Construction Math Made Simple

Trying to decide where to start with this subject was a little more daunting than usual. Should I start with elevations, fractions, squaring, volume or area? Once I gave it some thought I decided that it would be best to start with how to measure. When working with feet you often have to convert them to decimals to do the math and then convert them back. Also when using a grade rod you must check to see if you have a tenths rod where each foot is divided into tenths or a foot rod where it uses the regular feet and inch method. I have seen a couple of good mess-ups where someone assumed they were using a feet and inch rod and were actually using a tenths rod.

To begin with the decimals of a foot are: one inch is .0833, two inches is .167, three inches is .250, four inches is .333, five inches is .417, six inches is .50 of course, seven inches is .5833, eight inches is .667, nine inches is .750, ten inches is .833, eleven inches is .917, and twelve inches is 1.00 or one. To get your conversions closer every one hundredth is about an eighth of an inch so that two and an quarter inches would be .187. Confused yet? This is how a tenth rod works for elevation and how to convert your equations from decimals to feet and inches. Like all things the more you use it the easier it will become and before long you will do it without thinking.

Since we have discussed tenth rods lets get into elevations a little further. There isn't much to it except to remember that up is down and down is up. When working on an engineered project the engineer will give you a bench mark to establish the elevation of the project. Typically it will be a nail on a phone pole or a brass nail in a sidewalk and marked as BM in orange. This allows the builder to go back to this same spot daily or even two years later and set elevations from it.

For example, let's say our bench mark is set at 1200 feet above sea level and the finished sub-floor is set to be 1208 feet above sea level. If you set up your instrument and read twelve feet six inches on the rod then the floor should read? The rod at the floor should read four feet six inches which means you subtract to add height and add to reduce height. Make sure you know what type of rod you are using and make sure that your instrument is level in all directions.

Want to hear a funny story? I once had an inspector tell me he was going to take his instrument to the lake to check it for level thinking that the edge of the lake would be level all the way around. Theoretically he was correct, realistically that is impossible. To check an instrument for level you must shoot two points on each side east and west of your instrument, then move the unit to the far side and shoot back across both points to insure your getting an accurate reading. Do not try to adjust it yourself as you can do little to adjust it at home. That is one project best left to a technician.

Now on to squaring. Squaring a project is important no matter if it is a desk or a hundred thousand square foot warehouse. The desk you can square with a rule; the warehouse should be broken down into sizable chunks. I am assuming that if your squaring a warehouse you don't need to read this. If your checking the square of an out-building or a weekend cabin then I might be able to help. Let's begin with another example.

Say we are laying out a simple home 30' x 45'; if the last dimension was forty feet instead of forty-five then the cross corner measurement would be fifty feet. Carpenters often use the 3, 4, 5 method of squaring. When you have a triangle with a ninety degree corner angle and one side is three feet and the other is four then the third side or long side will always be five feet. This works if you double all of the measurements such as six, eight, ten or twelve, sixteen, twenty. However, if you have an odd side such as our example then you can just measure corner to corner until your cross measurements are the same, this will guarantee that you are square as long as your other measurements are correct.

I once laid out a home and the guy on the "dumb" end of the tape cut a foot (held the tape on one foot for a more accurate measurement) on the front of the home and didn't on the back. So I had an extra foot of length on the back wall and when I got my measurements the same cross corner to corner I assumed it was square. The truth was it was a perfect trapezoid. Luckily I caught the mistake before we got too far along. This would have been a good one if I hadn't have caught it. If your length and width measurements are wrong then nothing else will be right.

Back to our example, you can use the a²+b²=c². Which with our example would be (30x30)+(45x45)=c². Which when distilled down is 900+2025=the square root of 2925 or 54.083269' which is 54' 1¹/₈". This can get a little complicated for some people so another method would be to put a mark on your line at thirty feet so that you have a perfect thirty by thirty square. When squaring a square all you have to do is multiply one side by the square root of two which is 1.4142135 (yes, I know that off the top of my head because I use it a lot) So if you have marked your line at thirty feet then your cross measurement is 42.4264 or forty two feet and three sixteenths of an inch give or take a hair.

Before we move into area and volume let's discuss fractions. How many times have you wanted to put a picture in the center of a wall and had to measure over and over until you happened to land on center? This can be done in a much easier way if you know the trick. Let's say you measured eight feet nine and three quarters of and inch. Half of that would be four feet four and seven eighths of an inch. I just did that in my head without a construction calculator or a pencil or a tape.

Half of one half and inch is one quarter of an inch, right? And one half of a quarter of an inch is one eighth, right? The secret is that the denominator (the bottom number) doubles and the numerator (the top number) stays the same. This will divide a fraction in half perfectly every time. Make good use of this and soon it will be so easy that you will soon impress your co-workers with how fast your throwing out answers. Fractions are wonderful things and the more you work with them the more fun they are.

Now to area and volume. Starting with concrete, most of you know how to figure volume of any slab or footer or any other object for that matter. For those of you new to concrete you can use this equation. One yard of concrete will cover 27 cubic feet which works out to 81 square feet at four inches thick. If your figuring a slab six inches thick multiply your length times the width then multiply that by .50 which will give you your volume, then you can divide that by 27. Example a driveway 50' long by 12' wide, which equals 600 square feet and at six inches thick is 300 cubic feet which would take 11.11 yards. However when ordering concrete order extra, it is a hell of a lot cheaper to order an extra yard than to send back for a yard which will usually cost you a minimum of two or three yards in price. Check with your supplier. Also if you haven't watched your grade will an extra inch in depth here and there can cost you huge on a big slab, check and double check your grade before you order concrete.

Now for materials; say you need to know how many block you need for a project, if you take your area and multiply it by 112.5% that will give you your block count. For example if your foundation is forty feet long and twenty feet wide and six feet high then the area would be 120x6 or 720 square feet. When you multiply that by 112.5% you get 810 which is your block count. If you want a brick count multiply your square footage by 8.5 which in the case of the same foundation it would take 6120 brick. That is a standard sized brick if your bricks are larger or smaller you can adjust for it with a little math. What ever you do don't trust the guy selling you material to do it for you as he will always round up. Of course it doesn't hurt to add ten percent for waste and culls.

Other material conversions that you might find useful are as follows. When figuring 4x8 sheeting or plywood divide your total area by thirty two. (DUH) If your figuring shingles check the coverage per bundle, a typical bundle covers 33.33 square feet meaning three bundles covers a square ( a square is one hundred square feet) One roll of 15# felt covers 104 square feet. If you have any questions or comments feel free to contact me also one last thing but not the least, there are twelve eggs in a dozen.