The Quick, Cheap and EASY Way to Find the Center of a Circle

Gordon is building a new fixed-post mirror-grinding machine, and had to find the center of a big round turntable top he is building. Using little more than a "tricky" piece of paper, Gordon shares with you how to pinpoint the center of any circle. Amazingly, you don't need to measure anything! Use Gordon's trick for woodworking projects, scrapbooking, crafts, or any place you need to find the exact center of a circle.

[@mysleniedozwolone2361]

Hey Gordon, just wanted to thank you, you made my work much easier now ❤️

[@GordonWaite]

Happy to help

[@ultrametric9317]

A refinement on your method - you need a piece of cardboard or the like with at least one accurately square corner and perfectly rectilinear edges that meet there. You can even use a large carpenter's square. Tape the device so that the accurately square corner is coincident with the rim. Now mark where the two edges cross the rim. These two points are necessarily diametrically opposed. It works for any position of the tool, as long as the corner is exactly on the rim. Do it for a couple of positions and you'll have several diameters which meet in the center. Love your videos!

[@aimeedull5477]

Thank you for this hint!! It was easy and accurate, often those two words are rarely used together!! You saved my sanity! A. Dull

[@johnkashka803]

Great tip! I also have to find the center of a circle all the time, I have come up with many ways, but yours is by far the simplest.

[@bfhfhfhdj]

That’s a really good tip!!! Just tried it and I did some extra reference points and it was surprisingly accurate. Great for general DIY. Thank you for sharing.

[@JagiChan]

Awesome. That definitely is the cheapest method. Thanks for the detailed explanation and demonstration.

[@misswibb327]

BRAVO! So simple. You’ve saved me a little $ and a lot of time. Thank you!!

[@WoodfulProjects]

This is indeed the quick, easiest and cheapest method I've seen :). I usually use the "1. draw a line, 2. draw the perpendicular on the middle of this line" then repeat 2 or 3 times which will give you the center. You method is exactly the same but it removes the errors due to lack of accuracy while drawing the perpendicular line (which should be in the middle and 90°). Thanks for sharing. I think I'll remember this trick for long :)

[@larryseibold4287]

Excellent. I like that you did three vs two lines of intersection so that you could get a rough idea of the uncertainty center circle (dot if perfect). The optimization/elegance of techniques like this is to figure out how to work with imperfect tools resulting in the greatest accuracy in the minimum of time. I will add one obvious point: the short edge of the paper needs to be less than the diameter of the circle, ideally about 60% of the diameter for maximum accuracy.

[@Crackpot_Astronaut]

I have spent so much time trying to Google instructions on how to place table legs on a round table. I know that isn't what you intended here, but this brilliant! Most helpful video out there, for sure. Thank you!

[@GordonWaite]

You're very welcome!

[@mysteriousplankton]

So simple. I needed for a woodworking project and now it's a piece of cake.

[@JustinDGates]

Very cool! Alternatively, I was taught to trace the circular object onto a larger sheet of paper, carefully cut out the circle from the paper, then carefully fold the circle in half a few times over until you're left with a "pizza slice" sector. Using scissors, just snip a tiny portion off the small end of the "slice", then unfold. The new hole is the center of the paper circle, which you can carefully realign over your circular object and mark. Cheers!

[@GordonWaite]

Justin D. Gates That is a good method as well. I use that exact idea to put a "center spot" on my telescope mirrors. I just cut the hole the right size for the little notebook paper reinforcing ring that I stick in the middle.

[@astro_zane]

This really does work. Have used it to find the center of turntables and Dob bearings. Thanks Gordon!

[@GordonWaite]

You are welcome. Glad it was useful to you.

[@muddyfunker3014]

Quite simply brilliant. I love youtube for videos like this. Thanks buddy, this is a great idea and demo 👍

[@chipsammich2078]

Now that I've seen this video I'll have this gem forever.. Thanks for sharing this.

[@Jay-ph8tv]

Thank you so much for this very informative video. Made it very clear and understandable.

[@pops9190]

Excellent, it's locked into my memory bank forever now, thanks because I will be using it. Oh, and damn clever too.

[@bowlineobama]

Awesome trick!!! I will remember this for a long time. Thanks.

[@kdawdy6140]

You saved me! I had none of the tools many others used.

[@rcdavidk]

Brilliant. You used Euclidean geometry and created an isosceles triangle out of a piece of paper. Very nice. Thank you.

[@Grosminet9]

Thankyou so much for making this so easy to do!

