Instructables
Picture of How to Find the Center of a Circle
Finding the centers of things for woodworking is pretty important.  Squares and rectangles are pretty easy, you simply draw two diagonal lines from the opposite corners and the point where they cross is the center of your material. 

Finding the center of a circle on the other hand wasn't quite as intuitive to me, and until doing some searching of my own, I didn't know that there was a simple and easy trick.  Time to share.

Similar circle finding Instructables can be found here:
http://www.instructables.com/id/Find_the_Center_of_a_Circle
http://www.instructables.com/id/How-to-Find-the-Center-of-a-Circle

 
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Step 1: Draw some chords

Picture of Draw some chords
chord%20of%20a%20circle.jpg
A chord is a line that intersects any two points on the circumference of a circle. 

They are easy to draw...simply take a ruler, place it down on the edge of your circle so that it crosses the outer edge in two places, and use a pencil to mark a line.  You've just created a chord. 

Technically to find the center of a circle you only need one perfectly drawn chord but since people aren't machines and there's some user error in the process, draw a couple so that you can average the results.

I've drawn five chords near the perimeter of the circle in the photo below.  Disregard the lines pointing in towards for the center for the time being.

Step 2: Mark the centers and draw a perpendicular line

Picture of Mark the centers and draw a perpendicular line
circle1_36554_lg.gif
Use a ruler to find the midpoints of the chords that you just drew.  If your chord measures 11" from end to end, the center of the chord is 5.5" from the ends.

Mark that point.

Then, using a square, draw a line that is exactly 90 degrees to the chord pointing towards the center of your circle.  Make it a little longer then where you think the center of the circle resides.

Do this for all of your chords.

Step 3: The center is the point where they intersect

Picture of The center is the point where they intersect
The center of the circle is the point where all of these perpendicular lines intersect.  I drew 5 different chords with 5 perpendicular lines coming from them, and you can see that they all come within about 1/16th" from each other.  

This means that the system works...ain't geometry cool?
 That method is very correct but I think its much easier and more accurate to do this with a compass.
Check this video out

http://www.youtube.com/watch?v=YOJbWo41gU0

http://www.youtube.com/watch?v=6q9jE6rvOWE
That is the correct way to finding the center of a circle. Since all points in a circle are equidistant from the center (aka, the same distance from the center), you can place the chores in any place meanwhile it cross the circle perimeter in 2 points. This chore is the base of an isosceles triangle created with these 2 points and the center of the circle (the 3rd point). In fact this method really finds the middle point in the base of the triangle. It's "triangle geometry" applied to a circle :).

And must be done with a compass. Using a rule introduces some error, unless you have excellent tools, you are excellent drawings lines... Although compasses are usefull on paper, using with an already cut circle can be hard to set the compas in a border. Anyway in my opinion, using the compass still is more accurate than using a rule.

But really any method is valid if you accomplish your goal. :)
nphillips62 years ago
A simple method to find the center of a circle when all you have is a ruler is to:

1. Set ruler down across circle at any point.
2.Trace both sides of ruler onto circle.
3.Measure each of the two lines and mark their centers.
4.Use ruler to connect these two marks and extend to edges of circle.
5.Measure that lines center point and you have found your center!

Its a fast method that should get you at least as close to the absolute center as the method shown here and only requires a ruler and pencil.

Cheers.
I like this method. Way simpler than mine
Nice method, thanks.

tareko2 years ago
There is an even easier method:
Take a square, align the outside of the rectangle with any point inside the circle. Mark down on the circle, the two points where the sides of the square intersect the circle. Draw a line connecting these two points. You have just traced a diameter.
Repeat the process in a diferent location and get another diameter. Where the two diameters intersect, there is the center

