Whether your planning to put in new flooring, tile the walls or paint the ceiling, you need to know the area of the relevant surface so you can buy enough materials to cover it. Although the mathematics for computing area depends on the geometrical shape of the room, you can reduce most measurements to approximate rectangles, and the mathematics for calculating the area of a rectangle is simple.
Most rooms are rectangular, and to find the area of a rectangle, you need to measure its length and width and multiply those together. For example, to find how much hardwood you need to cover a rectangular floor, measure the length and width of the floor in inches and multiply those measurements to get the area in square inches. You need to know the square footage, though, so divide that number by the conversion factor to go from square feet to square inches: 144. If the floor is 123 inches wide (10 feet, 3 inches) and 149 inches (12 feet, 5 inches) long, the area is 18,327 square inches, or 127.3 square feet.
Useful Mathematical Formulas
When a room has features that make the walls, floor and ceiling shapes other than rectangular, you need to know two important mathematical formulas:
- The area of a triangle is given by the expression A = 1/2 b•h, where "b" is the base of the triangle and "h" is the height, or distance from the base to the apex.
- The area of a circle is given by the expression A = pi•r2, where "r" is the radius of the circle and pi is a constant equal to approximately 3.14.
Computing the Area
The first step in making use of these mathematical tools is to map out a rectangle that covers the bulk of the floor and compute its area. You'll be left with triangles -- if the room has more than four walls or the ceiling or floor have pointed features -- or semicircles -- if the walls are rounded or the ceiling is arched.
If you're left with a triangle after mapping out a rectangle on a floor or ceiling:
- Measure the distance between the two points from which the triangle begins to slope away from the rectangle and the distance from the line demarcating the rectangle to the apex of the triangle -- both in inches.
- Plug the numbers into the formula to compute the area of the triangle.
- Add this area to that of the rectangle before you make the conversion to square feet.
- Repeat the procedure for every triangular section, and and convert to square feet after adding all the results.
If you're trying to find area in a room with curved walls or an arched ceiling:
- Measure the distance between the points from which the curve slopes away from the main rectangle.
- Divide that distance by 2.
- Substitute it in the formula for the area of a circle.
- Divide the result of that computation by 2 because the curve is a semicircle, not a full circle.
- Add that number to the area of the rectangle.
- Repeat the operation for each curve on the surface you're measuring, add all the results to the area of the rectangle and convert from square inches to square feet.
The result is approximate, but it's close enough to allow you to estimate materials.
Chris Deziel is a contractor, builder and general fix-it pro who has been active in the construction trades for 40 years. He has degrees in science and humanities and years of teaching experience. An avid craftsman and musician, Deziel began writing on home improvement topics in 2010. He worked as an expert consultant with eHow Now and Pro Referral -- a Home Depot site. A DIYer by nature, Deziel regularly shares tips and tricks for a better home and garden at Hunker.com.