Construction Math 101

From a minor home repair to the construction of an entire house, virtually every construction project requires some mathematical calculations. From calculating the square footage of a room to more complicated figures like the area of a triangle or the number of board feet in a piece of lumber, a calculator and a few simple formulas are all you need.

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Area Measurements

Measuring and calculating area takes two of the three dimensions into account: width and length, as when measuring a floor, or width and height, as when measuring a wall. For the following examples, we'll use a rectangular room that is 10' wide and 12' long and has 8' high ceilings.

• Area of the floor or ceiling: To figure the area of the room, multiply the length by the width (10' x 12' = 120 square feet).
• Area of the walls: The area of each wall would either be 80 square feet (10 x 8 = 80) or 96 square feet (12 x 8 = 96). If you need the total square footage of the walls - for figuring paint or wallpaper for example - you can simplify the calculation by adding all the wall lengths together first, then multiplying by the height (10 + 12 + 10 + 12 = 44 x 8 = 352 square feet of total wall area).
• Area in square yards: There are a total of 9 square feet in a square yard, so to calculate the number of square yards in this room, as when ordering carpet, divide the total square footage of the floor by 9 (120 square feet / 9 = 13.33 square yards).
• Area in square inches: There are 144 square inches in a square foot, so to convert an area from square feet into square inches, simply multiply by 144 (120 square feet x 144 = 17,280 square inches).
• Area of a triangle: For the area of a triangle, use this formula: .5 x the base of the triangle x the height of the triangle. If you have a triangle - a gable end for example - that is 18 feet wide at the base and six feet high from the base to the peak, the calculation would be as follows (.5 x 18 x 6 = 54 square feet).
• Area of a circle: To calculate the area of a circle, the formula is: pi x radius 2 (pi = 3.1416). So, if you want to know the area of a circle with a 22-foot diameter - which would be an 11-foot radius - the calculation would be: (3.1416 x 11 x 11 = 380.13 square feet).
• Circumference of a circle: To calculate the circumference of the same circle - the total distance around it - use the formula: pi x diameter: (3.1416 x 22 = 69.12 feet).

Cubic Measurements

Cubic measurements take all three dimensions into consideration - width, length and height. This will tell you the volume of a given area and is useful for such things as knowing how much air is in a room when sizing an exhaust fan or the volume of a foundation form when ordering concrete.

• Volume of a room: To calculate the number of cubic feet in the room used in the examples above, multiply the width by the length by the height: (10' x 12' x 8' = 960 cubic feet).
• Volume in cubic feet: There are 27 cubic feet in a cubic yard. So, if you would like to convert cubic feet into cubic yards, which is used for such things as dirt, gravel and concrete, just divide the number of cubic feet by 27 to arrive at the number of cubic yards. For example, if you have a form that is 2' wide, 10' long, and 1 1/2' high, first figure the cubic feet, then convert to cubic yards: (2' x 10' x 1.5' = 30 cubic feet / 27 = 1.11 cubic yards).
• Volume in cubic inches: There are 1,728 cubic inches in a cubic foot. To convert the cubic feet in the above example into cubic inches, you would multiply by 1,728 (30 cubic feet x 1,728 = 51,840 cubic inches).

Board Feet

Most lumber is sold by the board foot, which is equal to a board that is one foot long, one foot wide, and one inch thick. If you would like to know how many board feet are in a given piece of lumber, use the following formula:

T x W x L / 12, where T = the thickness of the board in inches, W = the width of the board in inches, and L = the length of the board in feet.

For example, suppose you would like to know how many board feet are in a 16 foot long piece of 2 x 8 lumber. Applying the above formula, you would have the following: 2 x 8 x 16 / 12 = 21.33, so there are 21.33 board feet in that particular piece of lumber.

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