As you watch the kids head back to school, save a spot in your mental toolbox for these key concepts of geometry.
Back in high school, like so many other students, I scoffed when my math teachers insisted that the geometry formulas and algebraic equations we were learning would be useful in real life. Yeah right, I thought. I wanted to be a writer, not an engineer.
Fast-forward to when my wife and I remodeled our kitchen.
We spent weeks trying to think spatially inside our geometric cooking cube. What combination of cabinets and drawers would bring us neatly up to the door frame and still look symmetrical? How far could we extend the cabinet run on each side of the corner doorway while still leaving room to get a stove or refrigerator between them? How many sheets of drywall would we need and how many slabs of butcher block? How many boxes of tiles for the backsplash?
I hadn’t done that much math since the SATs. It made me realize that, as usual, my teachers had been right. While I’ve never used geometry in my line of work, it comes up in almost any home improvement project. In fact, math is a crucial component of a contractor’s skill set. “I never thought I’d be doing so much math,’’ said Bill Farnsworth, owner of Custom Contracting in Arlington. “I’m estimating and looking at numbers all the time.’’
Carpenter’s apprentices must master key mathematical concepts as part of their training. “We do a lot of geometry in our program,’’ said Lyle Hamm, director of apprenticeships at the New England Carpenters Training Fund in Millbury. After a basic first-year math class, Hamm said, apprentices learn more advanced concepts through hands-on training. “They don’t even realize they’re doing math.’’
Maybe our ninth-grade geometry class should have spent a semester volunteering with Habitat for Humanity.
Anyway, for DIYers, calculating square footage is probably the single most important mathematical formula, said Mark Philben, construction manager at Charlie Allen Renovations in Cambridge. “To price out a particular product, whether it’s carpeting, flooring, or tile, you need to calculate how much of it you’re going to need,’’ Philben said. “It’s pretty simple — length times width — and you always want to factor in about 10 to 15 percent waste. That’s pretty important.’’
So if you’re tiling a 6-by-7-foot bathroom, you’ll need 42 square feet of tile (6 x 7 = 42). Multiply that by 1.15, and you get about 48 square feet — enough to account for waste created by awkward edge cuts and a few inevitable mistakes.
Given the cost of construction materials, failing to make those calculations can be costly. Frank Guarino, owner of Cobra Painting in Holbrook, said customers who supply their own paint often overdo it — at a cost of up to $60 per gallon. “And once you buy paint and have it mixed, you own it,’’ he said. Guarino recommends asking your painter or measuring the room before visiting the paint store. “They can tell you exactly how much you’ll need, and they’re usually right on the button with it.’’
Beyond materials, calculating area can also help homeowners create a ballpark budget for home improvements. “The cost to remodel is anything from $200 to $300 per square foot in construction costs,’’ Philben said. “That’s to get it done right. Of course, it depends on what you’re doing. Kitchens and bathrooms are obviously much more expensive than a basement.’’
Speaking of basements, that’s where you might need to figure out the volume — length times width times height — of cement you’ll need to pour, measured in cubic feet. Volume is also important when installing a heating system or central air. “That has everything to do with how much heat load or cooling load you’re going to need,’’ Philben said. “If you’re living in a typical house built in the ’70s or ’80s, you’ll have 7½-foot ceilings. But in the city, the same size house will have 10- or 11-foot ceilings, so you’re going to have a much bigger volume.’’
And remember the Pythagorean theorem: a2 + b2 = c2? That crops up a lot, too. “For doors and windows to work, everything has to be square at 90-degree angles,’’ Philben said. “I grew up doing framing, and everyone in the field called it 6-8-10: Measure down 6 feet, across 8 feet, and you should be at 10 feet between [those two points] to check that your framing is square. If it’s not 10 feet, it’s not square, and it’s going to cause all kinds of problems,’’ he said.
