# What Angle Is That, Precisely?

I try to be helpful when readers have a question, but there is one question I’m often asked that I usually refuse to answer. The question relates to some project or drawing I’ve published, where I’ve used an angle other than 90 degrees. The reader wants to know why I omitted specifying the angle in degrees. The reason I don’t want to answer is that I truly want to be helpful, and most of the time knowing the degrees of the angle in question won’t help a bit if you’re trying to make the thing. The other reason I’m reluctant to answer is that I don’t know. It’s a rare occasion when the degree of an angle enters my thinking. Take for example the Morris chair I recently completed. The lower side rail drops 3/4″ over a 21-7/8″ length. To find the angle to cut the shoulders, I draw the parts full-size and set my adjustable bevel to the drawing. If I really want the number, I can draw the parts in AutoCAD and measure the angle. The number, by the way is 1.959 degrees, and the problem is that we don’t have anything in our shop capable of measuring angles that precisely.

Angles are the great paradox of woodworking. If you’re off even a tiny amount, joints won’t close. But measuring angles with a protractor is more difficult than you might think. And if you try to go by degrees, measuring, marking and transferring are all good opportunities to get further away from where you want to be. For me making a drawing or using a compass to bisect an odd angle gives me points that I can connect with a line, and I can cut (and trim) to a line. In the image above, four pieces 12″ long are mitered at 45.1 degrees, and this is the other problem inherent in angled cuts. A seemingly tiny error at each corner is multiplied as you go around the frame, and the gap at the end is 1/8″. That one-tenth of a degree, by the way is the accuracy and resolution claimed by a current crop of digital angle gauges. What sounds good on the catalog page leaves a gap you can drive a truck through. The methods I use have evolved over centuries of woodworking, but I know my advice to eschew numbers leaves many woodworkers cold. If you want the numbers, there is a new tool that will give them to you.

I’ve spent the last few days using a prototype of the AngleMaster Pro v2 from Bridge City Toolworks. As with all Bridge City tools, the workmanship and machining is flawless, and the results are impressive. Here’s the short version of how it works: The numbers displayed are a representation of the length of the hypotenuse of a triangle. Minute changes in the position of the outer legs change the length shown in the display, reading in 1/100s of millimeters. After taking a reading, you need to translate that number to an angle. At the risk of sounding trendy and trite, there is an app for that.

You can solve just about any type of angle problem by entering the numbers you know. You can find precise angle settings for mitering pieces of different widths, and you can get the compound angle settings for multi-sided tapering boxes. Enter an angle and it will give you the caliper setting. Enter the caliper setting and it will give you the angle. Enter rise and run and it will give you both. It calculates angles for segmented rings, and will give you the circumference of a circle. John Economaki’s blog goes into great detail about how the tool and the app work, and it’s worth a read.

In use, it worked well but it took me a while to get used to the incredibly small increments being measured. There are some accessory shoes that will make this easier to use in some settings and situations. Of course, this kind of precision device doesn’t come cheap, but if you’re after this level of work you’ll consider it a good value.

The company plans to make these tools in once a year runs. Pre-production orders will open soon at a price of \$289, without the digital caliper, for delivery in June. Obviously this is not a tool everyone will want or need, but it represents an important development not only in how we measure our work, but in how we think about it. Precise methods are often scoffed at in the woodworking community, but the dynamic nature of the material we work with isn’t an excuse for sloppy work. We may take different roads to get where we want to be, but joints that really fit are the goal, whether we prefer to work by the numbers or by eye. If you’re a numbers guy, you should take a closer look at this tool.

–Robert W. Lang

## 10 thoughts on “What Angle Is That, Precisely?”

1. Russ

If you have something drawn in SketchUp you can use the protractor tool, or there is a ruby called "dim_angle" that will actually add the angular dimension to the drawing. Executing the angle is another story!

