Introduction: 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 out…
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
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.
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.
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?
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!
