Straight Talk About Circles
Straight Talk About Cirlces
If you're going to deal with round things, you need to know about p (Pi). Pi, a number you'll use often in circle calculations, represents the number of diameter lengths of a circle it would take to equal the same circle's circumference-about 3.14159. About, because p is always approximate-its value has been calculated to more than 2.2 billion decimal places without ending or repeating. (Many calculators have a p key to make figuring simple.)
On the last page, Anatomy Of A Circle, you'll find some formulas to help you solve workshop problems involving circles. Using the circumference formulas, for instance, you can determine the length of veneer or laminate you'll need to edge a round tabletop. Or, if you know the distance required around a circular table to provide certain seating capacity (the circumference), you can easily figure the table's diameter by dividing by p. Area calculations come in handy when you're estimating finish coverage or material quantities.
Project plans and instructions ordinarily specify the diameter for circular parts. The radius usually is called out for corner rounds and other arcs (parts of circles). You already know how to draw a circle of a certain size: Set the distance between your compass legs or trammel points to the radius of the circle (half the diameter), and draw around the center. To avoid pricking the center with the compass point, stick on a piece of masking tape. You can lay out a corner radius just as easily, once you locate the center. To find the center and lay out a corner round in just three steps, first set your compass to the corner radius specified. Then, follow the steps in the photos below.
Finding the Center
Easy-to-use center-finding tools, such as the one shown in the opening photo or a centering head for a combination square, are readily available from woodworking-supply dealers. The devices work well on rounds up to 7" or 8" in diameter.
But you'll need to rely on layout methods to find the center on larger discs. The easiest way to do it (though a method prone to some error) is to stretch your tape measure across the diameter of the circle, and make a mark at the middle, as shown above. Then, move 90° around the edge, and repeat. Extend the marks until they cross, pinpointing the center.
If you prefer greater accuracy, try this method. First, draw a chord on the circle, shown as line AB in the illustration below. (A chord is a straight line that extends from one point on a circle to another, but doesn't pass through the center.) Then, draw a perpendicular chord at each end of the first one, shown as lines AC and BD in the drawing below.
Next, draw diagonal lines between the two perpendiculars, shown by the broken lines. The point where the diagonals cross marks the center of the circle.
Anatomy of A Circle
- Diameter (D) is the distance across a circle, measured directly over the center.
- Radius (R) is the distance from a point on a circle to the center. Radius equals half the diameter.
- Circumference (C) is the distance around the circle. To calculate circumference, just multiply the diameter times p.
- Area (A) is the number of square inches (or feet or centimeters or whatever unit you're using) contained in the circle. To figure the area, square the circle's radius (multiply it by itself); then multiply the result times p.