No compass, no measurents, no duvisions. Just a (90 degrees) square.
glorybe2 years ago
To get a dead accurate center on small dowels simply chuck the dowel in a lathe and put a tiny center drill in the tail stock and advance it until it touches the spinning dowel.
dado3 years ago
Finding the center of circles is of great interest to me, but I'm wondering how well / easy this would work for finding the centers of much smaller diameters. Say in the 3/4" size or so. Any advice for putting a pin in the exact center of a 3/4" or 1/2' dowel say? Thanks
Truehart dado3 years ago
Theoretically, the method works for any circle of any size. Practically, it all depends on how acurately you can draw the lines. As you can see in his 'ible he had about plus or minus a 1/16" and he was working with a decent diameter circle. If your dealing with finding centers of 3/4" OD on a regular basis then you might look into getting a combination square set that comes with a "center" head.
codydean3 years ago
at the end are you making a lid for a 5 gallon bucket
gemtree3 years ago
Thanks!
kleinjahr4 years ago
Oldie but goodie. Another method is to use hermaphrodite calipers to strike a series of arcs which intersect each other. Strike  lines through the intersections , where those lines cross is the center. Or you can simply make a center finder by clamping a straight edge to your carpenter's square so it bisects the right angle. Should be obvious how to use it. 
Rune Cutter4 years ago
I've been vexed by this for more years then I can say and you fixed it in seconds
conrad24684 years ago
 another way: draw 2 right triangles so that each of the vertices are touching the edge of the circle, where the hypotenuses intersect is also the center.
Kryptonite4 years ago
Awesome, nice job!

"Life is pointless, without geometry."
Morrighan4 years ago
My little sister is learning that at primary school! haha

Note: You will get better results if you use a compass to find the midpoints.
Chromatica4 years ago
 There is already a Ible on this that uses the same exact method.
Maybe because Euclid came up with it first?  Or the Egyptians before him?  Presentation is part of the package.

Or perhaps we should slam on people who write I'bles about using pre-existing Windows facilities, like streaming audio, since they are already clearly documented, so who needs yet another set of instructions?  I don't subscribe to that point of view.
 Well jezz. >sorry<
Jezz?

XD
 Its a oldie but a goodie.
Do you perhaps mean "Jeez"?
 OHHHHH!!! lol mispell
But hey we have been doing "it" for a while.
XD
Do you perhaps mean yet another word spelled with an i?
Yeah, but I've seen it both ways.
noahw (author)  Chromatica4 years ago
You're totally correct - we've already got a few of them.  I've even got a link to two other ones in my intro step. 

Just because we've got one of something of already doesn't mean that we can't have some more does it?
 No.
Yes, and one can do it fairly quickly with a simple steel square ( L shaped device).  I thought I had seen a device that makes it even easier though....but I can't find it anywhere.  It eliminates that need for a second (or more) measurements.
 
rimar20004 years ago
(removed by author or community request)
noahw (author)  rimar20004 years ago
I've written 132 Instructables over the last three years and also happen to be a full time employee of the website, so I've developed a bit of a thick skin when it comes to comments, but I really don't see what the big deal is here. 

If someone takes the time and effort to publish a nice Instructable that is well written and has some decent pictures, then that's something that the Instructables community should want and support. 

Just because it covers a topic that's already been documented doesn't mean that it isn't still a good addition to the site, or that it can't help someone new who hasn't seen the previous posts.  After all, how many titles start with "Yet Another..."?

Regardless, I'm of the mindset that everyone has something to share on this website, and a bunch of those things are bound to be the same.
bsantaana noahw4 years ago
Right on,write on, noah!
It is great for those of us who don't check the site everyday, who might not know that an Instructable has already been Ibled before.
rimar2000 noahw4 years ago
Yes, you are correct, pardon my comment. I will erase it.

the center of a circle can be found in an easier manner, so long as the circle isnt too huge. get out your old school compass (the thing thats pointy and has a pencil on one end used to draw circles) and you just make it the same size as the circle. then you just place the center of your compass (the pointy nonpencil end) on the edge of the circle you are looking for the center of and draw an arc threw the circle the center will be on that arc. then just repeat once more from another part of the circle. when your arcs meet it will be the center.
M.C. Langer4 years ago
I didn's know how to find the exact center of a circle. Now, I know!! Thank you Noah!!!!
kelseymh4 years ago
Hi, Noah!  It's been a long time since tenth grade, hasn't it :-)
noahw (author)  kelseymh4 years ago
It has!  Plus, I've buried those high school memories pretty deep. 

I don't have a brain scan or anything to prove this, but I bet that I store my knowledge of woodworking skills in a pretty different place than I store Barbara Heally, my 10th grade math teachers geometry lessons...ugh, that woman still give me the shivers...Barbara - if you're out there - screw you!