Video: Dividing a Circle into Three Without a Compass or Protractor

If you’ve ever wanted to divide a circle into three, you can do it very easily with just a ruler and a compass. I’m working on a sculptural piece of furniture that has three blades radiating from a cylinder, and as many of you know, the Shakers have an iconic candle table which also has three legs radiating off of a cylinder, so this little trick could come in handy.

So if a circle has 360° and we want to divide it into three, how do we find the 120° of each section without a protractor? It’s really very easy. I’m going to use whole numbers to keep everything simple. My circle is 4″ in diameter. Mark the centerpoint and draw a line from one side of the circle to the other through the center.

The radius is 2″. You need to take half of the radius, in this case 1″, and mark the halfway point from the center of the circle on the centerline. Take your ruler and draw a perpendicular line from this point to the outside diameter of the circle. This will give you two points. Connect these two points to the center point and you have the circle divided into three.

If you are interested in building the Shaker Candle Table, we have a collection on sale called The Ultimate Shake Project Collection. It includes three books on CD. Click here to buy it today.

–Ajax Alexandre

11 thoughts on “Video: Dividing a Circle into Three Without a Compass or Protractor

  1. dfrancis

    Great geometry technique! Someone needs to write a book on such techniques for woodworkers.

    But, no one is asking what is the hauntingly beautiful bagpipe music. So what is it?

  2. johnjory

    While that approach will work I have a more straight forward way that does not require accurately dividing the radius in two or even using a ruler/scale.
    After drawing the circle simply put the point of the compass on the circle you made and pace off radius measurements by simply going around the entire circumference placing the point where the other end of the compass intersected the circumference. Every other tick mark is 1/3 of the way around the circle.

    1. ruds

      Wrong! Each tick represents one RADIAN which is 57degrees, 17minutes & app so45 seconds, so if you double that you don’t have 12o degrees you have 114 degrees ,35 minutes and app. 30 sec
      Your method is indeed easy but not correct!

  3. hodgman@gmavt.net

    I like iwigle’s method. I was a draftsman for a number of years in the “old” days. We used two triangles (a 45 and a 60-30)and a compass to do all sorts of things that woodworker’s do today with gadgets and formulae we never heard of. If you know any old draftsmen, talk to them and maybe pick up a few tips.

  4. iwigle

    Simpler still.

    Mark the first of three points wherever you want it on the circle.
    Adlust your compass radius to match the circle’s radius.
    Place the point of the compass on your mark, and draw a new circle. The new circle will touch the original circle in two places.
    From each of the two new points, use your compass to draw new circles. These circles will cross the original circle at the original point, and at two new points.
    The original point, and the two new points, divide the circle exactly in three. No ruler required, no measurement required.

  5. nateswoodworks

    I think where this tip comes handy is in the field not so much on the paper. If you are making the table in which Ajax talks about you take the turned post and want to lay out for the legs branching off. I think the nice thing about this tip is the fact that you don’t have to try to step off the thirds with a divider on the outside edge of the piece. Very nice tip Ajax!!
    Nate

  6. Bob K

    Neat Trick but if the perpendicular line isn’t exact ( and how do you do that without a protractor or compass) then the circle will not be divided exactly into three parts. Like one of the other replies said, if you have the compass to draw the circle, just use it to divide the circumference into thirds?

  7. blaisepascal

    If I have a compass at hand, I’d just step two radiuses off along the perimeter (as if I were using dividers) to divide it into 3rds. Simpler than measuring half the radius and striking a perpendicular.

    1. hmann

      blaisepascal I agree this is the easiest, and if you didn’t have a compass/dividers you can just use a ruler and draw segments along the circles edge the length of the radius creating a circumscribed hexagon whereby connecting every other point would give the same result.

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