How to Find the Center of a Circle

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About: I've worked for Instructables off and on since 2006 building and documenting just about everything I enjoy doing. I am now the Creative Programs founder and manager for Autodesk and just finished building o...

Intro: 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:
https://www.instructables.com/id/Find_the_Center_of_a_Circle
https://www.instructables.com/id/How-to-Find-the-Center-of-a-Circle

Step 1: Draw Some Chords

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

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

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?

Step 4: Go to Town

Now that you know where the center of your circle is you can do all kinds of cool stuff...like drill a pilot hole for a circle cutting jig and cut perfect circles that are in the absolute center of your circular material!

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    38 Discussions

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    Tangski

    1 year ago

    Thanks for the idea...but you need only have 2 lines, about 90 of each other...find the centre...use a square, draw up from that from the centre dots and you have dead cent of your circle.:) No triangle...a least not one I see...LOL Good reminder and tutorial....I like how you did the grove...will use that!:)

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    nphillips6

    6 years ago on Step 4

    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.

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    Tangskinphillips6

    Reply 1 year ago

    Yes, I found if you just draw and find centres of any two lines, then use a square, set on the line where your centre dot is, draw up, you find dead centre. :) A square is very handy even in this instance:) Thanks everyone! Good reminder! Now, onto cutting out my centresLOL

    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. :)

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    tareko

    6 years ago on Step 4

    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.

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    glorybe

    6 years ago on Introduction

    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.

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    dado

    7 years ago on Introduction

    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

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    Truehartdado

    Reply 7 years ago on Introduction

    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.

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    codydean

    7 years ago on Introduction

    at the end are you making a lid for a 5 gallon bucket

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    kleinjahr

    8 years ago on Introduction

    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. 

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    Rune Cutter

    8 years ago on Introduction

    I've been vexed by this for more years then I can say and you fixed it in seconds

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    conrad2468

    8 years ago on Introduction

     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.

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    Morrighan

    8 years ago on Introduction

    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.

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    Chromatica

    8 years ago on Introduction

     There is already a Ible on this that uses the same exact method.