Circles require their own set of formulas, you might recall. If you’re planning a round fire pit or paver patio, you’ll need to figure out the area of the circle — square the radius, or the distance from the center to the edge, and multiply it by pi (approximately 3.14). And with pipes, always measure the outside diameter, the distance from one exterior edge across the center to the other. “The inside diameter doesn’t do you any good, because different pipe sizes are different gauges, some aren’t as thick,’’ Philben said.
Philben and Farnsworth agree on three of the most important tools to help you get your numbers straight: a tape measure, a triangle-shaped speed square (consider it a carpenter’s protractor), and an L-shaped framing square.
Construction calculators can handle a lot of the number crunching, too, but Philben still thinks it’s important to have an understanding of the math being used. “Garbage in, garbage out: You can get erroneous calculations out if you don’t understand what you’re putting in,’’ he said.
Many of the most common math mistakes made by pros and amateurs alike come down to mismeasurement — like the “one-inch’’ or “wrong-inch’’ mistake. “That’s when you’re so focused on cutting at 33 and 5/32, but you cut it at 34 and 5/32,’’ Philben said.
Indeed, everything starts with the tape measure. “Most mistakes are made with the tape, and learning to read it right is essential,’’ Farnsworth said. And tape measures can wear out over time, sabotaging your work, Philben said. “The end is on little grommets that allow it to move, and if that’s off — if it moves over time, that little hook on the end — if that eventually becomes loose, you can be getting bad measurements all the time.’’
When it comes time to make a cut, “you always want to save the line; don’t cut the line away,’’ Philben said. “You want it a little snug anyway, because wood will shrink. Brand-new studs have a moisture content that will evaporate a little. All wood does that.’’ For that reason, Philben said, you shouldn’t install hardwood flooring until the wood has had a chance to acclimate and release moisture. “It can leave gaps in the floor if you install it right when it’s delivered.’’
That brings us to another bit of DIY curriculum: all of the chemistry happening behind the scenes. Many products are chemically formulated to work with specific materials or in certain conditions, and the wrong combination can make it fail immediately. “The right product is key. If you’re doing something in a bathroom with a high moisture content, you need a different type of sealant or finish there,’’ Philben said. Likewise, one epoxy might be ideal for wood, while something like PVC glue wouldn’t work on any other material. “It would damage most other products because it’s very acidic.’’
Of course, math isn’t everything — there’s some art in the remodeler’s syllabus as well. Philben said his company’s founder, Charlie Allen, always talks about “where to tell the lie’’ in older houses and odd-shaped rooms. “If you can’t build it square, what kind of adjustments do you make so it works well but looks correct, too?’’ Philben explained. “Like if you put a square doorway in a crooked house, it’ll work right but look off. Oftentimes you have to cheat it and make adjustments so it doesn’t look so out of place in an older house . . . That’s more art than science, for sure.’’
What matters most of all? Preparation and focus. “These formulas need to work out at the very beginning, because the problems don’t manifest themselves until the finished product, when you get tapered tiles or doors that don’t close properly and need to be shaved because they’re not put in square,’’ Philben said. “If you cut corners early on, it shows up in the finished product, and it’s too late to make adjustments.’’
He’s right: I cut a few corners in math class a couple of decades ago, and the various results are now on display in our garage: gallons of excess paint, an array of wrong-sized pipe fittings and radiator valves, and a roughly 4-foot slab of butcher-block countertop that is exactly 1 inch shorter than the piece we needed for our kitchen. The brilliant thing about those mistakes is that the real-world challenges that spawned them helped me rekindle a genuine interest in and actual understanding of math.
So listen to your math teacher, kids. Even the English majors among you might use this stuff someday.
Jon Gorey blogs about homes at HouseandHammer.com. Send comments to firstname.lastname@example.org. Follow him on Twitter @jongorey. Subscribe to our free real estate newsletter — our weekly digest on buying, selling, and design — at pages.email.bostonglobe.com/AddressSignUp. Look for our special Fall House Hunt coverage starting Sept. 11.