How to Divide a Line Into Equal Parts Without Measuring




About: I'm a long time tinkerer and lover of Instructables, but recently I joined Techshop in San Francisco, and decided to really get creative. Right now I'm spending most of my time making sawdust in the wood-sho...
This is a trick I read about when trying to get through a woodworking project. I needed to divide a piece of wood into 5 equal sections, and the workpiece divided into a complex fraction. I struggled to work out the math and measurements in my head, and then with a calculator, but every time I marked up the board I was a little bit off.

But then I read about this trick, which allows one to divide any line (or straight object) into equal parts, or evenly spaced sections without directly measuring the line. It uses some basic principles of geometry - but don't worry, no complex math required.

(By the way, please forgive any shop noise and my "umms" this is my first video instructable :^P). If you have any other ideas or suggestions, please share them below in the comments.

The steps

  1. Choose the work-piece that you want to divide
  2. Choose how many sections you want to make
  3. Draw a diagonal line above the line being divided. The line should be divisible by number of sections desired
  4. Mark out equal points along the diagonal line
  5. Use a square / 90 degree angle to draw lines from the points on the diagonal line down to the original work-piece
  6. Done! Your line should now be cut into equal sections

I've used this at least two different ways in my woodworking

  1. To cut workpieces into equal parts, I just cut down the center of the line
  2. To space joints on a workpiece. For example, if I want to make 1/4 inch dado grooves on a workpiece, I draw more lines 1/8 inch to the right and left of my original line, creating a 1/4" mark for my cuts to follow.



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    13 Discussions


    4 years ago on Introduction

    What is the name of this method? My woodworking teacher has asked the class to figure this out.

    2 replies

    Reply 4 years ago on Introduction

    Haha, excellent question...but I have no idea if it has a name. It's just a trick someone showed me when I was struggling with spacing out some parts.


    Reply 2 months ago

    In Geometry, it is the method of similar triangles.

    You can increase the accuracy of your method by transferring the parallel lines by setting a drafting triangle against your longest line, and sliding the triangle's adjacent side along a straightedge until it matches your points.


    2 months ago

    Thanks for sharing!

    Yes I see I'm a bit late to the comment party, I can't believe I'm just now finding this Instructable!


    3 years ago on Introduction

    This might be nitpicking, but your instructable title includes "without measuring", and your first instruction in the video is that you'll be needing a measuring device. I get that we're measuring something that's easier to divide, but we're still measuring, so your title is incorrect.

    From your title, I'd have expected to be able to do this using pure geometry, instead of ever having to interact with arbitrary units of measure. This is not what you're showing, so it shouldn't be the implication of the title.


    4 years ago on Introduction

    Excellent tutorial! I wanted to add that a steeper division line is harder to accurately mark unless you rotate the paper until it becomes horizontal.

    Additionally, a shorter division line will help if your square is inaccurate. I use the edges of the paper to get parallel or perpendicular lines, leaving the square out, but that's just the way I learned to draft.

    One last thing: Even if you're working with inches, if you have an imperial/metric ruler it can be a whole lot easier to find a good multiple on the metric side!!!