Woodworking Essentials: The Mighty Compass - Popular Woodworking Magazine

A swing of an arc is the solution to many layout and construction problems.

By Robert W. Lang
Pages 54-55

If you think a compass is only for drawing circles, think again. This simple and inexpensive device can divide almost anything into precise and equal sections, construct complex polygons and find the precise settings for making miters on any angle. Most woodworkers own or have access to this incredibly powerful layout, design and problem-solving tool – but they don’t realize its capabilities.

Get your compass out of your toolbox and play along. If you have to, borrow one from the nearest grade-school student or buy a cheap one. By the time you reach the end of this article, you’ll likely want to get a nice one. At the very least, you’ll have a new-found respect for this simple device.

Divide by Two, Prove Square
People often turn to numbers when they don’t need to, and that can slow them down or lead to frustration. Where a compass really shines is dividing things in half. Many geometric constructions are based on two points being an equal distance from something else. The important part is that of equality, not the actual measurement.

Despite what you may have thought in high school, geometry is useful, relevant and empowering. Let’s start with a straight line of any length. Stick the point of the compass on one end of the line, and set the other end to anywhere beyond the halfway point. It doesn’t matter how far. Don’t worry about it; just set the distance by eye and swing an arc above and below the original line. Without changing the settings, stick the point of the compass on the other end of the line and swing arcs above and below from there.

The intersections of the arcs are at equal distances from each end of the line, and when you use a straightedge to draw from intersection to intersection, the new line crosses the original line at exactly the midpoint. Even better, it’s at a right angle to the original.

Stick the point of the compass on the intersection of the two lines and reset the distance to put the pencil lead on the end of the original line. Now swing an arc across the perpendicular line. Connect that intersection with the end of the first line, and you have just drawn a perfect 45° angle.

Video: See these techniques in action
In Our Store:By Hand & Eye” a new book by Jim Tolpin and George Walker.

From the October 2013 issue, #206