## 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.

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!

Nice

thanks

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

Can you elaborate on that ?

With graphics if possible ?

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.

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.

My method too.

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! :-)

Thanks for the comment

Thanks a lot very simple,

Got here from a quick google search. Didn't really read through all instructable, just the first image was enough. Thanks!

Great ibble !!! I've been trying to remember how to do this for ages now I know. Thank you for adding this. I can now get my water pump sorted out now.

Thank You. When I worked on the railroad we had tools and machines to do all that.

I had just made 57 2 inch round wood blocks and then couldn't figure how to find the centers. Thanks to this article I'll make a jig and drill them now.

you are awesome

Just used this. Thanks!

Thanks to you and all the comments. Please. Take credit. I smacked my head and went, "Of course," but didn't remember how to do this in spite of many math courses. And I brag that I do too use math in my daily life.

Thanks! Me and my grandpa are making a table for him because he wants one! I don't know why, but wateva!!!

a simpler method involves inscribing a right angle into the circle. the hypotenuse is a diameter, and then find the halfway point of the hypotenuse for the center

Or do it this way :

1. Draw a square around the circle.

2. Draw a line from top-left to bottom-right corner of square.

3. Draw a line from top-right to bottom-left corner of square.

4. Where the lines cross is the center.

I just got the biggest kick out of this it works perfecto.

Using this for locating pots in a project box!

your instructable is being applied as we speak, thanks ! ! !

In the first step, the line that you proposed was a chord, is technically a "secant", not a "chord".

okey dokey. thanks for the technical correction.

Thank you so much for this helpful technique. I wish I was smart enough to figure this out on my own; I've been stressing about perfectly centered holes on a number of recent projects and didn't know how to find the center. Thanks again - a huge help! clicclic

Thanks for the comments. I can't take credit for this though, as I'm sure it was drummed into my skull at school. I do try to think of things some people know as being so obvious they assume everybody must know it.

Well you put it here and it is something many will want to do.

I am starting a project in which I will need the centers of some circles.

I was going to do what you have done as part of my own instructable but now I will just give a link to this.

Thanks

fairly simple...=)

its so simple once you know it! thanks for sharing!

that is a cool way of finding the center.

thank you very much for your comment.