How to Measure the Height of a Tree

At a secret location in Northern California, the height of a tree named Hyperion has been measured with a world record measurement of 115.61 m! ^{[1] X Research Source} Believe it or not, an extremely long string has been used to measure heat, but there are other, easier ways to measure it yourself. If you don’t need to measure to the nearest centimeter, the measures below will give you a pretty close approximation, and can be applied to any height object. Telephone poles, buildings, or even the legendary bean tree: as long as you can see the top, you can measure it.

Table of Contents

Use a Sheet of Paper

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Use this method to determine the height of the tree without calculation. All you need is a piece of paper and a ruler. No calculation; However, if you want to learn how this method works, you may need a little knowledge of trigonometry.

The clinometer and meridian method requires calculation and understanding of why it works, but you don’t have to do so to figure out the height using this method.

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Fold the paper in half to create a triangle. If the paper is rectangular (not square), you must trim the paper to get a square. Fold one corner to form a triangle with the opposite side, cutting off the excess paper above the triangle. You will have the triangle you need.

The triangle will have one 90º angle and two 45º angles.

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Hold the triangle in front of one of your eyes. Hold the angle 90º and turn the rest of the triangle towards you. One side of the triangle will lie parallel to the ground and one side vertical. You can look along the longest edge by raising your eyes.

The longest side you are looking at is called the hypotenuse of the triangle.

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Back away from the tree until you can see the top of the tree coincides with the top of the triangle. Close one eye and look with the other eye along the hypotenuse until you can see exactly the top of the tree. Find the point where your gaze follows the hypotenuse of the triangle to the top of the tree.

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Mark this point and measure the distance from it to the base of the tree. This distance approximates the height of the tree. Add your height to that distance because you are looking at the tree from the height of your eyes to the ground. Now you have your answer!

To see how this works, see the section on “Using the Inclinometer and Viewing Meridian”. You don’t need to calculate anything in this method because there is a little trick here: tangent of the 45º angle (you used) is equal to 1. The equation can be simply written as: (Height of the tree) / (Approx. distance from the tree to the point where you see the top) = 1. Multiply the sides of the equation by (Distance from the tree to the point where you see the top) and you get: Height of the tree = Distance from the tree to the treetop the point where you see the top of the tree.

Compare Tree Shadows

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Use this method if you only have a ruler or ruler. You don’t need any other tools to perform this method, and you will get an exact estimate of the height of the tree. You only have to do multiplication and division calculations.

If you don’t want to do the math, you can go to the internet to use a pocket calculator to determine the height of a tree, such as this one, and fill in the measurements you find using the method above.

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Measure your height. Use a tape measure or tape measure to measure your height when standing upright. Measure while wearing the shoes that you will be wearing when performing this method. You need a piece of paper to write down your height measurements so you don’t forget the exact number.

The number you measure should have a uniform unit of measure, like measuring in centimeters, not both meters and centimeters. If you are not sure how to convert, you can use a tape measure (meter ruler). Use the length of the ruler and the length of the ruler’s shadow whenever you are asked to use it.
If you are in a wheelchair or cannot stand for any other reason, measure your height anywhere when you are out to measure the height of the tree.

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Stand on flat, sunny ground near a tree. Try to find a spot where your shadow stretches across flat ground to get an accurate measurement. For best results, use this method on a clear, sunny day. If it is cloudy, it is difficult to measure the shadow accurately.

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Measure the length of your shadow. Use a tape measure or tape measure to measure the distance from your heel to the top of your shadow. If there is no one to assist you, you can mark the end of the shadow by throwing a rock at it while you are standing. Or better yet, place the stone somewhere on the ground, then position yourself so that the top of the shadow coincides with the stone; Then measure the distance from where you stand to where the stone is.

Write and name each measurement as soon as you calculate it to avoid confusion.

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Measure the tree’s shadow length. Use a ruler to determine the length of the tree’s shadow from the base of the tree to the top of the shadow. This is most successful when the ground around the shadow is fairly flat; if the tree is on a slope, for example, the measurement will not be completely accurate. ^{[2] X Source of Study} Do this as soon as you have finished measuring your shadow as the sun’s displacement will change the length of the shadow.

If the tree’s shadow is in a steep position, there is another time of day when the shadow avoids the slope by shortening or swerving in another direction.

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Add 1/2 the width of the tree to the length of the tree’s shadow. Most trees grow upright, so the tallest top of the tree will be in the center of the tree. To calculate the length of the tree’s shadow, you need to add 1/2 the length of the trunk’s diameter to the tree’s shadow measurement. ^{[3] X Research Source} The reason is because the tallest tops usually have longer shadows than you can measure; some of the tops fall behind the trunk so you can’t see it.

Measure the width of the trunk with a ruler or a long tape measure, dividing it by two to get 1/2 the length of the tree. If you don’t know how to measure, draw a square close to the base of the tree and measure one side of the square.

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Calculate the height of the tree using the results you recorded. There are 3 results you have recorded including: your height, the length of your shadow, and the length of the tree’s shadow (including 1/2 the width of the trunk). The length of an object’s shadow is proportional to its length. In other words, dividing (your height) by (your shadow length) is equal to (the height of the tree) divided by (the length of the tree’s shadow). We can use this equation to find the height of the tree:

Multiply the tree’s shadow length by your height. If you are 1.5 m tall, and the tree’s shadow is 30.48 m long, multiply these two numbers together: 1.5 x 30.48 = 45.72).
Divide the result by your ball length. With the example above, if your shadow is 2.4 m long, doing the division calculation gives us: 45.72 / 2.4 = 19.05 m).
If your calculations are not very good, use an online calculator to determine the height of the tree, such as this one.

