Introduction: Pi Tape - Easily Measure the Diameter of Anything
Have you ever wanted to measure the diameter of a circular object and tried using a ruler to somehow find the diameter? Well, I have been in that situation many times. It's not always easy, especially if it's something like a hollow cylinder because you can't determine the midpoint to align your ruler.
That is where the Pi Tape comes in handy. All you need to do is wrap this tape around the object and it will directly give you the diameter!
It's extremely easy to make, so let's get making!!
Edit: I see a lot of people are confused that this is a standard tape measure. This is different from a standard tape measure. If you wrap a tape measure around an object, you'll be measuring it's circumference. This tape is designed to do the math for you and directly give you the diameter. So it has Pi hidden in it! Read ahead to find out!!
Transparent tape (optional)
Step 1: How It Works
Let's get the basics out of the way.
Suppose you want to measure the diameter of a cup. I'm using the Instructables cup here. We know that the diameter is the circle's largest chord and it always passes through the center of the circle. So in order to measure the diameter, you'll need to place your ruler on the top of the cup in such a way that it touches the center of the circle. But wait! The cup is hollow and you don't know where the center is. That's a problem.
To solve this problem, we can measure the circumference of the cup instead.
Because we know that the circumference of a circle is πD, we can obtain the diameter by dividing the circumference by π.
But π has a lot of digits after the decimal place (3.14159265358979...) and even just using 3.14 will make calculations hard if you don't have a calculator at that moment.
So we can make a tape with π divisions instead. Now when we divide it by π, we're just canceling out the π terms and the number left directly gives the diameter! Let's make it to find out if it works.
Step 2: Just Cut and Mark!
Cut out a long strip from a chart paper to make the tape. We need to make markings at every pi centimeters (or inches, it's your choice). Note that if your divisions are in cm then the diameter you obtain will also be in cm, and the same happens with inches.
You can use a ruler to make markings at 3.14cm, 6.28cm, and so on. But doing this will add an error with every division because you're approximating pi to two decimal places and multiplying a number to that approximation.
So, what we're going to do is take another strip of paper and make a marking at 3.14cm. Now we cut out this strip and use it as a template to make all the markings on our ruler.
Once all the markings are done, we will start writing numbers starting from 0. Don't label the first marking 1. Label it 0. We need some buffer before starting our number. You'll soon see the reason for doing this.
Step 3: Testing It
Now take a circular object whose diameter is known to you. This is to test if our pi tape is working.
Here I've taken the lid of a container whose diameter I know to be exactly 6.5 cm.
To find out it's diameter using the pi tape, just wrap it around the circumference and the point which coincides to the 0 reading is the diameter.
But wait. We see here that the diameter shown by our pi tape is around 6.6 to 6.7 cm. There's an error of around 2mm. Why so?
This is because when we wrap the tape around an object we're now adding the thickness of our tape on both sides of the object. So we're adding an error of 2×Thickness of the tape×pi. That's quite a lot of error even for a tape as thin as paper.
Fortunately, it's easy to solve this problem. All we need to do is make a marking before the 0 reading at the correct diameter value. In my case, I have to make a marking that coincides with 6.5cm. Now we have compensated for the thickness and can use this marking as our reading point. The number that coincides with this new point is the diameter of the object.
Step 4: We're Done!
As simple as that! Now you have your very own pi tape! I tried measuring the diameter of the Instructables cup and it comes out to be 8.6 cm. I don't have a Vernier caliper but I'm sure the folks at Instructables will know if my measurement is correct :p
Have fun making your own pi tape!
Participated in the
Pi Day Speed Challenge