[@notwrkn2mch]

That was one heck of a good tip...... I especially like the folded paper

[@michaelquillen2679]

Worked like a charm! Thanks.

[@redgeminiarts3674]

WOW! Thank you for sharing. That is easy!

[@thillaisundaramurthi]

nice..small suggestion to those who can't fold paper.. just draw a line at cetre of the paper lenth wise where you would have made a fold otherwise.. 🙏😊🎉

[@danseman1]

Thanks Gordon. Very ingenious.

[@jbritton6033]

Thank you that was so easy!!!

[@jdog4534]

Cool trick! I'm thinking you could cut the corners of the folded piece of paper, ..on the crease to use as a sort of stencil so you could run pencil against it or swipe a sharpie across it to leave an inked crowsfoot point. This is such a cool trick! Can't wait to try it..

[@louisecollet]

Thank you very much, just found my centre!!!!! Woot woot!!!!! I’m making a clock

[@mandalasastrosofianori8851]

Thank you!! simply genious! 😘

[@stoutlager6325]

Nice trick. I gave it a try on several rounds I needed to center find, this is fast and accurate. Thanks.

[@noiseintheoffice]

Good method! I've been using a compass set to the radius of the circle, and make arcs in the center. But it's hard to hold the sharp end at the edge of the circle. With your method I won't puncture my finger tip

[@andiortega4164]

Well, thank you super easy so many thanks

[@hkbb8627]

Thank you so much for this! It saved my bacon (and, not incidentally, let me impress my husband AND my Dad - 🤣).

[@gordbaker896]

Well done Gord.

[@GordonWaite]

Thanks, Gord! :)

[@nareene1473]

This was super fast and easy. Thankyou

[@stevedenisejohnson5778]

Brilliant! 👍

[@das250250]

Nice, even if the paper isn't exactly square if done consistently it will produce three lines that don't intersect exactly , but the centre will be the middle of that small triangle created in the centre

[@t0rb1naalborg44]

Indeed! You create 3 perpendicular bisectors to 3 chords. And you don't even have to crease the paper :-) just mark midpoints with a pencil, thereby the width of the paper will stay unchanged.

[@jeremyrundle5686]

BLOODY brilliant thank you

[@richardsisk1770]

Fantastic! I don’t need to buy a thing. Thank you!

[@CLCook-bj6iu]

Perfect sir, I appreciate the knowledge immensely. I have watched so many other videos trying to find the best method so I can fit the clock mechanism in the center of these 2’ rounds. It’d be a damn shame to ruin these pieces of art by screwing up the mount. Maybe I can send you a pic of them once they’re all done.

[@sd961960]

Brilliant!

[@collef1136]

Just wondering how you got into making mirrors for lasers. My son just graduated from photonics and that was one of his labs. He hasn’t really found a direction yet and was wondering how you started. Thank you from Ontario Canada. 👋 🇨🇦 love your method. Going to try it now. Seems easy. So very grateful

[@derekokeeffe9919]

This is a great video. Why would anyone click thumb down?!

[@GordonWaite]

Thanks! Glad you liked it.

[@sandipvaghela8521]

Thank you very much..

[@frostbite5081]

A real application of using the perpendicular bisectors of several lines tangent to a circle

[@asd67lkj]

So, the bottom of the page is a chord, and the mark at the bottom is the centre of the chord, and the mark at the top (From top to bottom) is a line at 90° from the cente of the chord... That simplifies a method I saw recently. Thanks, saved...

[@jons2447]

Thank you, Mr. Waite!

[@alexbattles1918]

Excellent advice, thank you tried this and it worked a treat

[@GordonWaite]

Great, thanks!

[@astronotyet]

That's awesome, thanks for sharing.

[@mikesmith2102]

This is good. I need to find the center of a 30" circle and the circle has a raised rim. The paper is flexible enough to bend down and still keep the crease straight.

[@GordonWaite]

Good! Enjoy your project!

[@thecarl168]

nice very simple

[@bmlsb]

Thank you sir. Exactly what I needed👍

[@GordonWaite]

Glad you enjoyed it.

[@XJWill1]

If you really can only afford a piece of paper, then that is a decent way. But if you can afford $10 for a carpenter's square (aka framing square), that will give you more accurate results (and also give you a handy tool for many other things). Since a right angle inscribed in the circle always defines a diameter with the hypotenuse of the corresponding triangle, just use the square to find two or three diameters and then you have the center.

