## 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 15.6meters 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!

## 63 Comments

Question 4 years ago on Step 8

What if another person tried to determine the height of the object and the person had a different height then the first person who tried to determine the height that means the height from the second person eyesight measurement to the ground will be different than the first persons measured so this means you will have 2 different angles of elevations and this will obviously give you 2 different answers if you solved it the same way, so does this mean it's accurate or not accurate if it is accurate how can find the actual height of the object with 2 different people with different heights?

Reply 4 years ago

Two people with different heights measuring from the same place will get different angle readings. When you plug those in to the Tangent, the difference in results will cancel out the difference in eye-height, giving both people the same total answer.

Reply 1 year ago

Pls how do you mean by plug in to the tangent? Thanks

Answer 2 years ago

Your calculation height are different too..

Question 2 years ago on Introduction

How did you get the 35° by clinometer? Did you subtract something with it? or it is the exact value you got? Thanks!

Question 3 years ago on Step 8

hi this is JAY ,If we measure like this we can get approximate measurement or exactly measurement?

Answer 2 years ago

Its exact as this is using mostly maths..

Question 3 years ago on Step 4

How’d yu get 1.64m please

Answer 2 years ago

Its his eye level height.

The height from which he took the angle..

4 years ago on Step 7

mam how can we get 10.92 when we multipley 35 degrre to 15.6m mam it actual answer is 546

Reply 4 years ago

You don’t multiply 35 deg x 15.6m, you multiply tangent(35deg) x 15.6m, as shown.

5 years ago

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

6 years ago

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

Reply 6 years ago

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)

7 years ago

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

7 years ago

THANK YOU SO MUCH

7 years ago

it was very helpful for my school project!

8 years ago on Introduction

9 years ago on Introduction

Fantastic! Thanks a lot!

9 years ago on Introduction

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