### How to Effectively Use an L Ruler, Carpenter’s Square, or Sashigane

An L ruler or sashigane is a hand tool many amateurs don’t know how to utilize effectively. One reason for this is because its functions seem quite obvious due to its shape and the tasks commonly associated with rulers. However, unbeknownst to many folks out there, a sashigane has a wide range of uses and functions, which may save you untold hours of work.

From here on I will refer to this tool in the Japanese vernacular — sashigane. The reason for this is because both an L ruler and carpenter’s square can be used to refer to one of any size and/or design (as long as it satisfies the “L” shape and/or functional criteria), whereas a sashigane has a specific size range and design (see image). Let’s list the various uses for the sashigane, starting with the more basic ones:

• Taking squares. By butting the edge of one of the sashigane legs on your stock — preferably the longer side for accuracy — you can draw out a perpendicular line.
• Taking shorter, intricate measurements. Measuring tapes are good for longer measurements, whereas a sashigane is extremely useful for smaller, confined areas, and those in which a flat, stiff ruler edge is more conducive to accuracy than the flimsy concave profile of a measuring tape. A sashigane can also be used with one hand, while a measuring tape often requires both.
• As a straight-edge. A simple but important task, drawing straight lines between 2 points no matter how short can be done quickly and easily with a sashigane.

From here I’ll go into the slightly technical uses of the sashigane.

• Determine slopes and angles. Here in Japan, we go by a form of percentage — not degrees — when defining for example, a roof pitch or slope. By knowing the slope of the roof, one can determine by calculation all the angles needed for the roofing joists, as well as the notching around horizontal rafters in the exterior plywood on the gable ends — without having to go up in person and take measurements.

For example, let’s take a roof with a 30 degree slope (58%). Knowing only this slope we can calculate the angle of the roofing joists at both the top and bottom of the roof so that their ends sit vertical once they’re in place. Take a number that’s easy to divide in two but that’s not too big, say 60 millimeters, and make 2 perpendicular lines across the joist 60 millimeters apart about 10 centimeters from the end.

30-60-90 triangle

Now line your sashigane up with the 2 lines. The shorter end should be lined up at the 30 millimeter mark, exactly half the distance of 60 mm, and the longer end should be lined up so that its edge intersects with the point where the line meets the joist-edge. The angle the long leg and the stock produce should now constitute a 30 degree slope. However, the angle the short leg and stock make – which is 60 degrees – is the angle you’d need to cut the joists at the top and bottom for a 30 degree roof slope.

This is an example of the 30-60-90 triangle, and can be proven easily via the pythagorean theorem. The side lengths of the triangle you just drew on the joist should be 30 (“B” in the illustration), 51.96, and 60 (“A” in the illustration) millimeters — the ratio 1: square-root of 3 (1.732): and 2. As you probably noticed, by using an initial number that’s easily divisible by 2, you can quickly determine your 1 and 2 legs, and the square-root of 3 leg will automatically be determined by using the above method.

By altering this ratio accordingly, you can derive any angle or slope-percentage you require, using only a sashigane!

45 degree angle

In short, by lining both legs of the sashigane to the edge of the stock at corresponding ratios, one can take a rise over run — for example, lining up 2 and 5 to the edge of the stock would constitute a 40 percent slope, and 2 and 4 would produce a 50 percent slope, and so on. Remember that this results in a percentage based slope, not degrees. You would need to convert for degrees.

I would recommend setting a miter saw, if you have one, at the correct angle and simply making the cuts this way. However, for those who don’t have one available, you should probably make a jig to streamline the process.

• Quick and easy division of lumber dimensions. As you can see from the image, by lining the sashigane up at key reference points along its length to the 2 stock edges, you can quickly make markings at even intervals regardless of the irregular dimensions of your stock. For example, if you need to divide the lumber into 3 even pieces as depicted in the illustration above, you would align the 0 and 9 to the two edges and mark the 3 and 6 intervals. This comes in handy when the lumber isn’t easily divisible by the number you require.