[@GoSlash27]

Likewise, even if you can't afford a carpenter's square this technique works with anything with a right angle with sides larger than the circle. Even if you don't have anything lying around that's square, it's still a trivial matter to make one either with pencil and compass or folding.

[@user-dn9vd9xg9p]

If you had a 4 inch diameter circle what size paper would you use? Would I use a 2" length paper?

[@GoSlash27]

Another way to do it is to use anything with a right angle that's physically larger than the circle itself. Simply place the 90° corner so it touches the edge of the circle and mark where the edges of the triangle intersect with the circle. These 2 points perfectly bisect the circle no matter how the right angle is placed. Do this a couple times with rotation, and the resulting lines intersect exactly at the center. *edit* Ironically, there's a video of this technique right now in my recommended video feed :D kzbin.info/www/bejne/pmHdm6uEjbpgrKs

[@Must_not_say_that]

Yes, that is a good way and surely easier than that which is presented.

[@siddharthaathawale4068]

Great explanation sirr

[@shrutipunewar7224]

Perfecto🙌🏻🙌🏻 thanks a lot sir😊

[@GordonWaite]

Welcome 👍

[@mitchellquinn]

Great method; less messing around than the same technique using a ruler and manually marking the half way point on the lines. However, having made lots of paper aeroplanes, I often find that despite my best efforts, it is surprisingly difficult to fold a piece of paper perfectly in half!

[@GordonWaite]

I know what you mean! I butt one edge up against the back of our counter, then fold it over until both edges are held in place by the backsplash. Better than I can usually do by hand!

[@mitchellquinn]

Damn .... that's a good technique ... why didn't I ever think of that?!?

[@blackie576]

Here are two much simpler methods, measure across the circle and find the highest measurement, then mark each side of the highest measurement and draw a line across, bisect the line and you have the centre point. (2) Draw a line on the outside of the circle just touching the edge, with a square draw another line at 90 degrees so it also just touches the outside of the circle, repeat this so that you have a perfect square on the outside of the circle then draw two lines from corner to corner of the square and where they intersect is the centre of your circle.

[@GordonWaite]

For your first method, you have to have a ruler or yardstick or tape measure that is bigger than the circle. Much easier and quicker to use a common piece of paper. For your second method, you have to either buy a square, or already have one on hand. Again, much easier and quicker and cheaper to use a piece of paper. Why do you want to make it so expensive and difficult? A piece of paper is convenient and cheap. No bisecting or measuring at all!

[@SmeeUncleJoe]

Brilliant !!

[@zachreyhelmberger894]

WOW!! I LOVE IT!!!!!

[@OmarFakhry]

loved it

[@jviking6336]

Very good 👍

[@robbinghudd]

Great, thanks.

[@barryparks7057]

simple but brilliant!!!!

[@GordonWaite]

Thanks, Barry. A easy one to add to your bag of tricks.

[@annaoaulinovna]

corners should touch circle. mark paper centers both sides of paper. make lines they will cross at center. if your item is perfect circular.

[@djC653]

What a great video/tip. What if your circle has a rounded edge? Do your best?

[@GordonWaite]

djC653 Yes, a rounded edge would be a little tougher. I think if you are consistent with defining "the edge" you could still get a fairly accurate result. Depends on how big that round-over is! Thanks, and best of luck with your projects!

[@thetoymaker9404]

@@GordonWaite the size of a A4 sheet is a factor?i mean if you used an A3 paper would it be the same finding the center?I try to make a circle pad for mounting in axle of a moter for sanding but howmatter i tried it always vibrates when i switch on

[@Bushcraft-xz6xd]

A useful way, I’ll remember that thanks! Maybe a bit more difficult the smaller the circle? Once you have found the exact centre of one circle it’s easy to make a jig by fixing two bits of wood at an exact right angle. Offer this to the side of your first circle so both tips of wood touch the edge and lay another very straight piece on top and fix at the intersecting part of this right angle and the centre point we already found. This can then be used for any sized circle. You can of course buy this type device and get it with most engineering set square sets!

[@jimlahey5798]

Amazing

[@alijassim7015]

The intersection of the normal of two different tangents\cords of the circle.

[@naturefreak689]

Thank you sir

[@anniepattinson6237]

How can you use this on a larger table?

[@GordonWaite]

Either get a bigger piece of paper, or a longer straight edge ruler.

[@ryansalinas2135]

Does it matter the size of the sheet of paper to the size of the circle?

[@terdallaujar8008]

It does. I tried this method on a smaller circle with a regular sheet of paper and it was not right.

