In a secret northern California location, a tree called Hyperion was measured at a record height of 115.61 meters! Believe it or not, the measurement was done using a very long tape measure, but there are much simpler methods to try. While you won't be able to be accurate to the centimeter, these methods will give you good approximations and work for any tall object, such as telephone poles, buildings, or magic bean trees - if you can see the top, you can measure them.
Steps
Method 1 of 4: Method 1: Use a Piece of Paper
Step 1. Use this method to find the height of a tree without resorting to mathematical calculations
All you need is a piece of paper and a tape measure. No calculations are needed; However, if you are interested in the theory of this method, you will need to know some notions of trigonometry.
The "Using a clinometer" method goes into the details of the calculations and reasoning that allow it to work, but you won't need these notions to find the height
Step 2. Fold a piece of paper in half to form a triangle
If the paper is rectangular, you will need to fold it into a square. Fold one corner over the other to form a triangle, then cut off the excess paper above it. Only the triangle you need should remain.
The triangle will have a right angle (90 °) and two angles of 45 °
Step 3. Hold the triangle in front of one eye
Keep the angle right and point the rest of the triangle towards you. One of the shorter sides should be horizontal (flat) and the other vertical (pointing straight up). You should be able to look along the longer side and looking up.
The longest side, the one that will guide your gaze, is the hypotenuse of the triangle
Step 4. Move away from the tree until you can align its tip with the tip of the triangle
Close one eye and use the other to look directly along the hypotenuse of the triangle, until you see the very top of the tree. You will need to find the point where your line of sight follows the longest side of the triangle to the top of the tree.
Step 5. Mark this point and measure the distance from the base of the tree
This distance will almost correspond to its height. Add your height to this value, because you were looking at the tree without having your eyes on the ground. Now you have your answer!
To learn how this method works, read the "Using a Clinometer" section. There is no need to do calculations for this method, thanks to a little trick: the tangent of an angle of 45 °, which you used, is equal to 1. The equation can be simplified like this: (Height of the tree) / (distance from the 'tree) = 1. Multiply each side by the distance from the tree and you get: height of the tree = distance from the tree
Method 2 of 4: Method 2: Compare the Shadows
Step 1. Use this method if you only have a tape measure or ruler
Without the help of additional equipment, you will be able to obtain an accurate estimate of the height of the tree. You will have to do multiplication and division, but no other complex calculations.
If you want to avoid calculating altogether, you can use an online tree height calculator, such as this one, and enter the measurements found using this method
Step 2. Measure your height
Use a tape measure to measure your standing height. Do this while wearing shoes. Since you will still need a piece of paper, write down your height so you don't forget it.
- You will need a single number, in meters or centimeters.
- If you are in a wheelchair or cannot stand for another reason, measure your height in the position you will hold to measure the tree.
Step 3. Stand on flat, sunny ground near the tree
Try to find a spot where the shadow on the ground is flat to get more accurate measurements. For best results, follow this method on a full sun day. If the sky is cloudy, it may be difficult to accurately measure the shadows.
Step 4. Measure the length of your shadow
Use a tape measure to calculate the distance between your heels and the tip of your shadow. If you don't have someone to assist you, you can mark the end of the shadow by throwing a stone at it while standing. Or even better, place the stone on the ground in any position, and then move so that the tip of the shadow coincides with the stone; finally measure from where you are, to the stone.
Write and name each measurement immediately after taking it to avoid confusion
Step 5. Measure the length of the tree shadow
Use the measuring tape to determine the length of the tree shadow from the base to the tip. This system works best if the ground around the tree is fairly flat. If the tree is on a slope, for example, your measurement won't be very accurate. You need to do this as quickly as possible after measuring your shadow, as the position of the sun in the sky (and therefore the length of the shadow) changes slowly, but steadily.
