Trades Math - Find The Center Of A Circle Using Squares

One of the easiest methods to find the center of a circle accurately is to use a compass and perpendicular bisectors. However, on a job site a compass is not always readily handy, but you’ll always find squares. So using those squares I’m going to show you how to accurately find the center of a circle using three different methods.

[@rex8255]

Machinist: That's WAY off! Carpenter: On the money! Nice!

[@D-proGram_Yousef]

As a carpenter I can honestly say.." I resemble that remark! " 😅

[@SmallSpoonBrigade]

@@D-proGram_Yousef The difference is purely the precision of the tools and how they fit together. Wood may well swell or shrink more with changes in moisture than what a machinist will tolerate with metal parts.

[@D-proGram_Yousef]

@@SmallSpoonBrigade Agreed. I am fully capable of splitting the proverbial hair and taking the time to find the finite absolute. But thank goodness I don't need to go there, too often having to be precise but it does pop up with concrete , foundations grades/elevations, stairs and landings,.. & finding square/ plum when you're 5 stories up hanging by your bootstraps while holding a nail gun and lumber pencil and sighting in a string line. All while it's raining sideways ..lol ahh good ol Washington State freezing rain. Carpenters, framers, siders etc seem to always be challenged for time so sometimes ill use what ever is handy. Until the finish work begins obviously. I've got nothing but respect for those welders machinist and fabricators that deal with exacts and the minutia for 8 hrs a day or more I don't have the bandwidth to do the precision long game. I'm pretty sure we're some of the last tradesmen the way things are looking. Since the next gens are pretty much no shows for the mens jobs up here. too toxic I guess LMAO 😅🤣 👍💪🔨🇺🇲

[@DixieDee]

@@D-proGram_Yousef It's scary to think of what this current generation is doing. They are more concerned with being mis-pronouned, than actually learning something useful! "Make America Masculine Again!" (Funny that the Acronym of that would be MAMA lol)

[@dannyh9010]

Cut to size, hammer to fit!

[@etherealeagle7680]

Perpendicular bisector of a chord passes through the center of a circle. Nice practical application of geometry. Thanks for posting.

[@txtradesman527]

Thank you for watching

[@jeromelee1627]

Yep

[@RobRoschewsk]

Except I remember bisecting the chords with a compass

[@howardharris576]

The perpendicular bisected of two tangents of the circle intersect at the center 4:26

[@avantesma1]

This video looks like workshop talk, but is actually pure Euclidian maths.

[@weejim48]

Brilliant, this to me is why KZbin was invented. Helping people solve problems & teaching people useful skills. Not for just having a rant or meltdown. Very informative, thank you. 👍👍🙏

[@PerpetualMan22]

I thought is was for fabricating videos about UFOs and other nonsense, writing a lie in the title and attaching some paid advertisement to put some fraud money in the evil pockets

[@brucewmclaughlin9072]

I see my 83026 hours on youtube is very beneficial

[@d3j4v00]

DIY stands for Dude, It’s on KZbin

[@KittyBikeOrders]

kzbin.infor6_Qz4T-WMc@@d3j4v00

[@sunriseboy4837]

Good call, brother!

[@tiltedstudio]

These are great! Just a quick note on method #1: the only thing that really matters about the square placement for the first two marks is that the apex of that square angle sits on the edge of the circle. You're marking two chord lines which meet on the circle edge and are perpendicular to each other. If you do this, the hypotenuse of the triangle created will by definition pass through the centre of the circle. The point is that you don't need to fret about making these lines the same length - it will work for any placement if the apex is on the circle.

[@cthulhufhtagn7520]

Additional triangles to double and triple check only take a few seconds

[@ramenandvitamins]

Thales' theorem!

[@c.j.g.6913]

And your explanation is why the average person struggles with math! The video presented clear simple explanations that work, without all the useless information.

[@tiltedstudio]

@@c.j.g.6913 at least 72 people had no problem parsing this additional information. Do you find the idea of additional clarification upsetting?

[@user-my3ff5lj6m]

I have worked in a machine shop over 40 years and never knew about this simple method. Thanks so much for sharing!

[@JavierBriz]

so you sold machines, or used them?

[@Leonardo-ql1qu]

American? MAGA?

[@balazslakatos9817]

worked as a cleaner?

[@Bob-of-Zoid]

How do you get to even study to be a machinist without having to show basic high school geometry first? I am an American, but went to school (partial) and apprenticed in Germany, and without that knowledge which you will be tested on in entrance exams, you couldn't even become a framing carpenter!

[@Bob-of-Zoid]

@@Leonardo-ql1qu Oh dear!