[@charleskennerly2086]

If you reverse the fold on the paper, you can get it to lay flat, and you won't have to fight it, and it may be a little more accurate

[@GordonWaite]

Good idea... Thanks!

[@elkanahgray9810]

That is because the edge of the paper having two corners on the circumference of the circle is parallel with the tangent line of the circle, and all tangent lines are perpendicular to the diameter of the circle. Why not just use the ruler to draw a 2" line with its endpoints on the circumference of the circle, then a perpendicular line drawn at the 1" midpoint will be the diameter. Now, you don't have to use the paper anymore...just the ruler and the pencil.

[@mjgayle52]

i was wondering if you were going to somehow find the intersection of two perpendicular bisectors of chords

[@GordonWaite]

Perhaps that's just what I did!

[@mjgayle52]

i believe so - very informative videos - now i need to save up some money

[@Must_not_say_that]

The largest measurement of the circle will give yiou the diameter. Surely that is the easiest and just as accurate? Another way is to place your marker near where you think the centre is and rotate the cirle. That will give you a small circle around the centre. Repeat as necessary for accuracy.

[@texasiguana]

brilliant

[@waterlilly62lori]

hi and love this idea, but paper size would have a definite impact on finding the center. What size paper for size circl

[@GordonWaite]

+waterlilly62lori I just use an 8.5 x 11 sheet. This will give you the center of a circle up to maybe 30 inches or so, and will be accurate to probably 1/16th or 1/8". A lot depends on how accurately you fold the paper, and how cleanly the edge of the circle is defined. Obviously, you need to make your marks fairly accurately as well. The nice part about the technique is you can fold a piece of plain old paper in half and find the center of a circle. If you need quick and dirty, that's fine. If you need accuracy, you only need to be careful about your accurate use of the tool.

[@waterlilly62lori]

So if I have a 6" circle, how would I find the center with a sheet of paper already bigger than itself?

[@GordonWaite]

+waterlilly62lori Just use a smaller piece of paper. Got a PostIt note hanging around? Same idea on a smaller scale.

[@royalmauryanknowledgenetwo3743]

How to find the center if the circle is little tempered during edging?

[@GordonWaite]

The method is generally accurate enough for most common operations. If the edge has been mangled, who can define the "true center" anyway?

[@flamencoprof]

If you trust the paper manufacturer. Does this beat simple compass & ruler ancient Greek methods?

[@GordonWaite]

I think so. You don't need a compass or a ruler. Just a piece of paper.

[@flamencoprof]

And a well-calibrated guillotine.

[@TheRealBoroNut]

Top tip - if your table is too heavy to rotate 120 degrees as shown in the video you can get a close approximation by walking round to the other side yourself. PS - don't make the same mistake as me and forget to take your paper with you.

[@alext9067]

Yeah, I would too. BTW have you fooled with what they are calling light buckets? Apparently, they use ship porthole windows to create mirrors that are pretty enormous. I don't know the dimensions, but the idea seems intriguing.

[@GordonWaite]

Porthole glass is normally 12" in diameter. I've never done one myself, as it is easy and reasonably cheap to get borosilicate glass, which is superior in several ways. We commonly do mirrors up to 25" in diameter or more, which qualify as "light buckets." The whole porthole/light bucket era started in the late 1960's when John Dobson started building large Newtonian telescopes out of stuff he could find in dumpsters and common hardware stores. I met him a couple times before he passed. One of the most interesting characters in the astronomy community! We owe him a lot.

[@alext9067]

Fantastic. I always wanted to build my own Newtonian. Never got around to it. A book I took out from the library spoke about using two blanks to grind together and the Foucault test w/ a razor blade and so on. Someone I knew had done a 4" one but I wanted to do a 6". I was surprised to see that your diagonal mirrors are oblong. The book said to use photographic filters because they were very highly precise. I need to look into all this again as soon as I can locate a flower pot and a mouse. Thank you for your response. Talk later. 25" or more.

[@GordonWaite]

Doing a full 25" telescope, mirror and all, is a great way to spend a year of your life. Doing a 6" is a great way to spend a month! These days you can get most of the parts pretty cheaply. Build the telescope first, then you'll have a good motive to finish the mirror!

[@alext9067]

Do you do your own vapor deposition? And do you use aluminum or something else? And why are you up at 4 in the morning?

[@GordonWaite]

We do not do our own coatings. We usually have mirrors coating either in standard aluminum, or one of the enhanced versions. I've always been a night person. That's what got me interested in astronomy back when I was just a kid!