If the shadow of the tree is on a slope, it is possible that at another time of day the position of the shadow is more favorable
Step 6. Add half the width of the tree to the length of the shadow
Most trees grow straight up, so the exact tip of the tree should be precisely in the center. To find the total length of its shadow, you should add half the trunk diameter to the measurement. This is because the tallest tip casts a longer shadow, but some of it falls on the tree itself and you can't see it.
Measure the width of the log with a long ruler or straight tape measure, then divide it by two and you will get half the width. If you have trouble figuring out how wide the trunk is, draw a square around its base and measure one side of that square
Step 7. Calculate the height of the tree using the numbers you marked
You should now have written three numbers: your height, the length of your shadow, and the length of the tree shadow (including half the width of the trunk). The lengths of the shadows are proportional to the heights of the object. In other words: the length of your shadow divided by your height will always be equal to the height of the tree shadow divided by the height of the tree. We can use this equation to calculate the height of the tree:
- Multiply the length of the tree shadow by your height. If you are 1.5 meters tall, and the shadow of the tree is 30.48 meters long, multiply these two values together: 1.5 x 30, 48 = 45.72.
- Divide the result by the length of your shadow. Following the example above, if your shadow is 2.4 meters long, divide the answer by that number: 45, 72/2, 4 = 19.05 meters).
- If you have trouble with calculations, you can find an online tree height calculator on this site.
Method 3 of 4: Method 3: Use a Pencil and Assistant
Step 1. Use this method as an alternative to the shadow method
While this method is less accurate, you can use it even if the weather is cloudy. Also, if you have a tape measure with you, you can avoid making calculations. Otherwise, you will have to find it later and perform some simple multiplications.
Step 2. Stand far enough away from the tree so that you can see it all - top to bottom - without moving your head
For a more accurate measurement, you should stand on ground at the same height as the base of the tree. Your vision shouldn't be obstructed.
Step 3. Hold the pencil at arm's length
You can use any small, straight object, such as a brush or ruler. Hold it in your hand and extend your arm forward, so that the pencil is in front of you at arm's length (between you and the tree).
Step 4. Close one eye and adjust the pencil so that the tip of the pencil aligns with the tip of the tree
It will be easier if you hold the pencil with the tip pointing up. The tip of the pencil should cover the tip of the tree as you look at it.
Step 5. Move your thumb up or down along the pencil so that the nail is aligned with the base of the tree
Now the pencil "covers" the entire height of the tree, from base to tip.
Step 6. Rotate the arm so that the pencil is horizontal (parallel to the ground)
Keep your arm extended the same distance and make sure your thumbnail is still aligned with the base of the tree.
Step 7. Have your friend move so that you can see him "through" the tip of the pencil
That is, its feet should be aligned with the graphite toe. It should be at the same distance from the tree, neither closer nor further from you. Since, depending on the height of the tree, you and your friend may be far apart, try using visual cues to guide them to where they need to go.
Step 8. If you have a tape measure with you, calculate the distance between your friend and the tree
Have it stay in place or mark the spot with a stick or stone. Then use the tape measure to determine the distance between that point and the base of the tree. The distance between you and your friend will be the height of the tree.
Step 9. If you don't have a tape measure with you, mark your friend's height and tree height on the pencil
Scratch or mark the pencil where your nail used to be; this will indicate the height of the tree according to your perspective. Use the same method as before to "cover" your friend with the pencil, with the tip at the height of his head and the nail at his feet. Make a second mark in this position of the nail.
Step 10. Find the answer when you have a tape measure available
You will need to determine the length of each mark and your friend's height, but you can do this when you are home, without having to go back to the tree. Use a scale ratio to find the height of the tree. For example, if your friend's height mark is 5cm from the tip of the pencil and the tree height mark is 17.5cm from the tip, the tree is 3.5 times your friend's height, since 17.5cm / 5cm = 3.5cm. If your friend is 180cm tall, the tree will be 180cm x 3.5 = 630cm tall.
