Introduction to Construction Math
Working with fractions and units
Construction math is mostly fractions, decimals, and unit conversion done accurately under time pressure. To add or subtract fractions you need a common denominator; to multiply or divide, convert to improper fractions or decimals. Reduce answers to lowest terms, because a tape measure marked in sixteenths will not read 8/16. Memorize the core conversions: 12 inches = 1 foot, 3 feet = 1 yard, 9 square feet = 1 square yard, and 27 cubic feet = 1 cubic yard. Metric prefixes (kilo, centi, milli) appear on drawings and in specification sheets.
Geometry you will actually use
Perimeter is the distance around; area is measured in square units; volume in cubic units. Rectangles: A = L × W. Triangles: A = ½ base × height. Circles: circumference = πd, area = πr². The 3-4-5 right triangle (and its multiples) lets you lay out square corners without a framing square. Follow order of operations: parentheses, exponents, multiply/divide, then add/subtract.
Common traps
Mixing linear and square units, forgetting to square or cube the conversion factor, and rounding too early in a multi-step problem. Carry the units through every step so errors show up on paper.
Worked example: concrete volume
A slab is 12 ft × 15 ft × 4 in thick. Area = 12 × 15 = 180 sq ft. Convert thickness: 4 ÷ 12 = 0.333 ft. Volume = 180 × 0.333 = 60 cu ft. Convert: 60 ÷ 27 = 2.22 cu yd, so order about 2¼ cubic yards.