2. Alan

I like math, but I don’t see why to express an angle in degrees for woodworking. The tangent is a more appropriate way to describe an angle, and that’s what you’ve given with "The lower side rail drops 3/4" over a 21-7/8" length." That’s what we’re doing when we say to use a 1:8 ratio for dovetails. Why would I want to call that 7.13 degrees?

When expressed as tangent my other measuring tools are fine. And if I’ve figured the angle of something that comes out in degrees, I can change it to tangent.

But I don’t like to pay a lot for my tools. If I did, this would be tempting.

3. Bill

Woodworking for engineers? Measuring joinery angles to the hundredth of a degree?

Makes one wonder how anyone ever managed to make any furniture or picture frames or even any woodworking before this latest in a line of unnecessary devices came along and made all of that apparently non-existent 18th and 19th century precise joinery possible.

OK, yeah, I’m a curmudgeon, but I think this tool is a bit silly. And nearly \$300? Get serious.

4. Jorge G

Well, you are actually paying twice as much. Remember you still have to get the iPhone/iPad. Besides, if I want to find out the radius of an arc, or I want to figure out the angles for a coopered door with 8 pieces, how would this help me? I still have to do the math with the abacus. ðŸ™‚

Like I said, I have many BCT tools, but this one is just an expensive toy.

5. Mitch Wilson

Robert
Please don’t placate the pocket protector crowd. They’re anally retentive. I know. When I was a kid, I was a bit of a math whiz who used to tinker with the adjustments on his slide rule to try and make it more accurate. In a previous lifetime, my avocation involved working in nanometers (although one instructor tried to convince us we dealt in angstroms, but we didn’t buy into that). The leisure and luxury of working with slight inaccuracies is wonderful. Keep using your dividers and rulers and a nice sharp pencil and marking knife. And there is little as discerning and accurate as your eyes and your fingertips. (Oh, and your tongue. Ever seen the homonculus on Jonathan Miller’s desk in his PBS series "The Body in Question"? However, I don’t advocate licking your wood. Tongue splinters, anyone?)

6. Greg Znajda

Wow! I’m amazed at the naysayers comments! This tool I worth twice the price simply to avoid having to " do the math. " good dog I want to make furniture not fiddle with my abacus!!! Read the blog and find out how bad those cheap 30 buck calipers are. I want good tools. Tools that hold an edge, are accurate, are easy to use and maintain and I’m willing to pay for them. I’ve worked with cheap tools and spent time tuning and retuning them. No thanks! China makes cheap and I want no part of it. Right on BCT!!!!

7. David

Hmmm – the issue at hand is a fundamental philosophical difference – should the home/semi-pro woodworker strive to use manufacturing goals in his/her shop (i.e., part interchangeability, make to spec instead of make to fit and multiple piece runs), or strive to make one piece at a time to the best of their ability?

I would argue that the latter requires eschewing making parts to the specs in a drawing, and requires making parts to fit the other pieces in a construction, instead of the (theoretically) much more efficient method of making all of the parts on the cut list to their exact drawing measurements and assembling the piece when all parts are milled.

Personally, my opinion is that one cannot make fine furniture by the latter method because of the fickle nature of wood, inability to obtain stock with the necessary dimensions, and wood’s inherent instability with even small changes in moisture content (making it impossible to make the pieces over several days and expect them to hold their intended dimensions).

But – I’m aware of lots of woodworkers that try.

8. robert

Looks like a fancy sine bar. You can make your own sine bar, and as noted earlier, the trig is free (well, it does cost time and study).

9. Jorge G

I have to agree with Jon on this one. I am a fan of BCT and have many of their tools, but this one seems superfluous to me. A protractor, a square, a calculator and a little knowledge will work just as good.

10. Jon

Basic trigonometry is free (well, except for the square that you need to make the right angle) and as accurate as you can measure.

If you own a set of dial/digital calipers as shown above (under \$30 for some semi-decent Chinese-made knock-offs, under \$100 for some pretty decent Mitutoyos, etc.) and own a calculator, you’re just a few steps away from precision angle measurements. On the plus side, the tools involved can be used for a hundred other things!