Note: If you have a tape measure with you to measure the tree, you won't need to do any other math. Read the previous step, in the section: "if you have a tape measure".
Method 4 of 4: Method 4: Using a Clinometer
Step 1. Use this method to get a more accurate measurement
The other methods are surprisingly accurate, but with a few more calculations and specialized tools you can get even more exact measurements. It's not as difficult as it sounds - you'll need a calculator that can calculate tangents, a plastic protractor, a straw, and a piece of string to build a clinometer. This tool measures the inclination of an object or, in this case, the angle between you and the top of the tree. A theodolite is a more complex instrument that performs the same task, but uses a telescope or laser for greater accuracy.
The "piece of paper method" uses paper as a clinometer. This system, in addition to being more accurate, allows you to measure height from any distance, without having to go back and forth to align the sheet with the tree
Step 2. Measure the distance from a predetermined position
Lean your back against the tree and walk to a point that is approximately the same height from the ground as the base of the tree and from which you can clearly see the top. Walk in a straight line and use a tape measure to determine the distance from the tree. You won't need to reach a precise distance, but for this method to work best you will need to be about 1-1.5 times the height of the tree.
Step 3. Measure the elevation angle from the top of the tree
Sight the top of the tree and use a clinometer or theodolite to measure the "elevation angle" between the tree and the ground. The elevation angle is the angle formed between two lines - the ground plane and your line of vision and a high point (in this case the tip of the tree) - with you as the vertex of the angle.
Step 4. Find the tangent of the elevation angle
You can find the tangent of an angle using a calculator or a table of trigonometric functions. The method for finding the tangent may differ depending on the calculator, but usually you just need to press the "TAN" button, enter the angle and then press the "equal" (=) key. For this, if the elevation angle is 60 °, you will simply have to press "TAN" and then enter "60" and press equal.
- Click this link to find an online bribe calculator.
- The tangent of an angle in a right triangle is defined by the side "opposite" to the angle, divided by the side "adjacent" to the angle. In this case, the opposite side is the height of the tree and the adjacent side is the distance from the tree.
Step 5. Multiply the distance from the tree by the tangent of the elevation angle
Remember, you measured the distance from the tree at the beginning of this method. Multiply it by the tangent you calculated. The number obtained indicates how far above the eye level the tree is, because it is the level from which you calculated the tangent.
If you've read the previous step on defining a tangent, you can understand why this method works. As described above, the tangent = (height of the tree) / (distance from the tree). Multiply each side of the equation by the distance from the tree and you get: tangent x distance from tree = tree height
Step 6. Add your height to the one calculated in the previous step
You will get the height of the tree. Since you used the clinometer at eye level and not at ground level, add your height to the measurement to get the total tree height. You can get a more accurate value by measuring your height at eye level, not above your head.
If you are using a static theodolite, add the ground clearance of the observation point to the calculated value, not your height
Advice
- You can increase the accuracy of the pencil method and those of the elevation angle by taking several measurements from various points around the tree.
- Many trees do not grow straight and are therefore not perfectly vertical. Using the elevation angle method, you can make a correction for leaning trees by measuring the distance between you and the top of the tree, rather than between you and the base of the tree.
- This can be a fun activity for children in the fourth to seventh year of education.
- To increase the accuracy of the shadow method, you can measure the shadow cast by a stiff tape measure or straight stick of a height known to you, instead of a person's height. Depending on how you stand, your height may vary (e.g. if you are slouching or if you are tilting your head slightly).
- Pay attention to the units of measurement, and always use the same units for all calculations.
- You can make a clinometer very simply using a protractor. Check out related wikiHow articles for instructions on this.
Warnings
- These methods don't work very well if the ground is sloped.
- While the elevation angle methods, when used correctly, can calculate the correct height of the tree with an error of between 60 and 90 cm, there is a strong component of the possibility of human error, especially if the tree is tilted or placed on a slope. If accuracy is absolutely necessary, consult the extension service or other similar agencies for support.
