Quick Tip to Find the Center of a Circle with a Square
George VondriskaDescription
If you think that framing squares only belong on a construction job site, you couldn’t be more wrong. They’re also very useful to have in your shop. Here’s a great example. Need to find the center of a circle? You may not believe it, but you can easily do this with a framing square. There are a handful of things you have to watch out for as you’re setting up the process, but we point them all out in this video. You won’t believe how easy this is to do.
How simple is it?
All that’s involved to make this happen, and make it happen accurately, is careful alignment between the legs of the square and the circle itself. If you take your time and pay attention as you do this step, your accuracy on locating the center of the circle will be very good.
More with framing squares
Framing squares are definitely not one trick ponies. There are many more ways you can use them in your shop. Have a look at these other great tricks:
- Make a circle with a framing square
- Use a framing square as a cutting guide
- Set angles on your miter gauge with a framing square
You can see what an amazingly versatile tool a framing square is. These are great tools to have in the shop, providing A LOT of bang for the buck.
So you're doing a project and you've got a circle, and you need to figure out where the center of that circle is for the next step in the project. So, here's a way you can do this, oddly enough, with a framing square to work with the circle to find the center. Here's how it goes. First step, outside corner of the framing square goes right on the circle like that. It's really important that ya get those lined up correctly. Then I'm gonna come up the leg, and draw a line where the leg crosses the circle. And I'm gonna do the same thing on the other leg. Flip the square, rinse and repeat. So on my side, I'm doing the same thing. I'm putting that corner right on the circle. Draw a line, draw a line. Now I'm gonna circle those so I can keep track of 'em. These are the two lines I just made, connect the dots. So I'm gonna use my square where those lines intersect the circle. Where these lines intersect the circle. And that point right there is the perfect center. So, pretty easy way to do it once ya get the hang of it just be real careful when you're laying the square on there, ya line everything up just right and you'll have perfect center every time.
George, my only problem is that the line marking the center is not a true perpendicular dot. I say this because since the lines run close together it makes the line marking the center run together for about an eighth of an inch or so. So, can I lay the two first square lines more away from each other?
Great process for finding the center. It is suggested that, instead of flipping the square, rotate the square roughly 90 degrees for a sharper point where the two diameters cross. Thank you.
There are two ways of finding the center that gives you a more acute bi-section. one would be to just use a ruler and measure the O.D. (outside diameter) and divide it by 2. Measure in half the O.D., and make a mark. Rotate the ruler 90 degrees and do the same. If you are drawing a circle using a compass or trammel points. Strike a straight base line, lay out the O.D. and mark the center.
Seems like a lot of extra work when you already know the center when drawing the circle in the first place. Just make a pencil mark where you are going to place the needle end of the compass and you have your center.
Greater accuracy would be achieved if the square were rotated 90 degrees to obtain the second diameter, in which case the two "lines" (diameters) would intersect at right angles rather than the very acute angles exhibited in the demo.
Bill Giles has a good discussion on errors. Not only is it difficult to see the intersections point when the diameters you draw are at a small angle with respect to each other, but the error is, in fact, somewhat greater than if your diameters are closer to perpendicular. Moreover, drawing a third diameter is a good error check, as the third intersection(s) should be coincident with the first intersection, if all is perfect.
Wow, that wasn't exactly intuitive and I agree with Bill that the very shallow acute angle makes it difficult to accurately find the exact intersection, especially if you're using a dull pencil. I would have drawn a square around the circle with the sides being exactly tangential and the leg of the square being placed on the last drawn line to ensure the new lines are exactly at right-angles. Once the square exists with the sides tangential to the circle, draw lines from opposite 90 degree inside corners and the resulting X is centre.
This works because the 90 degree angle points to making a semi circle on the circumference. If you were to put the point on one of the marks and then made your second set of marks then the “cut” would be near 90 degrees and less susceptible to error. With the narrow cut shown in the video a small error is exaggerated. Imagine if the angle between the two was tiny, then it would actually be quite hard to pinpoint the centre of the circle.