Content

• To step
• Method 1 of 4: Using a sheet of paper
• Method 2 of 4: Compare shadows
• Method 3 of 4: Use a pencil and an assistant
• Method 4 of 4: Using an inclinometer or transit
• Tips
• Warnings
• Necessities

In a secret location somewhere in northern California, there is a tree with a record height of 115.61 meters! Believe it or not, this tree has been measured with an extra long tape measure, but there are easier ways you can try this out for yourself. While your measurement will not be accurate to the centimeter, these methods will give a good estimate and will work for any tall object. Telephone poles, buildings or a beanstalk: as long as you can see the top, you can measure it.

To step

Method 1 of 4: Using a sheet of paper

1. Use this method to find the height of a tree without all the math. All you need is tape measure and paper. No calculations are required; but if you want to know how it works, you can use some trigonometry.
   • The method with an inclinometer or transit does require several calculations and explains why this works, but that is not necessary with this method.
2. Fold a piece of paper in half so that it forms a triangle. If the paper is rectangular (not square), you will have to make a square from a rectangular sheet of paper. Fold one corner over to form a triangle and cut or trim the extra paper above the triangle. You now have a suitable triangle.
   • The triangle has a right angle (90 degrees) and two angles of 45 degrees.
3. Keep the triangle in front of one eye. Hold the right angle (that of 90º), the rest of the triangle points in your direction. One of the short sides should be horizontal, the other vertical (straight up). You must be able to see along the hypotenuse.
   • The sloping (longest) side you look along is called the hypotenuse.
4. Walk down the tree until you can see the top, seen along the triangle. Close one eye and look with the other eye along the hypotenuse until you see the top of the tree. You are looking for the point that is on the line that extends along the hypotenuse.
5. Mark this spot on the ground and measure the distance to the base of the tree. This distance is almost the full height of the tree. Add your own height, because you were standing while measuring. Now you have a very reasonable estimate!
   • For an explanation, see "Using an inclinometer or transit" below. Calculations are not necessary, because you use a trick: the tangent of 45º is 1. The equation then becomes: (Height) / (Distance) = 1. Multiply each side by (distance) and you get: Height = Distance.

Method 2 of 4: Compare shadows

1. Use this method if you only have a tape measure or ruler. You do not need any other equipment for an accurate estimate of the height of the tree. You will have to multiply and divide a bit, but nothing else.
   • If you don't want to calculate at all, go to this site to enter your measurements and the height will be calculated for you.
2. Measure your own height. Use a measuring tape or measuring stick for this. Keep your shoes on and stand up straight and measure your height. Write down your height so you don't forget.
   • If you are in a wheelchair or cannot stand upright, measure the height depending on the position in which you are measuring, while measuring the tree.
3. Stand in a sunny, level spot near the tree. You need level ground to measure the shade properly. Do this on a sunny day for best results, otherwise the shade will be hard to see.
4. Measure the length of your shadow. Use a tape measure or measuring stick to measure the length of your shadow. If you don't have an assistant on hand, you can mark the head end of your shadow by placing a marker with a pebble and then positioning yourself so that the top of your shadow just touches the pebble; then measure the distance from heel to head end.
   • Write down every measurement you take so you don't mix them up.
5. Measure the length of the tree shade. To do this, use your tape measure and measure from the base of the tree to the top of the shade.This works best on reasonably flat, horizontal surfaces; your measurement will deviate considerably on a slope. Measure the shade of the tree immediately after measuring your own shade, because of the movement of the sun that changes shade length.
   • If the tree shadow falls on a slope, there may be a different time of the day when the shadow avoids the slope, either by being shorter or by pointing in the other direction.
6. Add half a tree width to the length of the tree shade. Most trees grow straight up, so the highest tip of the tree should be above the exact center of the tree. To determine the total length of its shadow, add half the diameter of the tree trunk to your shadow measurement. This is because the highest peak actually casts a longer shadow than you measure; some of it falls over the tree trunk, where you can't see it.
   • Measure the diameter of the trunk with a tape measure and divide it by 2. If you find it difficult to see the diameter of the trunk, draw a square on the ground around the trunk and measure one side.
7. Calculate the height of the tree using your measurements. You should now have three numbers: your height, your shadow length, and the tree shadow length (plus half a diameter). Your shadow length is proportional to the length of the object. In other words, (your shadow length) divided by (your height) is proportional to (the tree shadow length) divided by (the tree length). We can use this equation to find the length of the tree:
   • Multiply the tree shadow length by your height. If you are 1.5 meters tall and the length of the tree shadow is 30.48 meters, this will be: 1.5 x 30.48 = 45.72).
   • Divide the answer by your shadow length. If your shadow is 2.4 meters long, the effect will be 45.72 / 2.4 = 19.05 meters.
   • If you find these calculations tricky, use an online tree height calculator like this one.