[@bikerbobcat]

Artist and HVAC guy here, thank you so much for this. So simple, so useful.

[@txtradesman527]

Glad it was helpful!

[@pyme495]

If they taught it like this in high school math, more of us would've paid attention! 😃

[@ricksaunders3889]

Exactly.

[@paulyork2143]

Amen

[@Corwin256]

It might depend on the student, but I agree overall. Interestingly, as an adult, I was bummed that he didn't give a mathematically rigorous proof for the geometry, even though he offered a practical demonstration that the methods did work.

[@eglintonflats]

You mean, more dummies like me would pay attention

[@DrLumpy]

They did. You didn't pay attention.

[@IkanGelamaKuning]

My teacher taught me this in 1990. Thanks to him for this useful knowledge.

[@walsakaluk4630]

A bit hard for very small stock, but in the adsence of a centre square these methods are excellent first geometric principals for locating centres on circular material. NICE VIDEO AND EXCELLENT REMINDER TO PAY ATTENTION AT SCHOOL. 👌👍🖖

[@Kleiner_Lutz]

I'm gonna immediately forget about this again until I need it some day and have to rewatch this video

[@davidpetrus1748]

lol i was thinking of a way to remember how to find this video ha ha

[@Chigger]

Here's a reminder just in case you need it very soon.

[@gppizza8979]

here's another reminder just in case

[@marshallcollins8634]

Unfortunately I was a shitty student. I didn’t think I needed what they were teaching (especially MATH ) would do me any good. I was thoroughly convinced that I knew it all. I was sooo wrong on every aspect. That if not for spell check, this comment would probably look like a 2nd grader DONE it. I probably would know how to do this if the teacher would have told me (it will help you get GIRLS ) I wish I would’ve learned Math at least 4 or 5 times a day. Thank you for posting this now I have to subscribe to your channel, for this is NOW how I learn what I should have learned 50 years ago.

[@Chigger]

At least you're learning something. That's what education is.

[@bobadams1696]

Very good video. Clear and to the point, and very practical.

[@txtradesman527]

Glad it was helpful!

[@ChestnutForge]

Many thanks for this. It is a great training video I will use for others to learn from. As a blacksmith if you are a machinist or a welder, I will open a conversation on that basis. but within a few minutes I will be asking for solutions to this and other problems. That is because the smith needs to BUILD his tools and jigs. In my shop I have an engine lathe, a mill, 2 drill presses, a hundred year old ironworker, 2 anvils, press brake and will expect to make hammers, tongs, forges, bolster plates and rivet/rivet tools as needed. This video goes to the core competency necessary to create real world items from someone elses imagination.😀👍

[@adamgravelin3002]

i tried to google this the other day and google assumed i was doing all of this on paper. this is a great video for practical situations where you need to find the center. i ended up fumbling my way into the second method just trying different things, but i needed to draw a perfectly plumb line through the center of my circle and i ended up holding a framing square, a combo square and a level attatched to the combo square. it was a lot of moving parts to line up, but it did the trick.

[@txtradesman527]

Excellent improvisation!

[@stickyfox]

The angle formed by two secants is half the included arc angle. If you draw two secants at 90 degrees they will include 180 degrees or half the circle; making the triangle's base a diameter whether or not you drew an isosceles triangle. I forgot about this trig formula after high school but it comes up again and again in machining and drafting.

[@apeterson23]

You and ICWeld are my favorite tradesmen/fabricators/welders/mechanics on youtube! Lots of skills in those pockets

[@txtradesman527]

Thank you. I hope to be able to devote more time to this channel in the near future.

[@eadgbefreak]

I've always used method 3, which I learned in geometry class. Method 1 is cool too. Method 2 I know works well because they sell a jig, that basically "holds the squares" for you.

[@AsianTankPilot]

The last method is what I learned in board drafting. We used a compass find the middle of each chord.

[@azimuth4850]

Anytime a right angle is inscribed in a circle, the endpoints of the angle are the endpoints of a diameter. The radius of a circle is perpendicular to the tangent line through its endpoint on the circle's circumference. The perpendicular bisector of a chord is a line passing through the center of the circle such that it divides the chord into two equal parts and meets the chord at a right angle.

[@drumcdoo9050]

Excellent video and straight to the point ~ no B/S and stretching out video for 5 minutes describing the type of scribe, where you got the measuring tools from and how to unbox them etc, before describing tip!

[@HenrikMyrhaug]

I love the 1st method, because it uses some basic math that is pretty counter intuitive, but easy to prove. I remember my cousin asked me why a triangle with hypotenuse along the diameter of the circle and all 3 corners on the circle makes 90°, and I came up with a pretty clever proof. At first I thought we just had a straight edge, but when i realized it was a square, I was reminded of that theorem.

