Angle Math and Tools

Angle Math and Tools

Getting a handle on the angle math that comes up in woodworking is a step toward making your woodworking more precise, but the other half the battle is getting the your calculations to work out in the real world. Even if you're able to calculate the most complicated conjunctions of angled parts without working up a sweat, it won't do you much good if your saw's meter gauge promises you one angle and gives you another, or the 90 degree corner you're fitting with crown molding turns out to be 91-1/2 degrees.

To make sure the time you spend working out the math doesn't go to waste it's necessary to have tools that give you marking and measuring precision that matches the accuracy of your calculations. Using precision angle finders and guides will help ensure that your angle cuts are exactly what they're supposed to be and that the angle readings you take are accurate down to fractions of a degree, and rules with micro-fine guide holes will help make sure you get your angle cuts in the right place.

Woodworking Machinery Angle Scales and Terminology

Not all woodworking machinery angle scales are created alike. In fact, there are two different conventions for the calibration of angle scales in common use on woodworking machinery. One type of scale is calibrated to treat a square cut as a 90 degree cut, while the other scale treats a square cut as a 0 degree cut. Along with that, the terms used in woodworking to describe angled cuts don't make the origin of the angle measurement perfectly clear. The result is often some confusion about what it means to cut a piece of wood at a certain angle. Fortunately, the confusion is easily clarified by looking at a couple of woodworking terms that refer to angled cuts ("miter" and "bevel") and at how the two saw scales are set up the measure angles.

Miter Gauges, Miter Saws and Miter Cuts

The term "square cut" means to cut a board at a 90 degree angle relative to one of it's edges. The term "miter" - when it's used describe an angled cut - implies a comparison to a square cut. To make a miter cut means to make an other-than-square cut in a material in preparation for making a miter joint. In keeping with that, miter cuts are measured with respect to a square cut. Making a 22-1/2 degree miter cut, for example, means making a cut at 22-1/2 degrees in one direction or the other from square across the board.

You may have noticed that most power miter saws are adapted to this terminology. Most miter saw angle scales are set up so that the saw will make a square cut when the saw's angle scale is set at 0 degrees. One way to look at this is that the miter saw's scale is set up to measure the"amount of miter" that's being cut, and that setting the saw to cut 90 degrees straight across a board is, essentially, setting it to cut a "0 degree miter."

Table saw miter gauges, on the other hand, are typically calibrated to produce a square cut when they are set at 90 degrees. What the table saw miter gauge measures, in other words, is the angle of difference between the front edge of the miter gauge and plane of the saw blade. To get the same cut that a miter saw set at 30 degrees would produce, you'd have to set a typical miter gauge at 60 degrees.

A 30 Degree Miter Cut

Miter saw setting = 30°
90° - 30° = 60°
Table saw miter gauge setting = 60°

Switching between the two scales is very simple. As you probably remember from geometry class, the two acute (less than 90 degree angles) of every right triangle are complementary angles (add up to 90 degrees). Since the intersections of the edge of an angled cut and the reference lines of the two calibration systems form a right triangle, the setting that will produce identical cuts from one scale to the next are complementary angles.

Bevel Cuts

22-1/2 Degree Chamfer Bit

Strictly speaking the term "bevel" can describe any angled cut, but it usually refers to a cut that's angled relative to face of a material. The angle of a bevel cut is almost always measured against a square edge-cut. A 22-1/2 degree bevel setting on a table saw positions the saw blade at a 22-1/2 degree angle relative to it's most upright position. Most angle-cutting router bits follow the same convention (except that they use term "chamfer" instead of "bevel" to describe the angled cut they make) - the cutting edge of a 22-1/2 degree chamfer bit tips inward from the surface of the router's base or the surface of a table router table at a 67-1/2 degree angle.

Knowing the terminology and angle scale calibration conventions used in woodworking - along with a little common sense - is all it takes to get your tools set up to make the angled cuts you're after. Beginning on the next page, we'll take a look at some of the math that goes along with making angled cuts and building shapes with "odd angled" parts.