Method 3 of 4: Use a pencil and an assistant

1. Use this method as an alternative to the shading method. Although this method is less accurate, you can use it when the shading method is not working, such as on a cloudy day. Also, if you have a tape measure with you, you can avoid doing calculations. Otherwise, you will have to use a tape measure later on to do some simple multiplications.
2. Stand far enough from the tree that you can view the entire tree without turning your head. For the most accurate reading, stand so that it is on a patch of ground level with the base of the tree, not higher or lower. You need to have the tree in view as freely as possible.
3. Hold a pencil (or similar object) point up at arm's length (with your arms outstretched, between you and the tree).
4. Close one eye and move the pencil so that its tip "touches" the top of the tree. You look through the pencil, as it were.
5. Move your thumb up and down so that the tip of your thumb is in line with the base of the tree. Hold the pencil tip near the top of the tree (as mentioned in Step 3), while moving your thumb towards the base of the tree trunk. Now the pencil will take up the full height of the tree, from the base to the top.
6. Now rotate your arm so that the pencil is parallel to the ground (horizontal). Keep your arm outstretched at the same distance and make sure your thumbnail is aligned with the base of the trunk.
7. Have your assistant change positions each time so that you can see him or her along the pencil tip. Your assistant's feet should line up with the bottom of the pencil. He or she is about the same distance from the tree as you. Since you can be at a considerable distance from your assistant depending on the height of the tree, it is an idea to use hand signals to indicate that he / she should move closer or further away. or to the left or right.
8. Measure the distance between your assistant and the tree with a tape measure. Make sure the assistant's position is marked with a stick or rock. Then measure the distance from the mark to the tree. This distance is the height of the tree.
9. If you don't have a tape measure with you, mark the length of your assistant and the height of the tree on the pencil. Mark the position of your thumbnail on the pencil; this is the height of the tree from your perspective. Use the previous method to determine the length of your assistant with the pencil tip and thumbnail and mark this on the pencil by your thumbnail as well.
10. Calculate the answer with a tape measure. Measure the length of each marker and the length of your friend. You can also do this at home. Compare the difference in the length of the marks on the pencil to the length of your assistant. For example, if your assistant's height marker is 5cm and the tree is 17.5cm, then the tree is 3.5 times the height of your friend, because 17.5cm / 5cm = 3 , 5. If your assistant is 180 cm long, then the tree is 180 cm x 3.5 = 630 cm high.

Method 4 of 4: Using an inclinometer or transit

1. Use this method for a more accurate measurement. The other methods are amazingly precise, but with a little math and specialized tools, you can get better results. This isn't as daunting as it sounds: all you need is a calculator that can calculate the tangent of an angle, and a cheap plastic protractor, a straw and a piece of string, to make your own inclinometer. An inclinometer measures the slope of objects, or in this case the angle between you and the top of the tree. A transit is a somewhat more complicated device made for the same purpose, but uses a telescope or laser for more precision.
   • The paper method basically uses a piece of paper as an inclinometer. Not only is this method more accurate, but it also allows you to measure the height of objects from any distance, instead of switching positions yourself to align the paper with the tree top.
2. Measure the distance to the measurement position. Stand with your back to the tree and walk to a point that is roughly level with the base of the tree trunk, with a clear view of the top of the tree. Walk in a straight line and use a tape measure to measure the distance to the tree. This can be any distance, but make sure to use about 1-1.5 times the height of the tree for the distance as this will give the best result.
3. Measure the angle of inclination to the top of the tree. Look at the top of the tree and use an inclinometer or transit to calculate the angle between the top of the tree and the ground. This is the angle between the imaginary hypotenuse, the straight line from your eye to the top of the tree, and the horizontal line from your measurement position to the base of the tree trunk.
4. Determine the tangent of the slope angle. Use a calculator for this. The method for finding the tangent can be different depending on your calculator, but usually you just press a "TAN" button> the angle> "=". So if the tilt angle is 60 degrees, it goes like this: "TAN"> "60"> "=".
   • Click this link for an online tangent calculator.
   • The tangent of an angle in a right triangle is defined by the "opposite side of the corner, divided by the side adjacent to the corner. In this case, the opposite side is the height of the tree, and the adjacent side is the distance from the tree.
5. Multiply your distance from the tree by the tangent of the slope angle. Remember that you measured the distance to the tree at the beginning of this method. Multiply this by the tangent you calculated. The product indicates how high the tree is from eye level, because that is the level you calculated with the tangent.
   • If you have read the earlier intermediate step on tangent definition, you will understand why this method works. As described earlier: the tangent = (tree height) / (distance to tree). Multiply each side of the equation by the (distance to tree) and you get (tangent) x (distance to tree) = (the tree height)!
6. Add your own height to the height you calculated in the previous step. Now you have determined the height of the tree. Since the inclinometer was at eye level, it is necessary to add your height to the actual height of the tree. You can get a more accurate result by measuring your height to eye level, not the top of your head.
   • If you are using a transit on a tripod, add the height of the tripod to the calculation, instead of your height.

Tips

• You can improve the accuracy of the tilt angle and paper method by taking several measurements around the tree.
• This is also a fun activity for children from grades 6-8.
• Use a measuring stick for more precision with the shading method.
• Always use the same units (multiply and divide meters by meters, not meters by centimeters, for example)
• With a protractor you can make a simple inclinometer. Read this article for instructions.
• Many trees have an irregular shape and grow crooked. With the slope method you can compensate for this by measuring the distance between you and that point on the ground, seen directly from the top downwards, instead of the distance to the bottom of the tree.

Warnings

• Although the slope method can calculate height accurately to within one meter, it leaves a lot of room for error. If accuracy is necessary, get help from a specialist in this field.
• These methods will not work well if the tree is on a slope. A professional surveyor uses an electronic transit in these situations, but these are somewhat too expensive for home use.

Necessities

• An assistant (handy and more fun)
• A tape measure, yardstick, inclinometer, or transit
• A sheet of paper and a pencil