[@ImtheGhostMagnet]

A much simpler method, use the framing square and triangle to measure the diameter, devide by 2, you have the radius, scribe a line at the radius distance, rotate the circle and scribe a second radius line and where it bisects is the center.

[@davidboose5803]

Wow!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I am speechless, what a neat demonstration.

[@txtradesman527]

Glad you liked it!

[@fomoco300k]

You actually showed me four ways. Thank you!!

[@martinkuliza]

and as always basic math that we used to do in the old days impresses people today :P

[@Guido_XL]

Indeed. The old-school trigonometry that we used to learn and took for granted as the rational and straightforward way to do it, appears now as some sorcery from another dimension to the next generations, which is accustomed to "smart" phones and even AI to bail them out. Whenever I do some mental calculation in the presence of young colleagues, they respond astonished that something like that is humanly possible at all...

[@lowandslow3939]

Now THAT was a very useful video. Thank you so much.

[@txtradesman527]

Glad it was helpful!

[@fodank]

Thanks for this. Simple and true. Love it.

[@TheOfficialDjProduct]

I don't know if I'll ever need this. But interestingly enough you could do the last method with just a tape measure. Using it as a straight edge you could do 3 sides, then using the tape as a straight edge you could connect the 3 lines and find the center. And you could find the center on much larger circles (for however large your tape is), with whatever tolerance you allow.

[@beachpone]

you can also do these with powdered string if you want, it's kinda fun

[@JoseDiaz-er4ww]

Para aquellos que alguna vez llevamos la materia de "Geometria Descriptiva", esto es un dulce. Si carezco de escuadras, con un lapiz y un hilo, utilizandolos como compás, en 2 minutos encuentro el centro, el radio, el diametro, la circunferencia, el area y cualquier angulo.

[@rbaron7352]

Not only trades math, but basic geometry that is taught in any decent high school geometry course.

[@heyyoubuddy6749]

Thank you for showing us this trick!!

[@Jeff-rk8hq]

This dude has taught me so much I swear it’s the same dudes voice that does tx tool cribs or something does knots and amazing vise stands

[@txtradesman527]

One and the same.

[@Jeff-rk8hq]

@@txtradesman527 haha makes sense, I figured you knew Txtc or something by the name but i couldn’t be sure, anyways thanks for your vids though man I have really enjoyed and learned a shit ton from you so thank you for sharing…I have been planning to build a vise stand inspired by the one you made, I’ve just learned to weld (or weld enuf to stick 2 pieces of metal together l😂 ) so If you have any tips on sourcing or salvaging any of the materials for the build and having much more experience knowledge on the subject seeing as you’ve done it yourself figured you may have some wise advice on places to get metal for reasonable prices or even better places to salvage it

[@edgeofentropy3492]

OR, if you have access to a lathe, you can chuck this material up and use a center drill in the tail stock to find the center.

[@PenDragonsPig]

The angle in a semicircle is a right angle. Any lines from the ends of the diameter will intersect on the arc at a right angle. First year secondary school (🇬🇧) 54 years ago, circle theorems I guess, and never used- not in house, garden, farming, hunting, shooting/sniping, angling, ware house, dealer/croupier, degree in history, motorcycle, 4x2, 4x4, street, dirt.

[@vaughnslavin9784]

Thank you! Great trick of the trade!

[@txtradesman527]

You bet!

[@Ian-Casper]

Learned something today. I appreciate the format.

[@txtradesman527]

Most welcome.

[@OSAS726]

Awesome video! Thank you so much for posting this. here are some formula to determine other measurements of a circle r=radius Pi=3.1415927 2(Pi) radians=360 degrees Conversion formulas Radians to degrees (R) X 180/Pi Degrees to radians (D) X Pi/180 Area(A) A= (Pi)r^2 Circumference(C) C=(2)(Pi)(r) Radius(r) r=C/(2)(Pi) Arc length of a circle = radius X angle in radians. Sector of a circle = 1/2 X angle in radians X radius squared Angular velocity(w)= dR/dt A change of angle in radians over a change in time. Radians are really the most natural way to measure angles. Like the metric system is the most compatible with our base 10 number system. Neither are based on a convention, but are scientific in nature. Pi=C/(2)(r) or the ratio of the circumference to the diameter of any circle.

[@tokin42]

Snuggle it up into the corner of the framing square the use the 90 of the speed square on the other side to find the diameter of the circle. Move the speed square to the half way point of the measurement and mark. Do this with the speed square along both the side and top part of the framing square without moving anything but the speed square.

