The majority of woodworkers and carpenters rely on a hands-on approach for calculating angles, typically referring to them as miter angles. However by definition, obtuse angles are between 90 and 180 degrees. Acute angles are less than 90 degrees. The average miter saw cuts most angles with ease.
Cutting angles might seem intimidating to a beginner. But there are provisions for standard angles. Almost every miter saw has a preset lock for each one of them. The most common angles are 45, 30 and 22.5 degrees.
Degrees and Math
Accumulative angles should add up to 360 degrees. For example, two 45-degree angles add up to a 90-degree corner. Four 90-degree corners equal 360. The same principal applies to six-sided objects -- they require a 30-degree miter angle. Two 30-degree miters equal a 60-degree corner. Six corners at 60 degrees equals 360.
It's fine to use a calculator to figure the correct corner angles to cut for shapes with equal sides. The formula involves dividing 360 by the number of sides to arrive at the corner angle, and then dividing it by two to get the miter angle.
The hands-on approach is the easiest and most accurate way to calculate angles for woodworking or carpentry. Even if your angles work out on a calculator, they likely won't fit without gaps -- it's because walls, projects, cabinets, frames and objects are typically not square. Moldings twist, bend and warp. Saws are not 100 percent accurate, and operator error is common.
To Calculate Angles
Draw a Sketch
Draw a full-sized footprint of an angle on a piece of scrap wood. Use a straightedge to bisect the corner diagonally. The diagonal line represents the miter angle.
Make a Model
Place two similar pieces of scrap wood on the drawing. Align the ends of them together, as if they already had miters. Transfer the diagonal line to the square ends of the scrap wood with a pencil. The line doesn't have to be perfect.
Cut the Test Pieces
Place one of the pieces on the bed of a miter saw. Swing the blade to the left or right to match the pencil line. Lock the blade, and make the cut. Make an identical cut on the other scrap piece using the same angle -- only reversed to the left or right, as needed.
Trial and Error
Place the two pieces on the drawing, aligning them with it. Check the miter angle. If there's a gap on the inside, the angle is too sharp. If there's gap on the outside, the angle is too shallow.
Adjust and Finish
Adjust the blade 1 or 2 degrees at a time and recut your test pieces. Repeat if necessary until the gap is closed.
Using a Bevel Square
The bevel square -- woodworkers often refer to it as an angle-finder -- is a short, flat blade that swivels and locks on a handle.
Adjust the Bevel Square
Loosen the lock nut on the bevel square. Align the blade with any given angle on paper or scrap wood, or swivel the blade to match an angle on wood. Twist the nut to lock the blade.
Transfer the Angle
Swing the blade of a miter saw blade to the left or right, or optionally, swivel a miter gauge on a table saw to the left or right in the direction needed to match the angle on the bevel square.
Lock and Cut
Lock the blade at the angle, and make the cut.
You can also use a protractor to figure angles, but using one can be confusing for moldings and trim carpentry. Protractors read angles from the corner. Miter saws and miter gauges read angles from the fence. For example, the common 22.5-degree preset miter angle on a saw is exactly the same thing as a 67.5-degree angle taken off the corner with a protractor.