Formulas and Tables
(From the “Pocket Companion,” published by the Carnegie Steel Co.)

1. Weights

The average weight of wrought iron is 480 pounds per cubic foot. A bar 1 inch square and 3 feet long weighs, therefore, exactly 10 pounds. The weight of steel is 2 per cent greater than the weight of wrought iron, or 489.6 pounds. Cast iron weighs 450 pounds to the cubic foot.

2. Lengths

Circumference of circle = diameter × 3.1416.
Diameter of circle = circumference × 0.3183.
Side of square of equal periphery as circle = diameter × 0.7854.
Diameter of circle of equal periphery as square = side × 1.2732.
Side of an inscribed square = diameter of circle × 0.7071.
Length of arc = number of degrees × diameter × 0.008727.

3. Areas

Triangle = base × half altitude.
Parallelogram = base × altitude.
Trapezoid = half the sum of the parallel sides × altitude.
Trapezium, found by dividing into two triangles.
Circle = square of diameter × 0.7854; or,
= square of circumference × 0.07958.
Sector of circle = length of arc × half radius.

4. Standard Dimensions of Nuts and Bolts

Short diameter of rough nut = 112 × diameter of bolt + 18 inch.
Short diameter of finished nut = 112 × diameter of bolt + 116 inch.
Thickness of rough nut = diameter of bolt.
Thickness of finished nut = diameter of bolt − 116 inch.
Short diameter of rough head = 112 × diameter of bolt + 18 inch.
Short diameter of finished head = 112 × diameter of bolt + 116 inch.
Thickness of rough head = 12 short diameter of head.
Thickness of finished head = diameter of bolt − 116 inch.