[@user-zh6xz3rj9n]

Here is another method. Inscribe ANY parallelogram you like inside the circle. Then criss-cross the corners of the parallelogram. The center of the circle is the center of the parallelogram.

[@LibertyTalk76]

Simple genius is simply awesome. Thank you.

[@txtradesman527]

You're welcome!

[@bignicebear2428]

It's right there, in the middle. 😂

[@Oddman1980]

Useful things my math teacher failed to mention #468

[@txtradesman527]

😂

[@olgajoachimosmundsen4647]

Can also set the circle against a wall and measure out x. Then you rotate it untill you create a pattern that reveals centre

[@asd67lkj]

Thank you. I need that information at the moment, Liked and saved...

[@Fabricationskills]

Really informative Your way of explaining is very impressive

[@txtradesman527]

Thank you sir

[@Patat0four]

Put on a piece of paper and draw the circle. Fold I half and using the transparency of the paper to align the two half circles. Fold again again using transparency to align the quarter of circle. Cut a tiny piece of the corner, unfold and boom, hole would be right in the circle and the round piece you want to mark.

[@jwbnscacpt]

Very good information. Thanks!

[@AffordBindEquipment]

Two pieces of wood or metal about 12 inches long, screw together at one end, attach a pencil or pen on one leg. Protractor. Make arcs to center around perimeter and center is shown, even if the arcs aren’t perfectly on center. Way faster and you can keep the new tool for the next time.

[@petersack5074]

Wow. i'm 68, and skilled, in the shop. WHY were we not taught this, in high school ? . In industrial arts, class ??....oh well....never too late, i guess....living,....is Learning...thankyou too much...

[@MyKharli]

i used to just use a tape measure or any straight line to find the widest part aka the diameter and draw a line , repeat around the circle and the center will be where the lines cross .

[@iansun42]

Yeah, I came up with the third one on my own after reading the title, I’m pretty cool

[@zitternden]

Fantastically simple. Thanks!

[@JonathanNatale]

User stuartburton1167 is correct: "On the first method you should’ve said that each leg of the square should read the same length to the edge." This can be proved by contradiction as follows. Draw it out such that each leg of the square is the same length to the edge. Then draw it out (wih a diffent color pen) such that the length to the edge of one leg of the square is the NOT even close to the length to the edge of the other leg of the square. Contemplate the result on the tree of woo, TX Tradesman.

[@txtradesman527]

I didn’t say that the two legs of the square had to be equal distance to the edge of the circle, because they don’t have to be. It’s called Thales’ Theorem.

[@blackie576]

A simpler method is to draw a square on the outsise of the circle so that the lines just touch the circle, all angles are at 90 degrees then disect the square and you have the centre, another simple method is to measure across the circle until you get the largest measurement, draw a line and then disect it.

[@John-yt5zr]

Excellent information, thanks for sharing this with us 👏👏👏

[@txtradesman527]

My pleasure

[@idselseno2306]

Why is Ave so nice and politely spoken here. Maybe I'm lost here. 😂

[@gerryroush8391]

Learned this as part of my welding course My Father said I did not know enough curse words to be a plumber And that a bricklayer makes as much as a machinist😮

[@MicahThomason]

I arbitrarily prefer the last method. Good video.

[@txtradesman527]

Thank you

[@jarredmattingly5369]

Using a perpendicular bisectors of chords. Each time you take a random chord and bisect it with a perpendicular line you'll pass through the center. Imagine the diameter of a circle... The bisector there is actually the center and any chord you can draw will have its perpendicular bisector pass through the center. In the real world there's error introduced by us using the rule, using the protractor, drawing the lines, or measuring, and any other not mentioned right now. Doing the chord trick requires a minimum of two iterations to actually find the center, but due to error doing it a few more times may help with precision, or confidence at least.

[@jean-lucpattein653]

Super astuces. Thanks 👍🏽👍🏽👍🏽

[@Drinksfromtap]

Ahh, so this is the type of content you get when your watch history has a KPop band TxT and talking hands maker videos 😂 great video, I use the first trick to cut cake but didn’t know about the second two. Thanks.

[@Heraclitean]

To cut cake? yikes.

[@Drinksfromtap]

@@Heraclitean I don’t use a square but I use the concept :) and if you’re saying it’s weird I admit it and it drives my wife nuts!

[@alanhean6504]

Much appreciated ❤

[@doc145]

Draw 2 chords. Mark the center of the chords. Using a square draw 90 on each chord at the center of the chords. Where they intersect is the center.

[@txtradesman527]

Yes, we know

[@RhumRunner41]

Great tips. I use no. 1 all the time. However, you did not mention that both legs of the square must be crossing the edge of the circle at the same measurement. Do otherwise and you’ll be chasing the center point.