[@spiritofscouse]

Hi what can we do when the circle is only 20 cm

[@GordonWaite]

Get a smaller piece of paper.

[@nirvanix88]

Neat!

[@JJBRICKS]

where did you get this table???

[@GordonWaite]

I made it myself. Two layers of Baltic Birch plywood glued together with the grain at right angles. Laminate top, bottom and edge. We make them all the time for our mirror grinding machines.

[@Balgore8]

How are you supposed to do this on a telescope mirror? Need advice where you dont need to draw lines on the mirror...

[@GordonWaite]

My method was used for finding the center of a turntable, not a mirror. If you want the center of a mirror, put the mirror on a big sheet of paper, and trace the circle around the outside. Cut it out with scissors. Fold it in half, and then into quarters. Open it up and the intersection of the folds will mark the center of the mirror.

[@latouselatrec]

or use apiece of wide masking tape

[@joshua43214]

a carbide tipped scribe works well

[@GoSlash27]

Use a plastic carpenter's square (google the technique). Mark the vertical edge of the mirror for the bisectors (not the face). Tape string from one side to the other to mark the bisectors. Place your target where the strings intersect. Voila! Perfect center without ever touching the surface!

[@t.d.mich.7064]

Geometric theory says "the perpendicular bisector of a chord, passes through the center of the circle". There are many ways to do this. This is a less than accurate way of doing it, although useful for everyday purposes. Clever!

[@MatttKelly]

10 points for whoever tells me what the line vetween the 2 corners is called

[@rohitkhanna]

secant

[@clayz1]

On Amazon, or your local hardware store. Search for tri square. It's the ruler with two or three attachments, one square edged, one is a protractor, the other is the vee shaped part you are looking for. That's the center finder. Cheap at under 30 US dollars, especially when you consider the time saving weighed against your hourly rate.

[@GordonWaite]

Not cheaper than a piece of paper! But a tri-square is a handy tool to have around. Mine has a level in it as well.

[@clayz1]

GordonWaite Just want to say that making real astronomy mirror is good. Very good.

[@GordonWaite]

You should give it a try. The most perfect thing you can build with your own two hands...

[@orangefield1974]

Make sure you get one of high quality I bought one on eBay 😪😪the attachments where not accurate at finding the centre you can make your own from a cheap mechanical drawing kit

[@junelxxii7892]

👌

[@mashtali1]

what is the expensive way?

[@haydentharp4104]

the most expensive way is to use a thousand rulers, a compass, and a mont blanc pen

[@romeliapolly5242]

Hmmm... I finally followed Ann's advice and took Woodglut. It's great for beginners and has some advanced stuff too.

[@1959Berre]

What's a "cenner"?

[@GordonWaite]

You've never been to Iowa, or you would know! ;)

[@ixamraxi]

Most readily available tools maybe, but certainly not easiest method. Make yourself a simple circle center line jig like this: s-media-cache-ak0.pinimg.com/236x/41/ab/78/41ab78aee7decb6afab3fbddedf24883.jpg

[@GordonWaite]

+Amra I would make the argument that if you are starting with nothing, it is quicker, cheaper AND easier to fold a piece of paper than to try to build your jig! ;) Thanks, Amra!

[@ixamraxi]

Thanks for the reply! I absolutely agree with you for starting out. But, if you have to find the center on circular objects a lot, a jig such as the one I linked is *much* faster and easier, It fits nearly all circles and all you do is grab it, press it against the edge and draw your line. Its literally that fast and easy. No need to take the time to line up the corners of the paper and fold perfectly, then line up the corners of the paper to the edge of the mirror and draw dots, then line up a ruler to the dots and draw the line... I would dare to say there is some risk for cumulative error in that method, at least for people not as practiced as yourself. Cheaper? Absolutely. Easier? Only until the jig is made. Faster? Not a chance! Also, Loving your series on that 12" f4.9 so far, can't wait to see the next installment! That is a beautiful mirror, and I would love to see that project all the way to completion.

[@rahkeemyoung1149]

at what price is the average citizen paying to figure out the center of a circle?

[@GordonWaite]

A Starrett center finder is $39.99. Rockler sells one for $9.99. And the Woodstock Center Finder is $5.50. My method costs about a penny for the sheet of paper.

[@jjsd250]

Wth, Use a speed square instead of paper.

[@GordonWaite]

Quick, cheap and easy... a piece of paper is more commonly available than a speed square, for most people.

[@mariobasic477]

Complicated. .........