Using Pencils and Helpers

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Use this method instead of the shadow method. Although less accurate, you can use this method when the shadow method doesn’t work, on a cloudy day, for example. Moreover, if you have a tape measure, you don’t have to calculate anything. If not, then you’ll need a ruler and do some simple multiplication.

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Stand far enough away that you can see the entire tree from base to top without moving your head. For the most accurate measurement, you need to stand on the ground level with the ground around the base of the tree, not higher or lower. Obstacle-free vision is better.

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Straighten your hand holding a pencil. You can replace the pencil with anything small and straight, like a paint stick or a ruler. Holding the pencil in your hand, straighten your arm so that the pen is directly in front of you (between you and the tree).

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Close one eye and tilt the pen up or down so you can see the tip of the pencil coincide with the top of the tree. The easiest way is to turn the pointed end of the pencil upwards. The tip of the pen will cover the top of the tree when you look at the tree “through” the pencil.

Move your thumb up or down the pencil until the tip of the pen is in line with the stump. While keeping the pen in the same position as the tip of the tree (as in step 3), move your thumb to a point on the pen that coincides with the point at the base of the tree (monocular view). Now the pencil covers the entire length of the tree from root to tip.

Rotate the arm so that the pen is horizontal (parallel to the ground). Keep your outstretched arm at the same distance and make sure the pen stays in line with the stump.

Ask the helper – maybe a friend – to move so you can see them “through” the pencil. Meaning their legs are in line with the tip of the pencil. The distance between you and the helper should be the same as the distance between you and the tree, neither further nor closer. Depending on the height of the tree, you can stand away from your friend, gesture with your hand (not holding a pencil) to tell them to stand further, closer, or move left or right.

Using the Inclinometer and Meridian Viewer

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Using this method will give more accurate results. The above methods are also accurate, but with a little more calculation and specialized tools you will have more accurate results. It sounds surreal, but it’s not: all you need is a calculator that can calculate the “tank”, a plastic protractor, a straw, a piece of string so you can make your own inclinometer. An inclinometer measures the angle of an object, in this case the angle between you and the top of a tree. Meridian sighting devices serve the same purpose but are more complex, using telescopes or lasers for more precise results.

Same paper as the Sheet Method but this method, in addition to being more accurate, allows you to measure the length of any distance, instead of moving back and forth so that the paper aligns with the tree trunk.

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Measure the distance to the aiming position. Stand with your back to the tree and come out to a point where the ground is level with the ground around the base of the tree and from where you can clearly see the top of the tree. Go straight, using a tape measure to measure the distance between you and the tree. You don’t have to be at a predetermined distance from the tree, but often this method works best when you are 1-1.5 times its height from the tree.

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Measure the elevation angle to the top of the tree. Look at the top of the tree and use an inclinometer or meridian to measure the “angle of elevation” between the tree and the ground. The elevation angle is the angle made by two lines—the line on the ground and your eye’s line of sight to a point (in this case, the top of a tree)—that is, to you, the vertex of the angle.

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Find the tangent of the lift angle. You can find the tangent of an angle using a calculator or trigonometric function table. This method of finding tangent can vary depending on the calculator you use, but usually you just need to press the “TAN” key, enter the angle value, and press the “equal” (=) key. If the lift angle is 60 degrees, you just need to press the “TAN” key, enter the number “60”, and press the equal key.

Click here to go to the website for calculating the tangent of an angle.
The tangent of an angle in a right triangle is calculated by dividing the adjacent side of the angle by the side opposite the angle. In this case, the opposite edge is the height of the tree, the adjacent edge is the distance between you and the tree. ^{[4] X Research Sources}

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Multiply the distance between you and the tree by the tangent of the elevation angle. Remember that you measured that distance in the first place. Multiply this distance by the calculated tangent value. The result will be the height of the tree as seen by your eyes because that’s the position you use to calculate the tangent of an angle.

If you read the previous step about defining the tangent of an angle, you can see why this method works. As said, tangent of an angle = (height of the tree) / (distance to the tree). Multiply each side of the equation by (distance to tree) and you get (tangent of an angle) x (distance to tree) = (height of tree from your eyes)!

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Add your height to the above result. You get the exact height of the tree. Since you are using an inclinometer and looking at the meridian from your eyes, not from the ground, you must add up your height to get the exact height of the tree. You may get more accurate results if you measure your height from your eyes instead of from the top of your head.

If you’re using a paper meridian, add the distance from the point your eye sees the meridian to the ground instead of your height.

Advice

You can increase the accuracy of the pencil and lift method by measuring several times from different points around the tree.
Many trees are not perfectly straight. So, if you’re using the lift angle method, you can adjust by measuring the distance between you and the point on the ground just below the treetop, instead of measuring the distance between you and the base of the tree.
You can use tree height measurements as an entertaining activity for kids in grades 4 through 7.
To increase the accuracy of the shadow method, you can measure the shadow of a ruler or a straight stick of known length instead of using the person’s height.
Use uniform units (for example, multiply and divide meters by meters, centimeters by centimeters)
You can create an inclinometer using a protractor. See also related articles in the same category for how to do it.

Warning

These methods will not work if the tree grows on a slope. Professionals will use a meridian to measure it, but this is too expensive for you to do.
For the lift angle method, if you follow the steps correctly, you can calculate the correct height with an error of 0.6-0.9 m, it is also very easy to make mistakes especially when the tree is bent or growing in the wrong place. slope. If accuracy is required, contact your local metrology service or similar organization for assistance.

Things you need

A friend (optional but with help it will be faster and more enjoyable)
Roll ruler or sewing ruler
Or an inclinometer or a meridian sight
Or a piece of paper
With a pencil (for each method)

Steps