[@panos3051]

Not true. en.wikipedia.org/wiki/Thales%27s_theorem

[@djdjdjwjhehdi]

equal length is not necessary

[@michaeldunagan8268]

OUTSTANDING! Now if there was only a way to find the center of a 6 mm circle on a Toyota aluminium intake plenum....🤔

[@nitdiver5]

Where I need this is some 6” ceiling lights come with a template with no marked center or center hole. Thank you.

[@ronnym1977]

I like the second one best.

[@mariolopez-ri8wd]

Some new thing I learn today thanks ...

[@mnFlatLander]

WHERE HAVE YOU BEEN ALL MY LIFE?!?!?!?

[@-Tac0caT-]

Ha - I did this just the other day. Google is now watching me... I needed to find the center of my street cul de sac. Using string, a 30 foot tape measure, and a laser grid maker, I used option 3. Basically, all 3 options are the same, with the goal of making a chord, bisecting it, and drawing a perpendicular. Two of those intersect in the middle.

[@txtradesman527]

Nice

[@VultureXV]

Just FYI, you need something with a 90 degree reference for this. If you don't have something with 90 degrees, use a compass and straightedge and construct a 90 degree angle.

[@mikelastname]

If you don't have anything other than a writing stick, freehand draw three chords approximately equally around the outside of the circle and you will end up with a small triangle in the centre then freehand a line from each apex of the triangle to approximately the centre of the opposite side of the triangle and you should be very close to the centre, and if not, remember to bring more tools with you next time. It's a bit convoluted, but if you push the circle up against a wall so the wall becomes tangential to the circle, then put one side of your square on the wall so the very corner meets the circle where the circle touches the wall - scribe a line down the side of the square which goes through the centre. rotate the circle and do it again. If you have a lathe, it doesn't matter where you mark the centre - after a couple hundred revs, the circle will be concentric with YOUR centre.😂

[@ussxrequin]

This was very informative, thank you (:

[@txtradesman527]

You're so welcome!

[@doberfart]

Very useful, thank you!

[@txtradesman527]

Glad it was helpful!

[@1979Spica]

So that’s how Tool designs their album covers.

[@Leogendary13]

1:45 Instructions unclear I summoned an ancient deity

[@amandahanson8188]

Answered my questions. Great video. You earned my sub. Cheers from Wisconsin.

[@txtradesman527]

Thanks for the sub!

[@jobmunene3263]

Wonderful application.

[@thelimike]

Some people going to be impressed

[@kapasitorcpt9249]

Could you have made a line from the tip f the 1st two lines to the 3rd using the 90deg f the square?

[@christopherdean1326]

The second method seemed like the obvious, and simplest, way. When I saw the the two different squares, that is what I assumed the answer would be.

[@chrisjohannes179]

Easier would be to hold a square tangential to a circle, then another right angle perpendicular to that point. Trace that diameter and half is the centerpoint at the radius.

[@PerpetualMan22]

Seems like so much work , when it is so easy to just measure from the edge of the circle from two points approximately 90° off the edge

[@charly-s]

Divide a rectangle with a 45 degree tendon and put it outside your circle. Twice different positions, two pencil strokes along the 45 degree tendon and the circle‘s center is yours!

[@davetaylor4741]

I knew one. Now I know three.

[@themonsterunderyourbed9408]

Tried the first method and I ended up summoning a demon.

[@billscurlock6570]

I’m 79 years old and I never knew that !!!

[@michaeldevlin517]

In the old days we just used to measure the diameter and divide by two. You could use either of those squares. Try it!😄

[@txtradesman527]

The problem is that you were guessing at the diameter. With the Thales’ Theorem in the first example you are not.

[@BensWorkshop]

Good tips.

[@jamescrydeman540]

simply draw two chords equidistant from an edge ,on opposite sides of the circle but parallel to each other. the two diagonals joining opposing ends of the chords will bisect the circle.

[@txtradesman527]

Requires that the chords are parallel.

[@DixieDee]

Great info! Thanks.

[@mattjohnson2848]

Great video, thank you 😊

[@bruce-le-smith]

super helpful thank you

[@paulmaryon9088]

That was great, thank you

[@txtradesman527]

You're very welcome!

[@danalaniz7314]

Excellent. Thank you!

[@txtradesman527]

You're very welcome!

[@cribbsprojects]

Magic! Great video...

[@rossab123]

Move a ruler across until it meets the biggest point. Mark the middle and that's the center

[@ChristIsLord229]

It can be done with dividers also

[@davidoickle1778]

Good stuff!