How to Find the Center of a Circle

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Introduction: How to Find the Center of a Circle

This is simply a method to find the center of a circle, using very simple techniques. You'll need a ruler, a pencil and some way of measuring right angles.

You might want to use this technique to know where to drill the hole in the middle or draw concentric circles on the surface.

I can't take any credit for this as I probably learnt it at school, many eons ago. I just thought I'd add it because I saw lots of methods for drawing circles, using bits of string, wooden battens etc. but nothing for reverse engineering the problem.

If it's not correct then I can only blame my very poor memory.

Step 1: Draw a Chord Across the Circle

Draw a line across the circle near the edge so it cuts the circumference in two places. This is called a chord.

If you can also make the chord a nice easy length i.e. 10, 20, 24, etc this might make life easier in the next step.

Step 2: Find the Mid Point of the Chord

Draw a line perpendicular to the chord, half way along it's length.

Now you know why it's easier to pick an easy length to start with.

Make sure it goes past where the center of the circle should be. You can go straight across if that's easier.

Step 3: Repeat Step 2 for Another Chord

Repeat step 2 for another chord.

This should be enough to find the center of the circle, but you can add more if needed.

Step 4: Use More Chords for Accuracy

If you're not that confident of your measurements, then you can use as many chords as you like, until you're happy with the result.

Once you have the center marked you can use this information for other things, like drilling a hole in the middle, drawing concentric rings etc.

That's it, short and sweet.

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36 Discussions

This is a great Instructable, but you need to add a main image of the final project to the intro step. Please do that and leave me a message when you have so that we can publish your work. Thanks!

a bit hard, I wish there was an easier way to find the middle of a circle:(

Or, you can inscribe a right triangle in your circle and the center is at hypotenusa / 2

A clear Instructable. If you use a tangent instead of a chord you automatically have the point from where to draw the perpendicular.

A simple and accurate way to find a right angle to any line is as follows :

- Take a divider (pair of compasses) and set it to a length greater than half the length of the line, it doesn't matter exactly how long as long as it is more than half, but you need to keep the divider set to the same length throughout.

- Set the point of the compass at one end of the line (in this case where the secant intersects with the circle and draw a circle.

-Repeat the process with the point set at the other end of the line so you now have two circles which intersect each other.

- Draw a straight line between the two points where the circles intersect, this will cross the original line at it's mid-point at 90 degrees to it.

This is generally a more accurate method than measuring the midpoint with a ruler and using a square to find the right angle and doesn't require any measurements or calculations.

2 replies

Thank you Chris. I'm going to try that!
Another thought for people trying to apply this stuff to objects in the real world - it's very likely that your 'circle' is not actually a circle.

You can also use this technique to prove that your ruler or your square or their operator is broken. Like I just did.

8 year old instructable.... still giving, and going strong. Thank you! :-)