Using a Clinometer to Measure Height

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Introduction: Using a Clinometer to Measure Height

In this Instructable, I'll show you how to use a clinometer to measure the height of a tall object (for help constructing your own clinometer from basic classroom materials, click here).

What you will need;

Clinometer
Tape measure
Paper
Pen or pencil
Assistant

Step 1: Pick a Spot

Pick a spot to measure your object (I measured a telephone pole).  You should be far enough away from your object that you can see the top of it, and you need to be on level ground with the base of the object.  I like to set something down by my feet once I've picked my spot, so that I can easily come back to it.

Step 2: Measure Angle

Here's where we bust out our handy clinometer.  Look through the straw of your clinometer at the top of the light pole (or whatever object you're measuring).  The weighted string should hang down freely, crossing the protractor portion of the clinometer.  Read the angle shown, and subtract from 90° to find your angle of vision from your eye to the top of the pole (it can be helpful here to have an assistant to read the measurement while you look through the straw).  Record your results on your paper.

From my spot, my clinometer (read by my assistant) showed 55°.  Subtracting from 90°, that indicated that I looked at an angle of 35° to the top of the telephone pole.

Step 3: Measure Distance

Once you have your angle of vision, use your tape measure to find the distance from the spot you're standing to the base of the object you're measuring (an assistant comes in handy here, too).  We must know how far away you are to accurately calculate the height.

My spot was 15.6 meters from the base of the telephone pole I measured.

Step 4: Find Your Eye-height

The last piece of data you need to calculate the height of your object is the height from the ground to your eye (your eye-height).  Have your assistant help you measure this using your tape measure.

My eye height was recorded for this example as 1.64 meters.

Step 5: Draw a Picture

Time to move inside.  In calculating the height of the object you just measured, I find it helpful to begin by drawing a picture and labeling it with all of the information I have.

Step 6: Model As a Triangle

The next step is to simplify your drawing to model your system as a right triangle.  Label your triangle with the angle you read on your clinometer as well as the distance you were standing from the object (we don't need the eye-height just yet).

Step 7: Solve for X

We can find x in this triangle (which represents the portion of the height from eye-level up) by using some basic trigonometry, specifically the tangent ratio of the triangle:

tan(angle) = x / distance

Multiply by the distance on both sides and you get:

x = tan(angle) * distance

Use a calculator to multiply these together and get a decimal value (be sure your calculator is in 'degrees' mode, rather than 'radians'!).


In my example:

tan(35°) = x / 15.6

x = tan(35°) * 15.6

x = 10.92 meters





Step 8: Combine With Eye Height

To find the height of your object, bring this x value back to the original drawing.  By labeling it, we can see that the height of the object, h, is equal to the x value we just found plus the eye-height we measured earlier:

h = x + (eye-height)


In my example:

h = 10.92m + 1.64m
h = 12.56m


There you have it!  A few basic classroom materials and a little bit of trigonometry and you can measure the height of anything around you!

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52 Comments

Thank u very much. I would have been lost and fail my math assignment.

I used my phone with a straw on top and the compass app (the apple compass has a level, which is nice)

1 reply

another thing i noticed is that if you keep walking towards the object until the clinometer says 45 degrees, the distance between you and the object is exactly the height of the object (+ your eye height)

Thank you very much. With out this it is impossible to complete my math activity

THANK YOU SO MUCH

it was very helpful for my school project!

I used this in class with my students it worked great!

Great instructable. im glad to see this tool on the site.
People have been mentioning the BSA method, which is fine, but the accuracy compared to a protractor and tape measure will be much less. And if you don't need accuracy, why even use the stick, just eye-ball it. (My two cents)

BSA handbook has an easier method that doesn't require an assistant or math or a protractor. Just cut a stick at eye level push stick into ground and lie down with feet against stick. When top of object is level with top of stick, mark where you eye is and measure to base of the tall object.

1 reply

Ok great, make an instructable.

There is a little mistake in your logic , formula
4. must be H=P(sin phi)
5. mus be X=P(cos phi )

try it with a value phi = 85 and you will see when you trace it on scale

Shows how long it's been since I used any algebra on purpose, but how did you get the 35 degrees for the angle?

user

I'm not seeing where you used the eye height in your calculations. Did I miss something?

2 replies

We added the eye-height to the height (x) we found in the Tangent calculation to get the final height.

If you are in Britain, the clinometer shown here is called a protractor available at most stationers, this method only works on level ground, more maths if your on a slope

1 reply

The green plastic protractor is the main piece of equipment here, but clinometer is the name we used for the entire device when assembled (made up of protractor, straw, string, and weight).

A few years ago (taking a Trig review course at the time) I did something similar. My approach was more expensive than yours; my goal was best possible accuracy.

Coincidentally, I measured a telephone pole too.

Rather than making eye-level measurements, I made ground-level measurements, and measured the angle of elevation at night (since I was using a laser pointer for aiming).

The attached photo shows a level with integrated laser pointer, and a 360-degree protractor.

Clinometer.jpg