These formulas read: “area equals pi times the radius squared” and “area equals .7854 times the diameter squared.” Pi is a mathematical ratio frequently used when making calculations about circles. For most practical purposes, pi can be assumed to be equal to 3.14. Figure 4-21 illustrates the use of the area formulas for circles. Volume of a rectangular tank is found by multiplying length, width, and height as shown in Figure 4-22. an offset scale in which the units are less than one inch in fact, 1.414 of these units is equal to one inch, Figure 4-19. To use the 45° scale, measure as you would when measuring the run, except use the other side of the rule. It is important to remember that in all cases, travel (hypotenuse) is greater than the actual length of the pipe that must be cut. Fitting allowances must be subtracted from the travel to obtain the actual pipe length. Fitting allowances vary by size of pipe and are discussed in Chapters 19 and 20. Computing Area and Volume The surface area of a square or rectangular surface can be computed by multiplying the length times the width, Figure 4-20. However, computing the area of circles requires the use of one of two special formulas: Area = πr2 or Area = .7854d2 45° A Run Travel Offset Goodheart-Willcox Publisher Figure 4-17. A plumber commonly uses the terms travel, run, and offset. Compare these terms to the ones used in Figure 4-13. Travel = Offset × Constant Travel = 10″ × 1.414 Travel = 14.14″ Goodheart-Willcox Publisher Figure 4-18. Calculating the travel for 45° offsets using a constant. Travel Run 45° Offset scale Standard English rule 7.07″ Travel 5″ Run Goodheart-Willcox Publisher Figure 4-19. To determine the travel length, measure the run distance with the 45° offset scale. Plumber’s rule: A measuring device that has a stan- dard scale on one side and a scale for measuring the length of 45º offsets on the other side. 8′ 4′ Area = Length × Width Area = 8′ × 4′ Area = 32 square feet Goodheart-Willcox Publisher Figure 4-20. This formula can be used to compute the area of a rectangular surface. Chapter 4 Mathematics for Plumbers 79 Copyright Goodheart-Willcox Co., Inc.