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.

There are lots of other methods out there for solving this problem.

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.

Comments

[admin]

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!

[Yandy Reyes]

Can we add mathematics to this to add educational value to the presentation.

[Yandy Reyes]

?

[MALUIA]

I will use this to drill a hole in the center of 30 different posts. A "combination square" is a nice companion for this method. (Image credit wikipedia)

[ThatNavyGuyChad]

I'm not sure how accurate this would be, but couldn't you just slide a ruler (or preferred measuring tool) across the circle and mark a line through at the peak number (longest measurement)? Do this at a couple different angles to get the center point of the circle?

[mlolyang123]

a bit hard, I wish there was an easier way to find the middle of a circle:(

[JithinP7]

1.Draw a chord
2.Draw a right angle on one end of the chord and extend it so that it intersects the circumference of the circle.
3. Connect the other point of the chord with the point of intersection of extended angle.
4. Find the midpoint of the newly formed line segment which is the center of the circle.

[bunglesmate]

Do you have a link to the instructable with diagrams?

[ptolemy_xxv]

easiest way to find the center of the circle. draw a square (square has four equal sides and four right angles) inside the circle with the corners exactly on the circular line then draw a straight line from one corner of the square to its opposite corner do it also on the other two corners left, the center of the circle will be the intersection point of the two straight lines drawn from the four corners of the square.

[deepcut71]

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.

[PracticalApplication]

To be a square “around” the circle the sides would have to be tangential. To draw a tangent you need a line from the center...

[DoğaD]

Maybe not necessarily? Say, you draw your first tangential line for which you don't need to know the center of the circle. Then, you draw another line which sits at 90 degrees to that line AND also is tangential to the circle. Repeat twice (or once is enough though) and you have your tangential square.

[PracticalApplication]

Drawing a square around the circle “works” (sort of ) for pencil and paper exercises, but not for something like a 60 inch table top.

[bunglesmate]

could you provide a link to your instructable?

[PhilNolan3D]

A chord?

[PracticalApplication]

Any line drawn between two points on a circle

[snowfalcon1]

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

[bunglesmate]

could you provide the link on your instructable?

[ptolemy_xxv]

easiest way to find the center of the circle. draw a square (square has four equal sides and four right angles) inside the circle with the corners exactly on the circular line then draw a straight line from one corner of the square to its opposite corner do it also on the other two corners left, the center of the circle will be the intersection point of the two straight lines drawn from the four corners of the square.

[Luis E.I1]

Or, you can inscribe a right triangle in your circle and the center is at hypotenusa / 2