusing them later

#### Step 5. Measure the length of the tree's shadow

Use your measuring tape to determine the measurement from the base of the tree to the tip of the shadow. It works best if the ground around the shadow is more or less level. If the tree is on a slope, for example, the measurement will not be as accurate. Measure this length immediately after measuring your shadow, as the sun's movement will cause it to change.

### If the tree's shadow is on a slope, there may be a different time of day when the shadow avoids the slope by getting shorter or pointing in another direction

#### Step 6. Add half the tree's width to the length of its shadow

Most trees grow straight up, so the tallest tip should be above the exact middle. To get the full length of the shadow, you'll need to add half the trunk's diameter to the shadow, because the taller tip is actually casting a longer shadow than your measurement; part of it is falling over the top of the trunk, and you can't see it.

### Measure the trunk width using a long ruler or measuring tape and divide it by 2. If you are having trouble finding this measurement, draw a square along the base of the trunk and measure one side of that square

#### Step 7. Calculate the height of the tree using the numbers you wrote down

You will now have three measurements: your height, the length of your shadow, and the length of the tree's shadow (plus half the width of its trunk). Shadow lengths are proportional to the object's height. In other words, the length of your shadow divided by its height will equal the length of the tree's shadow divided by its height. We can use this equation to find the height of the tree:

• Multiply the length of the tree's shadow by its height. If you measure 1.5 m and the shade of the tree is 30, 38 m, multiply one by the other: 1, 5 x 30, 48 = 45, 72.
• If you're having trouble doing the math, use a calculator.

### Method 3 of 4: Using a Pencil and Wizard

#### Step 1. This method is an alternative to the shadow

Although less accurate, it can be used when the shadow method doesn't work, such as on a cloudy day, and also, if you have a measuring tape, you can avoid doing calculations. If not, you'll need to find one later and do some simple multiplications.

#### Step 2. Move away from the tree until you can see it completely without moving your head

For more accurate measurements, you should be in a location that is level with the ground at the base of the tree and where your view of the tree is as clear as possible.

#### Step 3. Hold a pencil at arm level

You can use any small, straight object, such as a brush or ruler. Hold it in one hand and extend your arm to place the pencil in front of you (between you and the tree).

#### Step 4. Close one eye and raise or lower the pencil so you can see the top of the tree on top of the pencil

It will be easier if you turn the object so that the tip is up, covering the tip of the tree in the line of sight when you see it "through" the pencil.

#### Step 5. Move your thumb across the pencil until the tip of his nail lines up with the base of the tree

While holding the pencil so that the tip of the pencil is aligned with the top of the tree as in step 3, move your thumb to the point on the pencil that covers where the tree meets the ground (again while looking "through" the pencil with one eye only). Now the pencil "covers" the entire height of the tree, from the base to the tip.

#### Step 6. Rotate the arm to make the pencil horizontal

Keep your arm straight at the same distance and your thumbnail still in line with the base of the tree.

#### Step 7. Ask your friend to stay in a place where you can see him "through" the tip of his pencil

That is, your friend's foot should be aligned with the tip of the pencil. It should be the same distance from you as the tree, neither closer nor farther. Since, depending on the height of the tree, you may need to move a little away from your friend, consider combining hand signals to tell your friend to go further, come closer, go left or right.

#### Step 8. If you have a measuring tape with you, measure the distance between your friend and the tree

Ask him to stay in place or mark you with a stick or a rock and then use the measuring tape to measure the distance between that point and the base of the tree. That will be the height of the tree.

#### Step 9. If you don't have a measuring tape with you, mark your friend's height and the tree's height on the pencil by scratching it or making a mark where your thumb is

This is the height of the tree from your perspective. Use the same method as before to arrange the pencil so that it covers your friend, with the tip on his head and the thumbnail on his toes, and make a second mark in the position of your thumb.

You will need to measure the length of each mark and your friend's height, but you can do this after you go home, without having to go back to the tree. Scale the difference in pencil lengths up to your friend's height. For example, if the mark is showing that your friend is 5 cm, and the tree is 17, 5 cm, the tree is 3.5 times taller than your friend, since 17, 5 / 5 = 3, 5. If your friend is 180 cm tall, the tree will be 180 x 3, 5 = 630 cm.

• Note: if you take a measuring tape when you're near the tree, you won't need to do any calculations: read step 8 carefully.

### Method 4 of 4: Using an Inclinometer or Theodolite

#### Step 1. Use this method to get a more accurate measurement

The others are surprisingly accurate, but with a little more math and specialized tools, you can get a more accurate reading. It's not as difficult as it sounds: all you need is a calculator that can calculate tangents and a protractor, a straw and a piece of string so you can make your own inclinometer. This device measures the inclination of objects, or in this case the angle between you and the top of the tree. The theodolite is a more complicated tool used for the same purpose, but it uses a telescope or laser to be more precise.

### The piece of paper method actually uses paper as an inclinometer. The following method, in addition to being more accurate, allows you to measure height from any distance rather than moving back and forth to align the paper with the tree

#### Step 2. Measure the distance to an observation point

Stand with your back to the tree and walk to a spot that is level with the ground at the base of the tree and where you can see the top of it unobstructed. Walk in a straight line and use a measuring tape to measure your distance to the tree. You don't need to be any pre-set distance from the tree, but this method generally works best if you are about one to one and a half times the height of the tree.

#### Step 3. Measure the elevation angle to the top of the tree

Visualize the top of it and use an inclinometer or a theodolite to measure the "elevation angle" between the tree and the ground. This angle is the one formed between two lines (the flat floor and your line of sight) to some high point (in this case, the top of the tree) with you as the vertex.

#### Step 4. Find the tangent of the elevation angle

You can calculate it using a calculator or a table of trigonometric functions. The way to find the tangent can be different depending on the calculator, but generally you just press the "TAN" button, enter the angle and then press the equal (=).

• Click this link to go to an online tangent calculator.
• The tangent of an angle in a right triangle is calculated by dividing the side opposite the angle by the side adjacent to the angle. In this case, the opposite side is the height of the tree and the adjacent side is your distance from it.

#### Step 5. Multiply the distance from the tree by the tangent of the elevation angle

Remember that you measured your distance to the tree at the beginning of this method. Multiply it by the tangent you calculated, and the resulting number will be the height of the tree above your eye level, since that is where you calculated the tangent.

### If you've read the previous substep regarding tangent definition, you can see why this method works. As described above, tangent = tree height/distance to tree. Multiply each side of the equation by the distance to the tree and you get: tangent x distance to tree = height of the tree

#### Step 6. Add your height to the result you got in the previous step

Now, you know the height of the tree. Since you used the inclinometer or theodolite at eye level, not the ground, add your height to the measurement to get the total height of the tree. You can get a more accurate result by measuring your height down to eye level, not the top of your head.

## Tips

• You can improve the accuracy of the pencil method and elevation angle by taking several measurements from different points around the tree.
• Many trees are not perfectly vertical. You can adjust the elevation angle method for an inclined tree by measuring the distance between you and the point on the ground directly below the top of the tree, rather than measuring the distance between you and the base of the tree.
• This activity can be fun for children in grades 4-7.
• To increase the accuracy of the shadow method, you can measure the shadow created by a meter or other similar measuring instrument, rather than using a person's height.
• Be consistent with your measurement units (multiply and divide meters by meters or centimeters by centimeters, for example).